ECONOMIC-TECENOLOGICAL MODELING AND DESIGN CRITERIA 
FOR PROGRAMMABLE ASSEMBLY MACHINES 
by 
PAUL MICHAEL LYNCH 
S. B., M3. ssac husetts Institute of Technoloqy 
( 19 70) 
S.M., MasS3chusetts Institute of Technology 
(1972) 
MECH.E., M3.ssachusetts Institute of Technology 
(19 75) 
SUBMITTED IN PARTIAL FULFILLMENT 
OF THE REQUIREMENTS FOR THE 
DEGREE OF 
DOCTOR OF PHILOSOPHY 
at the 
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 
June, 1976 
Signature redacted 
Signature of Author .• ·• ; . ;" .,. l't.--;-.-.--.-. ~ ••• ,'• ••• <· ........... . 
Department of Mechanical Eng~n~ring, June 8, 1976 
Signature redacted 
Certified by •••• _., •• ,,~·;.:··---...,.\. ••• ,. _hb;~i~. s~~;;~i~~; 
Signature redacted 
k cepted by •••••••••••••••••••••••••••••••••••••••••.•.••. 
Chairman, Dep:1.rtment Committee on Gra.duate Students 
2ECONOMIC-TECHNOLOGICAL MODELING AND DESIGN CRITERIA
FOR PROGRAMMABLE ASSEMBLY MACHINES
by
PAUL MICHAEL LYNCH
Submitted to the Department of Mechanical Engineering
on June 8, 1976, in partial fulfillment of the require-
ments for the Degree of Doctor of Philosophy.
ABSTRACT
Programmable assembly is a new industrial production
technology in which one piece of equipment may be
programmed by computer or other means to assemble many
different parts to one or more products. The versatility
of programmable assembly equipment will allow it to
compete with alternate assembly methods--manual and-
special purpose mechanized methods--under certain cir-
cumstances. These circumstances typically include those
where the required production volume of a product is too
low to allow economical special purpose automation or
where variation between different styles of the same
product produces assembly problems that are difficult to
solve by special purpose automation. Manual and special
purpose automation assembly have certain characteristics
and limitations which determine their economic and tech-
nological applicability. Programmable assembly shares
some of the characteristics of each.
In this thesis the properties of all three assembly
methods are modeled using a common base of assumptions
and modeling techniques. Sources of costs and benefits
are identified and- quantified where possible. This
model:
1) Allows programmable assembly methods to be
compared to the other two methods.
2) Is extended to hybrid systems consisting of
manual and special purpose stations together as
3well as programmable and special purpose
stations together.
3) Leads to the derivation of a numerical measure of
the economic performonce of a programmable assem-
bler' This numerical measurO is the product
of the average assembly time for a single part
and the total cost of the assembler (the price-
time product).
4) Permits estimation of bounds on the price-time
product that should be met so that designs of
programmable assemblers will be economic in
comparison to the alternative assembly methods
and permits study of how these bounds are affected
by important parameters.
5) Establishes a design criterion for programmable
assemblers in terms of the price-time product.
Under the given assumptions, the model not only predicts
that programmable assembly has economic promise, but also
identifies key research needs to fulfill that promise.
An example assembler design process is presented to
show how the price-time product may be used to resolve
tradeoff issues when used with models for the cott and
performance of an assembler. A sensitivity study based
on this example is used to show how areas for further
research with maximut potential impact on the price-time
product may be identified.
Finally, the economic modeling can be used as a basic
component of the assessment of the impact of programmable
assembly on the national economy.
Thesis Supervisor: Dr. Daniel E. Whitney
Title: Lecturer, Department of Mechanical
Engineering
4ACKNOWLEDGEMENT
My sincerest appreciation to my thesis committee:
Dr. Daniel E. Whitney, for patience, guidance, encouragement,
and support; Prof. Richard S. Sidell, for help and expertise;
Prof. Albert L. Hopkins, Jr., for ideas and perspective;
and Dr. Nake M. Kamrany, for his experience and perspective
from a different discipline.
My thanks to Anthony Kondoleon, whose companion work
was very helpful, to my wife Kay for her long support, help
in preparing and editing the draft and doing the preliminary
typing. I also thank Mrs. Betty Laurie and Mrs. Fay Greenberg
for the typing of the final draft.
The work of this thesis was supported by NSF contract
number APR74-18173 A02.
Publication of this thesis does not constitute approval
by the Draper Laboratory or the National Science Foundation
of the findings or conclusions contained herein. It is
published for the exchange and stimulation of ideas.
5TABLE OF CONTENTS
Page
TITLE PAGE.. ..............................----. 1
ABSTRACT...........................................--.2
ACKNOWLEDGMENT.......................................4...4
TABLE OF CONTENTS........ ............................ 5
LIST OF TABLES............. . ....................... 11
LIST OF FIGURES...... ............................... 12
1. INTRODUCTION............ . .... ........... ...... 16
2. BACKGROUND OF ASSEMBLY TECHNOLOGY................22
2.1 Present Assembly Technology...................22
2.1.1 Manual Assembly....................... 22
2.1.11 The Human Assembler...............22
2.1.1.2 Time and Motion Study............. 23
2.1.1.3 The Cost of Manual Assembly........25
2.1.2 Transfer Assembly Machines.............26
2.1.2.1 Description of Transfer
Machines.................. 26
2.1.2.2 The Design and Manufacture of
Transfer Assembly Machines........39
2.1.2.3 The Cost of Transfer Assembly
Machines.............................42
2.2 Highlights of Programmable Assembler
Technology Research at the Charles Stark
Draper Laboratory....................... 46
6 
2.3 Review of the Literature ..•................• 51 
3. DESCRIPTION OF THE ASSEMBLY PROCESS .•.•......... 55 
4. EMERGING PROGRAMMABLE ASSEMBLY TECHNOLOGY ...•.•• 67
4.1 Basic Concepts of Programmable Assembly
Systems •..•..........•••..........•...•..... 68 
4.2 Economic Advantages of Programmable 
Assembly .•...........•.••................... 71 
4.2.l Multipart Assembly ..•••.•.••.......... 72 
4.2.2 Multiproduct Assembly ...•............• 75 
4.2.3 Adaptive Assembly •••.•................ 76 
4.2.4 Reduction of Engineering Time ......... 78 
4. 3 Sununary.. . . . . . . • . . . . • . • • . . . . . . . . . • . . . . . . . . . • 79 
5. CONFIGURATIONS OF PROGRAMMABLE ASSEMBLY
TECHNOLOGY. . • . • . • • • • . . • • . • . . • . • . . • . . • . • . . . . . . . • • 81 
5.1 Programmable Assembler Configurations .....•. 82 
5.1.1 Degrees of Freedom of Motion Device •.. 83 
5.1.2 Principal Assembly Directions 
and Axes. . . . . • . . . • . . . . • • . . . . . . . . . . . . . . 8 5 
5.2 Programmable Assembly System 
Configurations.. • • • • . • • . • . • • . • • • . • . . . . . • . • • . 89 
5.2.1 Principal Configuration Modes •••.•.••• 90 
5.2.2 Operating Characteristics of the 
Principal Modes •.••••••••••.••...••••• 94 
5.2.3 Combinations of the Modes •••..•••••.•• 98 
5.3 System Efficiencies ......................... 99 
75.3.1 Assembly Station Capacity..............101
5.3.2 Configuration Efficiency...............103
5.3.3 Utilization Efficiency.................106
5.3.4 Net Station Efficiency.................106
5.3.5 Example Calculation of System
Efficiencies...........................108
5.4 Summary..................................... 113
6. SIMPLE ECONOMIC MODELS OF ALTERNATE ASSEMBLY
METHODS...........................................115
6.1 Simple Alternate Economic Models.............116
6.1.1 Modeling Manual Assembly Costs.........116
6.1.2 Modeling Transfer Machine Assembly
Costs................................. 117
6.1.3 Modeling Programmable Assembly
Costs................................. 122
6.1.4 A Comparative Example..................127
6.1.5 Product Volume Analysis................136
6.2 Hybrid Alternate Models..................... 143
6.2.1 Modeling Hybrid Transfer-
Programmable Assembly...................144
6.2.2 Modeling Hybrid Transfer-
Manual Assembly....................... 157
6.3 Improved Simple Economic Models..............163
6.3.1 Manual Assembly with Equipment
Costs............................... 164
86.3.2 Transfer Assembly with Labor Costs....165
6.3.3 Programmable Assembly with
Labor Costs...........................168
6.3.4 A Comparative Example Using the
Improved Models.......................172
6.4 Summary..................................... 177
7. CONSEQUENCES OF THE ECONOMIC MODELS.............179
7.1 Variation of Parameters of the
Comparative Example........................180
7.2 Significance of the Price-Time Product......186
7.3 Programmable Assembler Station Design.......188
7.3.1 Choosing Between Alternate
Assembler Designs.....................188
7.3.2 Parallelism and the Price-Time
Product...............................192
7.3.3 Minimization of the Price-Time
Product with Integral Station
Number................................194
7.3.4 Ways of Reducing the Price-Time
Product................................201
7.4 Maximization of Configuration Efficiency....205
7.5 Summary............................... ...... 207
8. EXAMPLE DESIGN PROCESS FOR A THREE AXIS
PROGRAMMABLE ASSEMBLER..........................210
8.1 Introduction.................................210
8.2 Physical Description.......................212
8.3 Actuator Selection Process....................215
8.3.1 Selection Process Outline..............215
8.3.2 Motion Cycle for Single Part
Assembly Time..........................216
8.3.3 Torque Requirements for a Single
Degree of Freedom.......................218
8.3.4 Torque Limitation of Electric
Actuators...............................226
8.3.5 Model for Single Part Assembly
Time.................................. 233
8.3.6 Empirical and Assumed Relationships... 237
8.4 Modeling Station Price.......................245
8.4.1 The Basic Model....................... 245
8.4.2 Empirical Price Relationships..........251
8.5 Sample Results................................257
8.5.1 Sample Price-Time Curves...............257
8.5.2 Sensitivities of Price-Time Product
to Component Variation.................261
8.6 Summary: Consequences for Research and
Development of Assembler Stations and
Components.................. . .............. 269
9. ECONOMIC IMPACT ANALYSIS: BACKGROUND AND
APPLICATION TO PROGRAMMABLE ASSEMBLY........ 272
9.1 Introduction......................... 272
9.2 Types of Economic Impact.................... 273
9.3 Economic Impact Analysis.................... 275
9
I
10
9.3.1 General Description...................
9.3.2 Example of Economic Impact Analysis...
9.3.3 Inclusion of Dynamic Factors.........
9.4 Economic Impact Analysis of Programmable
Assembly......................................
9.4.1 The Impact Analysis Process...........
9.4.2 Extension of Impact Analysis to
Product Families......................
9.4.3 Identification of Impact Costs........
9.5 Summary......................................
10. CONCLUSIONS OF RECOMMENDATIONS FOR FURTHER
RESEARCH........................................
REFERENCES..
APPENDIX 1:
APPENDIX 2:
APPENDIX 3:
275
277
280
283
283
293
294
296
297
3fA
LIST OF VARIABLE DEFINITIONS............307
ANNUAL RATE OF RETURN AS AN
APPROXIMATION TO THE RETURN
ON INVESTMENT.......................... 316
THE I.C. INSERTION MACHINE: A
CURRENTLY AVAILABLE PROGRAMMABLE
ASSEMBLER...........................319
BIOGRAPHY....................a'a.-a ''''aaa -*a -'*.a -'0 321
11 
LIST OF TABLES 
Table Page 
1.1 Fraction of Production Workers in Assembly 
in Sample Industries ............•........•..... 18 
2.1 Cost Breakdown for Transfer Assembly Machine ..• 44 
2.2 Cost Ranges for Typical Hardware CompGnents 
of a Transfer Assembly Machine Station ..••..... 45 
3.1 Breakdown of Assembly Task Steps for 
Washer Gearcase. • . • . . . . . • • . . . . . . . . . . • . • • . • . . . . . 59 
3.2 General Task Definitions .••.......•..•......•.. 60 
3.3 Breakdown of "Accommodation" Task Steps 
for Washer Gearcase •.•••.••.••.•....•.•.•....•. 62 
3.4 Accommodation Task Definitions ........••.••..•. 63 
8.1 Three Axis Assembler Design Sequence •.••......• 236 
8. 2 Variable Component -costs·· for Example Three
Axis Assembler Design ••••.•••..•.•....•.••••••. 248 
8.3 Components with Assumed Constant Costs ••••••.•. 250 
8.4 Values for Constant Price for Example 
Three Axis Assembler Design ••••.•••••.••••••••• 256 
8.5 Example Design State for Three Axis
Assembler Design--Physical Data ••••.•••••••••.• 263 
8.6 Example Design State for Three Axis
Assembler Design--Price Breakdown ...••••••••..• 264 
8.7 Major Price-Time Product Sensitivities for 
Example Three Axis Assembler Design •••••••••••• 266 
12
LIST OF FIGURES
Figure Page
2.1 Rotary Index Table............................ 28
2.2 In-line Indexing Machine........................29
2.3 Schematic of Transfer Assembly Machine
Components.................................... 32
2.4 Vibratory Bowl Feeder...........................34
2.5 Transfer Machine Size and Time to Build.........47
2.6 Transfer Assembly Machine Cost per Part
versus Product Dimension...................... 48
3.1 Gear Case Assembly..............................57
4.1 Example Design for Programmable Assembler
Motion Device................................. 69
4.2 Multipart Assembly..............................74
5.1 Assemblers with Various Degrees of Freedom.... 84
5.2 Product Assembly Axes and Directions...........87
5.3 Principal Configuration Modes...................91
5.4 Serial versus Parallel Modes.................. 96
5.5 Example Configuration Efficiency Calculation.. 109
6.1 Simple Variation of System Configuration for
Assembly of One Product....................... 124
6.2 Comparison of Assembly Costs as a Function of
Annual Volume ............................... 129
6.3 Comparison of Assembly Costs as a Function
13
of Annual Volume with Integral Station
Number....................................... 134
6.4 System Volume Boundaries versus Station
Price for Assembler Part Assembly Time
of 3 sec..................................... 139
6.5 Example System Volume Boundary Chart..........142
6.6 Comparison of Hybrid Transfer-Programmable
Assembly Systems................................150
6.7 Example of Savings of Hybrid Transfer-
Programmable System on Product Family..........154
6.8 Comparison of Hybrid Transfer-Manual
Assembly Systems................................160
6.9 Comparison of Unit Assembly Costs Using
Improved Model..................................173
7.1 Comparison of Unit Assembly Costs with
Price-Time Product Equal to 90,000 $-sec..... 181
7.2 Comparison of Unit Assembly Costs with
Price-Time Product Equal to 200,000$-sec......182
7.3 Comparison of Unit Assembly Costs with
Price-Time Product Equal to 50,000 S-sec..... 183
7.4 Price-Time Product Data for Hypothetical
Set of Assemblers............................ 189
7.5 Example Assembler Design Problem to
Minimize Price-Time Product.................. 191
7.6 Parallelism of Programmable Assembly Stations 193
14
7.7 Price-Capacity Chart...........................196
7.8 Price-Capacity Comparison for Optimal
versus Suboptimal Assembler Designs............199
7.9 Comparison of Assembler Price-Capacity
Curves for Individual Assembler Design
Problems...................................... 202
8.1 Sketch of Example Three Axis Assembler.........213
8.2 Modeling Gross Motion..........................219
8.3 Model of Single Assembler Axis.................222
8.4 Torque Requirements for Single Part Assembly
Cycle......................................... 227
8.5 Gross Motion in Part Assembly Cycle............229
8.6 Torque History with Gravitational
Component..................................... 231
8.7 Motor Torqie Versus Motor Power................238
8.8 Motor Mass versus Motor Power................. 240
8.9 Motor Length versus Motor Power............... 241
8.10 Motor Rotor Inertia Versus Motor Power........ 242
8.11 Motor Cost Versus Motor Power................. 252
8.12 Amplifier Cost versus Motor Power..............253
8.13 Ball Screw Price versus Length................ 255
8.14 Price-Time Curves for Example Three Axis
Design.. . ....................-............. 259
9.1 Economic Impact Analysis Method............... 276
9.2 Simple Example of Economic Impact Analysis.
Using a Hypothetical Automobile Engine........ 278
15
9.3 Graphical Derivation of Impact Function.........286
9.4 Cost-Volume Distribution Function...............289
9.5 Application of Impact Function to
Distribution Data...............................291
16
1. INTRODUCTION
Programmable assembly is a new production technology
in which one piece of equipment may be programmed by com-
puter or other means to assemble many different parts to
one or more products. The anticipated virtues of program-
mable assembly stem from its ability to be taught different
assembly tasks, in contrast to conventional automatic as-
sembly equipment. The latter is built to do one assembly
task for all of its economic life. Programmable assembly
equipment can assemble different products at different pha-
ses of its economic life. Thus, the economic and techno-
logical characteristics of programmable assembly can be ex-
pected to differ from current automatic or manual assembly
methods.
This thesis work relates the performance of program-
mable assembly equipment to the economics of its application
in order to develop a criterion for design and research in
programmable assembly technology. The need for design and
research in programmable assembly technology is related to
the national need for increased assembly productivity.
Some economists have noted the recent decline in the
rate of increase of productivity in the United States and
have associated with it many .of the present economic trou-
bles. Productivity can be defined as the total output of
goods and services provided by a cuuntry divided by the
17
total quantity of labor, capital, and material resources
used to produce those goods and services.
The rate of increase of productivity measures the speed
with which an economic system is learning to make more and
better products from a given quantity of resources; it is an
important factor in the economic health of an industrialized
country and has been an important factor in the rise of real
wages of the people in this country. Long term trend data
over the period since 1900 indicates that the fraction of
the total national output that goes to wages has remained
relatively constant (1). However, the total national output
has grown faster than the labor force in large part due to
improved productivity of'production technology and methods.
The result has been a steady increase in the real wages for
each worker over the long term. Improving econoinic produc-
tivity is an important process, and improving assembly pro-
ductivity is a par& of it.
At the present time assembly is a labor intensive pro-
cess, and a significant fraction of the direct labor in many
industries is occupied in the assembly process. Table 1.1
lists a number of industries of widely divergent type show-
ing the fraction of direct production workers that are in-
volved in assembly. For these industries assembly took a
larger share of the total direct labor than any other manu-
facturing process. Thus, the rewards for improving assembly
productivity are potentially very great.
18 
Table 1.1: Fraction of Production Workers 
in Assembly in Sample Industries 
Industry 
Motor Vehicles 
Aircraft 
Telephone and Telegraph 
Farm Machinery 
Household Refrigerators and Freezers 
Typewriters 
Household Cooking Equipment 
Motorcycles, Bicycles and Parts 
Source: 1967 Census of Manufactures, 
U.S. Bureau of the Census 
Assembly Worker Fraction 
45 .6 % 
25.6% 
58.9% 
20.1% 
32.0% 
35.9% 
38.1% 
26.3% 
19 
On the level of individual firms, increased assembly 
productivity means reduced production costs, especially if 
assembly is a.large fraction of the direct labor. Hence, if 
new methods are developed which improve assembly productiv­
ity, then they will be readily accepted by those firms. 
Previously, assembly has been a difficult process to 
automate from a technological point of view. The difficulty 
in automating assembly stems mainly from two sources. First, 
the assembly process jtself is complex, involving a number 
of fairly complicated motions and decisions. These complex 
motions are often necessary because of the inherent va�ia­
tion in the dimensions and quality of the parts that must be 
assembled. Second, the human assembler is very well adapted 
to the requirements of the assembly process (including in­
spbction and testing), making it difficult for automated 
assembly to compete directly with manual assembly, except 
in certain limited cases. 
The emergence of programmable assembly means that man­
ufacturers will be able to choose among three principal 
types of assembly: manual, automated by mechanical equip­
ment, and automated by programmable equipment, each with its 
own advantages and disadvantages. How should the supplier 
of programmable assembly equipment design it so that it has 
the best possible chance in competition with the other meth­
ods of assembly? How can the purchaser of programmable as­
sembly equipment choose among competing types? What are 
20
the principal economic factors influencing the application
of programmable assembly?
The fundamental way in which a firm will choose among
the three alternatives will be to analyze each alternative
and then to apply an economic criterion to indicate which
method will maximize the firm's profits. This selection may
take the form of choosing the system with the lowest assem-
bly cost per unit, or the highest "return on investment."
These methods are not the same, but they are intended to
have the same result -- maximization of the profits.
To evaluate the operation and application of program-
mable assembly, it is necessary to understand what variables
of the alternate assembly technologies, especially program-
mable assembly, will influence the results of the selection
process. The results can be influenced by economic vari-
ables, such as wage scales, tax rates, cost of equipment,
and cost of capital; by technological variables, such as
time to complete an assembly, accuracy of assembly motions,
and reproducibility of the assembly process from one assem-
bly to the next; and by product variables, such as size,
weight,. part clearances, number of styles of product, and
life of the product.
The problem of understanding the implications of this
selection process for programmable assembly will be attacked
by developing a consistent set of models and assumptions for
the three alternative methods of assembly. This framework
21
of models and assumptions will have two sides: an economic
side and a technological side. On the economic side will
be models and assumptions concerning labor rates, capital
rates, tax rates, cost of equipment needed, and so on. On
the technological side will be models and assumptions con-
cerning what is required to accomplish assembly by each of
the different methods in terms of equipment, capacity, num-
ber of man-hours, and so on.
The topics of this thesis are organized as follows:
The motivation and purpose for the research is discussed in
Chapter 1. Background material concerning present assembly
technology and research work related to programmable assembly
is contained in Chapter 2, along with a review of the liter-
ature. Chapters 3 through 7 develop the medel of program-
mable assembly, beginning with the assembly process (Chap-
ter 3), and proceeding to the nature of programmability
(Chapter 4), models of programmable assembly system config-
urations (Chapter 5), economic models of assembly methods
(Chapter 6), and the development of a design criterion for
programmable assembly equipment (Chapter 7). The use of the
design criterion developed in Chapter 7 is illustrated by
example in Chapter 8. The extension of the economic modeling
of Chapter 6 to a national impact analysis of programmable
assembly technology is discussed in Chapter 9, and the con-
clusions and recommendations for further research are given
in Chapter 10.
22
2. BACKGROUND OF ASSEMBLY TECHNOLOGY
2.1 Present Assembly Technology
This section examines the principal methods of assem-
bly today -- manual and transfer machine methods. These
methods are first described, the important characteristics
of each are detailed, and the advantages and disadvantages
of each are discussed. Finally, a general outline of the
factors affecting the cost of each method is presented.
2.1.1 Manual Assembly
Manual assembly was the first method of assembly and
was the first method to be studied scientifically. This
section describes the characteristics of the human assem-
bler, the time and motion study approach for manual assem-
bly, and the cost of manual assembly.
2.1.1.1 The Human Assembler
When the human assembler assembles a product, he by
nature performs more than simple assembly; he also performs
inspection of the parts being assembled and inspection of
the quality of the completed product. If two parts are to
be assembled and the human assembler finds that one is
23
faulty and cannot be assembled, then he can quickly reject
that part and try a new one. To make this decision, the
human assembler uses inputs from his senses -- touch, sight,
and sound -- and he applies judgment, using what his senses
tell him.
The human assembler can adapt easily to small changes
in the assembly process. For example, if a new part is
added to the product design, it is easy to retrain the as-
sembly worker to add that part. This is conscious retrain-
ing. The human assembler also adapts in an unconscious way
when he adjusts his assembly motions to accommodate drift
in the part dimensions and other slowly varying influences
on the assembly process..
However, the assembly worker is subject to errors and
variations to which assembly machines are not subject. He
may occasionally "forget" to perform part of his task se-
quence without realizing it. His performance is influenced
by a host of factors that affect his state of mind and his
individual assembly times will vary from one unit to the
next. The very versatility of the human assembler gives him
the ability to make errors that a machine cannot.
2.1.1.2 Time and Motion Study
Manual manufacturing processes of all kinds, including
manual assembly, have been analyzed by means of time and
24
motion studies since the early part of this century. Prob-
ably the most widely used and freely published method of
this type is the Methods - Time Measurement (MTM) approach
developed in the late 1940's. For a detailed description
of MTM see Karger and Bayha (2).
The basic assumption of MTM and the methods like it is
that any manual operation or process can be separated into
basic motions, that each basic motion can be assigned a pre-
determined execution time, and that these basic motion times
can be used to compute an overall manual operation time.
Some of the basic motions include reach, move, turn, crank,
apply pressure, grasp, release, position, and disengage.
The execution time of each basic motion is assigned
based on certain important variables describing that motion.
For example, one of the important variables influencing the
MTM estimate for a "reach" motion is the length of the reach.
Another example concerns the MTM operation "position0 which
involves placing one object in a specific position relative
to another. Some of the important variables that affect the
MTM estimate of position time would be the tightness of fit
of the parts, the degree of symmetry, and the ease of han-
dling. These variables do not all have scientific, quanti-
fiable definitions. Hence, application of MTM and similar
methods depends on judgment to some degree.
25
2.1.1.3 The Cost of Manual Assembly
Any particular manual assembly task will take a fairly
predictable amount of time to be accomplished by an average
assembly worker. Since direct labor is usually paid by the
hour, the cost of manual labor for a simple manual operation
can be estimated by multiplying the labor rate by the total
man-hours required.
The labor rate is the cost incurred for one worker for
a given time period. This rate is greater than the wages
received by the worker because it must include other pay-
ments the company makes, such as those to Social Security,
pension funds, and fringe benefits, for the benefit of that
worker.
The number of man-hours necessary for the assembly of
a product unit is roughly proportional to the number of
parts being assembled. This means that, generally, a prod-
uct with ten parts will take approximately twice as long to
assemble as a product with five parts (assuming products and
parts of comparable size and assembly difficulty). This is
a rough model, which will be used throughout this thesis.
It must be used with caution, however, and it is best used
in combination with similar mouwls for the alternate assem-
bly methods to assess relative differences in assembly meth-
ods for the same product. For example, factors which will
tend to affect the assembly difficulty for a particular
26
product will tend to affect the absolute assembly costs for
all three methods in a similar way. Therefore, the relative
costs of the three assembly methods will be less affected.
Other labor payment systems, such as a piece rate sys-
tem, may not explicitly be related to the assembly time.
However, even in these systems the labor cost per unit of
product is relatively constant and ist related to the nominal
assembly time for the product.
2.1.2 Transfer Assembly Machines
Transfer assembly machines represent the currently
available technology for replacing manual assembly labor.
In this section their physical construction and method of
design will be discussed and the cost of the transfer ma-
chine will be related to the design and construction process.
2.1.2.1 Description of Transfer Assembly Machines
In current transfer machine technology the assembly
process is divided into a series of simple motions of ap-
proximately equal duration. Simple mechanisms are built to
accomplish each of these motions and are arranged in sequence
as stations along a tradsfer mechanism. This transfer mech-
anism carries each product unit in an indexing motion past
every station where each simple assembly task is performed
27
in sequence. Examples of transfer machines are the rotary
index table (see Figure 2.1) and the in-line indexing table
(see Figure 2.2).
Current transfer assembly machines are special purpose
devices, usually one of a kind. They may be partially con-
structed of standard components, but the total machine is
unique to the product being assembled.
The fine division of assembly tasks of the transfer
machine is an important factor in its high rate of produc-
tion. Because all the assembly motions are performed si-
multaneously, each at a separate work station, a completed
product unit is produced at the end of the machine every
index cycle -- the time from the beginning of bne operation
at a station to the beginning of the same operation on the
next product unit. Index cycle times between one and five
seconds are very common.
There are two categories of transfer machines: syn-
chronous and non-synchronous. The conveying system of a
synchronous transfer machine moves all of the product units
in process from one station to the next simultaneously, while
in a non-synchronous machine the products move from one sta-
tion to the next independently. The two types of synchronous
transfer machines are the rotary index (or "dial")
table and the in-line indexing table. General descriptions
of these two machines and of a non-synchronous machine are
given following:
28
Figure 2.s Rotary Index Table
(1) Six station index table
(2) - (6) Work stations
(7) Parts feeding equipment
(8) Pallet or nest
29
Figure 2.2a In-line Index Machine
Part Feeder Work
Station
Pallet
N%% Chassis
30
Rotary Index Table
The size of the rotary table varies from one to five
feet in diameter. The chief factor limiting the size of the
table is its rotary inertia. As the diameter of the table
increases, the inertia also increases and eventually becomes
too large for rapid indexing rates.
The indexing motion of the table is usually provided
by a cam drive. The positioning accuracy of the indexing
equipment is such that accuracies of + .001 inch can be
maintained at the outer radius of the table, and the indexing
device can provide a range of index angles allowing from four
to thirty-six index positions around the circumference. In-
dex times from one half second to two seconds are common.
In-Line -Indexing Table
The in-line indexing table may vary in length from a few
feet to several yards. Often the driving mechanism and chas-
sis structure of the transfer machine are made up of standard
components. The products.being assembled are mounted on pal-
lets fixed to a chain or steel band which is moved by the
cam drive. The pallet size, which usually runs from four to
eight inches, is fixed in the original design of the set of
standard components from which the individual machines are
constructed. These individual machines are then restricted
to that pallet size.' However, any one machine may be designed
with many or few stations by using the appropriate number of
chassis modules, or "bays", and a corresponding length of
31
pallet chain.
The positioning accuracy for a pallet at a station is
usually about +.003 inches, although methods exist for ob-
taining greater accuracy. Index times from one to five
seconds are common, although much shorter times are possible.
Non-Synchronous Machine
In non-synchronous transfer machines the parts are
mounted on pallets which travel along conveyors connecting
the individual stations. Each station contains its own in-
dexing mechanism. When the station is finished with its as-
sembly operations on a particular product unit, the indexing
mechanism ejects that product unit and brings in the next
product unit waiting in line at the station.
The major components of a transfer assembly machine for
the assembly of a single part to the subassembly are shown
schematically in Figure 2.3. Their function and interaction
will now be discussed.
1) Nest
The nest is the space that is provided to hold the par-
tially completed assembly on the index device; for example,
it may be a jig which holds the base part of the product.
In the case of rotary index tables, the nest is sometimes
cut directly out from the metal of the dial.
2) Pallet.
In non-synchronous systems and in-line systems the nest
is part of or connected to a pallet. The pallet is connected
32
Figure 2.3 s Schematic of Transfer Assembly
Machine Components
Part Feeder
Feed Track
(Vibratory
Bowl Feeder)
Part Placement Part
Devi*e Gripper
part
Sensor
Part Escapement
Nests Index DeviceHolding Section
* 0Devoted to
This Part
Pallet.
33
to the indexing chain or band in the in-line system, and
rides on a conveyor path in the non-synchronous system.
3) Parts Feeding Equipment
The parts feeding equipment may vary greatly in its
sophistication and may incorporate a wide variety of de-
vices. The function of the feeding equipment is to move part
units from storage positions near the machine to a presenta-
tion site at the station where the part assembly is to take
place. Other equipment takes the part unit from the presen-
tation site and assembles it.
There are two main approaches to parts feeding. In one
approach parts are taken in a bulk form with random orienta-
tions in boxes or bins. -These parts are then dumped into de-
vices that orient them and then present them to the assembly
equipment. In the other approach the parts are stored in an
oriented form, such as in egg crates, on tapes, or in maga-
zines or stacks. In this case all the parts feeding equip-
ment must do is hold the stored parts or perhaps move them
serially toward the station. The problems of designing feed-
ing equipment to orient the parts is avoided in the second
approach, although this savings in equipment may be offset
by the additional expense of storing the parts in a preori-
ented fashion.
The most common example of parts feeding equipment for
small parts is the vibratory bowl feeder, shown sketched in
Figure 2.4. The bowl is vibrated in a helical fashion so
34
Figure 2.4a Vibratory Bowl Feeder
Direction of Parts
Movement
Track
Parts Exit Bowl
Nero and Enter
Food Track
Bowl
Base Containing Vibration Equipment
35
that the parts "dance" up the inclined spiral tracks on the
inside of the bowl. The parts begin at the bottom of the
bowl disoriented. Special metal shapes, or "tooling,"
mounted along the spiral track cause the parts to emerge
oriented from the top edge. The feeding of screws and fas-
teners is a typical application of a bowl feeder; an opera-
tor will pour a box of screws into a bowl feeder which then
orients the screws and feeds them to automatic screw driving
equipment. The feeder must not only be provided with special
features to orient the screws, but to reject or divert sub-
standard parts and foreign bodies that are often mixed in
with the good parts. Although very significant progress has
been made by Boothroyd (3) and others in the analysis of the
performance of bowl feeders, the practice of bowl feeder de-
sign is more of an art than a science at present.
The vibratory feeder track operates on a principle simi-
lar to the vibratory bowl feeder. It is typically used to
move the oriented parts from the exit of the bowl feeder to
the part escapement equipment described below.
4) Escapement
The escapement is a device that discharges one (or more)
parts at a time from the feeder track. It is a gating mech-
anism that separates the one part that is needed from the
rest lined.up behind it in the part unit queue. It also lo-
cates the part in a precise position so that the assembly
equipment can take it.
36
5) Part Gripper
The part gripper grasps the part that is gated by the
escaperrent. The gripper is often specially tooled so that
its "fingers" conform to the shape of the part so that the
part is held precisely while it is being assembled to the
product.
6) Placement Device
The placement device carries the part gripper and the
part that the gripper is holding on a predetermined trajec-
tory. A typical placement, or "pick and place," unit exe-
cutes a trajectory in the shape of an inverted U: a sequence
consisting of a lift, swing, drop, lift, swing back, and drop
again. One end of this trajectory corresponds to the location
of the part held in the escapement, and the other end corre-
sponds to the assembled position of the part in the product.
The path of the device is controlled by cams, links, and cer-
tain adjustments. Some devices have no adjustment; the only
way to change the path is to cut a new cam to replace the old
one. Other units allow some adjustment of certain segments
of the path without requiring replacement of the cam.
7) Sensor
It is good assembly machine design practice to install a
sensor to check for the successful assembly of the part. Al-
though this can sometimes be done at the same station that
does the assembly, usually it is done at an inspection station
following the assembly station.
37
This concludes the listing of the major assembly machine
components. In practice, the components vary in the specif-
ics of size, use, and complexity depending on the type of
machine -and the type of assembly operation. Transfer ma-
chines, in general, have their own advantages and disadvan-
tages, and these are now discussed briefly.
If a transfer machine is used two or three shifts per
day, annual production volumes in the millions are easily ob-
tained. For example, a transfer machine with a two second
cycle time can assemble roughly three million parts per shift
per year. However, the transfer machine is expensive. This
expense is partially due to the fine division of tasks, which
means that hardware and design work are needed for each of
many simple assembly motions. The cost of a single work sta-
tion can be tens of thousands of dollars. As a result, trans-
fer machines are an economic alternative to manual assembly
only for products which require a high production volume.
When a high production volume exists, the cost of the entire
machine is spread out over enough product units to bring down
the assembly cost per unit to a level competitive with manual
assembly. For a simple example, a transfer machine with a
two second cycle time working two shifts for two years could
assemble about 12 million units. If the itiachine were re-
quired to "pay for itself" in those two years, then, even if
the machine cost one million dollars, the assembly cost for
one product unit, excluding operating expenses, would be only
38
about eight cents. (In Chapter 6 a more quantitative model
for the unit assembly cost for a transfer machine will be
developed along these lines.)
Transfer machines have certain drawbacks. First of all,
they are not easily changed to accommodate significant chan-
ges in the product design. This means that the transfer
machine is not a good investment if the product design is
not stable for a sufficient number of years to repay the cost
of the machine. This important issue, calculating repayment,
is discussed in detail in Chapter 6. Secondly, they are re-
stricted to products in which the individual assembly motions
are sufficiently simple. The recognition of this fact has
led to the design of the assembly machine and product to-
gether as a system in some firms. However, designing trans-
fer assembly machines for existing products is often diffi-
cult or impossible because the product design does not lend
itself to mechanized assembly and, for other reasons, this
design cannot be changed.
In short, transfer machines make good economic sense in
many applications, especially for high volume products for
which the product assembly process can be accomplished by
existing transfer machine technology and where the product
design is relatively stable over time. However, as will be
discussed in later chapters, where the production volume is
not high, where the needs of the product assembly process
tax the presently available transfer machine technology, or
39
where the product design is subject to change, programmable
assembly may be competitive with the transfer machine.
2.1.2.2 The Design and Manufacture of Transfer Assembly
Machines
The transfer assembly machine design and manufacturing
process has three distinct phases: first, the initial plan-
ning and engineering stage; second, the assembly of the
basic equipment; and, third, a testing and debugging process
that may involve redesigning parts of the transfer machine.
A typical design and manufacturing process is described
below:
The initial planning and engineering stage is a layout
process in which the basic components of the system are cho-
sen and arranged. The designers of the transfer machine are
supplied with drawings of all of the parts in the product to
be assembled which provides them with nominal dimensional
information. Using their experience they may be able to make
reasonable assumptions concerning the type of part variations
to expect because explicit data is rarely available -- even
the manufacturer does not have this information. The de-
signers then develop an assembly task sequence for the assem-
bly of the product and lay out the arrangement of the trans-
fer machine stations using an appropriate indexing device.
If the transfer machine is to be built on a synchronous
40
indexing chassis such as an in-line indexing table or a
rotary index table, then the allocation of the stations on
the index device is fairly routine. The initial station is
usually the loading station for the base part of the assem-
bly. It is good practice to allow two stations for the as-
sembly of each additional part -- one station to assemble
the part and the second station to check to see that the as-
sembly operation was completed satisfactorily. It is also
good design practice to leave some station locations empty
to allow room for future modifications of the machine. Usu-
ally, the last station is allocated for the unloading of
the finished product unit, but sometimes one more station
is used to unload rejects.
The initial planning and engineering stage may take
anywhere from two weeks for a very simple assembly machine
to several months for a more complex system.
The second stage is the construction of the machine
from basic components. Depending on many factors, this may
be a straightforward process that can often be done within
a matter of weeks, frequently a fraction of the time re-
quired to design the system.
The third stage is the tryout and debugging stage.
This stage begins with a trial run of the machine. This
trial run identifies the problems of the completed machine
which must be corrected for proper operation.
The principal difficulties lie in the valiation of the
41
parts that must be assembled. These supposedly identical
parts actually vary slightly one from the next in dimension,
or they can have rough edges, flashing, and dirt attached.
Occasionally, there are foreign bodies mixed in with the
good parts. All of these irregularities can affect the per-
formance of the equipment that must feed and assemble the
parts. It is this unpredictable irregularity that makes
reliable parts feeding and assembly so difficult to analyze
-- it is nearly impossible to predict and plan for the many
possible types of irregularities. In practice experimenta-
tion is the only way currently in use to discover which
variations of the parts will actually affect the performance
of an assembly machine. Once the problems are idel .fied,
the process of analyzing the difficulties and redesigning
can begin. The time necessary for this debugging and re-
design process is highly variable, but it can easily take
six months for an in-line synchronous machine that assembles
six to ten parts.
Transfer assembly machine builders are roughly divided
into three classes. First are the standard chassis manufac-
turers who construct their machines from a stock chassis and
standard components. This reduces the amount of design time
and machine shop effort, but there is still a considerable
amount of special engineering and debugging left to be done.
The second class is the non-standard chassis builders. Their
designs may vary greatly from machine to machine. The third
42
class consists of the in-house automation groups of the
major manufacturing companies.
Of the independent makers of automatic assembly ma-
chines, or transfer assembly machines, eighteen belong to
the assembly machines group of the National Machine Tool
Builders Association. These represent most of the large
assembly machine makers, but it is difficult to determine
exactly what fraction of the transfer assembly machine mar-
ket they represent. Their total orders for automatic as-
sembly machines for calendar 1975 were between $10 and $15
million. This contrasts to an estimated purchase of $839.9
million worth of assembly equipment of all kinds (including
manual equipment) in calendar 1976 (4). This means that
automatic assembly machines account for only a small frac-
tion of the total assembly equipment business.
2.1.2.3 The Cost of Transfer Assembly Machines
The cost of a transfer machine (its purchase price) can
be broken down into two components: hardware costs and labor
costs associated with the design and construction of the ma-
chine. This section first discusses the typical breakdown
of these costs. Then, the effect of number of product parts
and product size on these costs is considered.
Data concerning the major costs of a transfer assembly
machine was collected in discussions with various firms
43
presently making automatic assembly machines. This data is
summarized in Table 2.1. The data is in rough agreement
with similar data from Prenting (5) who reported component
costs from 25 to 35 percent; engineering, machine shop, and
system building at 40 to 50 percent; and debugging expense
anywhere from 10 to 50 percent of the total cost.
The engineering design cost is a significant fraction
of the total cost because each transfer assembly machine is
designed for a specific product. This means that each trans-
fer assembly machine is unique, and therefore the full en-
gineering design cost is charged to only one machine. Like
the engineering design cost, debugging costs also are applied
to only one machine. However, debugging costs are hard to
predict because debugging is, by definition-, the solving of
unforeseen problems.
The breakdown of hardware costs for one type of trans-
fer machine (an in-line indexing table) is given in Table 2.2.
Because the cost ranges of several of the components are
large, and because any given part assembly may not use all
of the components listed, the hardware costs for the assem-
bly of two different parts assembled on one machine may vary
greatly.
The number of parts being assembled into the product
unit affects the total cost of both the hardware and the de-
sign and construction labor. A machine that assembles a
product with twice as many parts as the product of a second
44
Table 2.1 Cost Breakdown for Transfer Assembly
Machine
Component Costs
Engineering Labor
Machine Shop Labor
Machine Assembly and
Tryout (Debugging)
Nominal
Percentage
40
20
20
20
Percentage
Range_
30 - 50
15 - 25
15 - 25
15 - 25
45
Table 2.2 Cost Ranges for Typical Hardware Compo-
nents of a Transfer Assembly Machine
Station (assumes in-line indexing table --
product size up to eight inches)
Section of index table
(for one part assembly)
Bowl feeder (tooled)
Feeder track
Vibratory feeder track (tooled)
Part escapement
Placement device
Part detector
Pick up device
Control wiring
$535 - $4770
$1800 - $7000
$165 - $300
$500 - $700
$100 - $200
$860 - $3290
$50 - $200
$115 - $125
$100 - $500
machine will have approximately twice as many work stations
and will cost approximately twice as much as the second ma-
chine (assuming comparable product and part sizes). There-
fore, it is reasonable to consider the cost of a transfer
machine on a per part cost basis.
The cost of the assembly machine is also a function of
the size of the product. As product parts become larger,
larger and more expensive equipment is required to handle
them, and longer periods of time are required to design,
build, and debug them. Rough data on machine design, build,
and debug time versus machine size (obtained by surveying
machine builders) is given in Figure 2.5.
The cost per part of the assembly machine as a function
of the size of the product is illustrated in Figure 2.6. As
indicated, different types of assembly machines are used de-
pending upon the size of the product. Rotary index tables
are the cheapest transfer machine method, followed by in-line
indexing machines, and finally by non-synchronous systems.
2.2 Highlights of Programmable Assembler Technology
Research at the Charles Stark Draper Laboratory
During the assembly process there is a large amount of
information processing required for the assembly motions.
This information processing is handled very easily in manual
assembly by the human assembler. Transfer assembly machines
46
47
Figure 2.5e Transfer Maahine Size and Time to Build
101
0.11-
n'0i
Ut
Nonsynchronous
a-.. 00 ,- 00
o 0 0i
Standard
Rotary
Small
Rotary
10 100 1000
Machine Size (ft)
Sourcest Survey of Machine Builders
I*
I
-O
e4
I I
II
48
Figure 2.6. Transfer Machine Cost per Part versus
Product Dimension
64
a
4,v
5r4
1 2 5 10 20 50 100
Product Dimension (in)
Sources Survey of Machine Builders
106 1
.m.. -.
- -- I IVr tIlII I I I- JI '1l
Nonsynchronous -
S I I I I I I I i
I n-line : i4j:i31111i111 LL
i I I I I I III~~
I I I 1 TII I I -
o o 0 " 0000000.
0 0 0 0 0 0 0 0 0 0 0- -- f-l-r - - - -n r -0 0 0i a0 0 r fr'aT --0o00_00000000 C i II inirrn
Standard
Rotary
Small
Rotary
1 I- 1111111 1 1 111111
49
are constructed so that the part motion information is
stored in the geometry of the cams and levers of the ma-
chine itself. The advent of relatively low cost and phys-
ically compact computing equipment offers a new approach for
handling this information processing; the result is program-
mable assembly.
Besides the availability of microcomputers and micro-
processors, programmable assembly requires the availability
of suitable assembler technology; that is, equipment that
can be directed to do assembly under computer control. Re-
search on assembler technology has been conducted at the
Charles Stark Draper Laboratory for the past several years,
and this section will report some of the highlights of this
research. For more detail concerning this work see Nevins
et al (6), (7), and (8).
The research at Draper Lab in this area greP out of an
investigation of manipulators being used in the space pro-
gram. A manipulator is an arm-like structure which is usu-
ally controlled by a person from a remote position. How-
ever, when manipulators in space are controlled from the
ground, the transmission delays caused by the long distances
involved often make manipulation difficult. Therefore, the
concept of supervisory control was introduced -- a certain
level of intelligence is assigned to the remote manipulator
so that continuous control between earth and space is un-
necessary. From this research grew an appreciation for
50
quantitative definition of manipulation tasks and of the
sensory information and control algorithms required to
carry them out. This appreciation has been applied to the
industrial assembly problem for the last four years.
Work has since been carried on in the development of
computer control of assembly hardware. The design of a high
performance six axis hydraulic assembler was carried out on
paper and provided information on the potential performance
capacity of a range of assembler hardware. A force sensor
design which mounts at the "wrist" of an assembler device
and provides strain gage readings which are "resolved" into
three force components and three torque components within a
computer has been developed.
The concept of resolution of motions and forces into
appropriate coordinate systems is an important problem for
remote manipulators. General purpose manipulators usually
have at least six degrees of freedom of motion. They are
usually constructed so that a simple straight line of motion
of the end point, or "hand," of the manipulator may require
various motions by all of the axes.
D. E. Whitney (9) developed "resolved motion rate con-
trol" as a means of controlling remote manipulators by com-
mands to be interpreted in a coordinate system fixed to the
hand of the remote manipulator. Thus, in order to achieve
forward motion of the hand, the operator of a remote manip-
ulation system need only issue a command to move forward,
51
rather than attempt to issue many commands to the various
joint actuators of the remote manipulator. Resolved motion
rate control requires computer processing in order to ac-
complish the coordinate transformations.
Resolved motion rate control can be combined with
"wrist" force sensor information resolved in the same hand
coordinate system to guide the assembler hand motion. This
process has been designated "accommodation" and can be used
to control the manipulator when contact is made with a fixed
object. Frequently in the assembly of parts, such as a peg
into a hole, force information obtained in this way can be
used to modify the motion of the assembler so that smoother
and more effective assembly motions take place.
Work is currently being done to develop computer soft-
ware systems with expanded capacity for dealing with the
different aspects of information processing in programmable
assembly.
2.3 Review of the Literature
There is very little literature in the area of economic
criteria for the design of programmable assembly systems or
component assembly equipment. There has, however, been work
done in related areas that is well worth mentioning.
Boothroyd has done work in the area of automatic assem-
bly. In particular, his 1968 book Mechanized Assembly, with
52 
co-author A. H. Redford (3), discusses many of the compo­
nents of transfer assembly machines. The strength of the 
book is the detail of analysis of the construction and per­
formance of the important components of the transfer assem­
bly machine, particularly the parts feeding and orienting 
equipment. He discusses the performance and economics of 
transfer assembly machines insofar as they are dominated by 
the quality of the parts being assembled. The cost/perfor­
mance process he models is the effect of downtime associated 
with machine stoppage caused by poor quality parts, and he 
addresses the problem of how much of the assembly process 
to mechanize based on the part quality and machine perfor­
mance at a given part quality. There is no general economic 
model or analysis, however. 
An Introduction to Mechanical Assembly, by Tipping (10), 
is a descriptive book about the major components of transfer 
assembly machines. The book is particularly oriented toward 
the user of the transfer assembly machine and emphasizes 
that a detailed feasibility study and economic analysis be 
done for the particular installation to determine the best 
way to mechanize the assembly process. It does not address 
models that relate cost and performance. 
T. o. Prenting has addressed the economics of transfer
assembly machines in a series of papers and articles in the 
1960's. In particular, "Automatic Assembly the Economic 
Considerations" (5) describes the cost sources in construe-
53
ting a transfer assembly machine and provides some data on
the cost composition. With co-author M. D. Kilbridge in
the article "Assembly: Last Frontier of Automation," (11),
Prenting discusses in general terms principal characteris-
tics of transfer assembly machines and their economics.
A series of reports from the Stanford Research Insti-
tute entitled "Exploratory Research in Advanced Automation",
(12), (13), and (14), concern work on automation based on
programmable computer controlled manipulators. The work
concerns the use of vision systems to locate and identify
parts and products in random positions, the development of
end effectors and sensors to aid in the manipulation, and
the development of hardware and software to aid in the
teaching and controlling of the manipulators by various
means such as joysticks and voice control. Their work does
not include any analysis of the potential economics of these
experimental systems.
Work at the Stanford Artificial Intelligence Laboratory
of the Computer Science Department of Stanford University
has included the development of a programming language for
programmable assembly raported in "AL: A Programming System
for Automation" (15). This work assumes the existence of
very general purpose assembly manipulators and an unstruc-
tured assembly environment. The purpose of the development
of this language is to aid in the programming and set up of
assembly tasks, thereby reducing the time and cost of imple-
54
mentation of individual assembly processes. The scope of
the work does not include an analysis of the economic im-
pact of the reduced set up time.
Heginbotham (16) has considered the problem of the
economics of the application of industrial robots, but did
not specifically include the performance of the robots in
his analysis. Heginbothim is chief editor of and a regular
contributor to "The Industrial Robot"(17), a journal
published in Great Britain which reports developments in
the field of industrial robot technology including assembly
applications.
Abraham, Yaroshuk, and Beres (18) have analyzed the
problem of selecting suitable products for a hypothetical
programmable assembly system. Their method depends on cer-
tain key variables related to the candidate product and hy-
pothetical assembly system. These variables include man-
hours per unit of assembly, batch size, number of different
styles, annual volume per style, automation equipment cost,
setup time, and setup cost. Their analysis includes the de-
velopment of graphical aides to help identify candidate
products for assembly on flexible automated assembly systems.
At the Charles Stark Draper Laboratory a programmable
assembly automation project sponsored by the National Science
Foundation is in progress. The reports issued to date from
the project cover a range of work relating to programmable
assembly systems. The reports are titled "Exploratory
.9p
55
Research in Industrial Modular Assembly" (6), (7), and (8).
All three reports cover work progress in the areas of the
description of the assembly tasks and analysis of task
geometry; the development of control systems for program-
mable assembly hardware; the development of sensor technol-
ogy suitable for assembly tasks and programmable hardware
control; and the development of computer software to control
the programmable assembler equipment, to organize the execu-
tion of the assembly task sequence, and to teach the assem-
bly task sequence to the system. Both theoretical and ex-
perimental work has been done in these areas. Progress in
the analysis of the economics of programmable assembly sys-
tems -- part of the work -leading to this thesis -- has also
been described in these reports.
In general, assembly is not an area where there is much
ongoing research. What there is tends to be technical in
nature, with technical feasibility, rather than economic
viability, being the guide.
3. DESCRIPTION OF THE ASSEMBLY PROCESS
Assembly is the process by which a collection of parts
is transformed into a product unit. It is a process in
which objects are moved in relation to each other and often
in contact with each other. The assembly process can be
viewed in terms of assembly tasks and an assembly sequence.
I-
56
An assembly sequence is an ordered set of steps which, when
executed in order, will assemble the parts into the final
unit. Each of these steps is the execution of an assembly
task. Examples of assembly task steps are: Place a part
in a specified position, push part A against part B with
specified force; and, insert part A into.part B. Examples
of assembly tasks are: position, push, and fetch. The
function of an assembly task is ssentially the same each
time it is performed, but the exact details of its .xecu-
tion may vary from time to time, and the identity of the
parts involved will change. In general, an assembly se-
quence is not unique because one can think of more than one
way of assembling most products.
To investigate the nature of assembly tasks, a case
study was performed with a washing machine gearcase (see
Figure 3.1). The objective of the study was to go through
the process of specifying an assembly sequence for the gear-
case that could conceivably be done by a programmable as-
sembly machine. No attempt was made to optimize the assem-
bly sequence.
Two conditions were imposed: First, the sequence was
restricted to one which could be executed by a "one-armed"
assembly device. The purpose of this constraint was to
force consideration of the simpler one-armed assembler
rather than some device that was more complex (and there-
fore more distant in the future). Second, any tools were
57
Figure 3.1. Gear Case Assembly
42
44-70
7 5 707
4146 73
45 58
>46N
58 72292
3230 
-7
33 __J52\
55
56
64
6
~6L
58
allowed so long as they could be used by a single arm assem-
bler. The intent of this assumption was to avoid the prob-
lem of having to conceive of a universal part gripper that
could be used to manipulate all the parts. The purpose of
the study was to examine assembly tasks; the design details
of the tools used in the tasks was of lesser importance.
There were a total of 34 parts involved, and the part
size ranged from about 1/4 inch to 1 foot. The resulting
assembly sequence contained a total of 221 steps. There
were a total of 17 different tasks used.
Of the 17 tasks usc'd, 9 were very similar in their
method of execution. Specifically, they used "accommoda-
tion," a process which uses contact force to modify the
motion of the parts in such a way as to facilitate assembly.
These 9 tasks have been lumped together under the title
"Accommodation" in Table 3. . This table shows the fre-
quency of the tasks in the assembly sequence as a count, a
percentage of total steps in sequence, and also as a count
normalized with respect to the number of parts in the assem-
bly. On the average, 6.5 task steps were performed per
part. The corresponding task definitions are given in
Table 3.2.
Certain tasks such as "fetch" and "position" have nor-
malized frequency counts approximately equal to one, which
means they are performed an average of once for each part.
Therefore, these particular tasks are probably required in
59
Table 3.1 Breakdown of Assembly Task Steps
for Washer Gearcase (34 parts)
Number
of Steps
Percent of
Total
Operations
per Part
Fetch
Grasp
Position
Interface
Release
Return
Cycle
Detect
"Accommodation"
Total
Task
33
21
36
33
17
34
15
1
31
221
14.9
9.5
16.3
14.9
7,7
15.4
6.8
.5
14.0
100.0
.97
.62
1.06
.97
.50
1.00
.44
.03
.91
6.50
61
the assembly of each part regardless of the specific part
identity. This means that they are essential functions of
any general assembly operation, and any programmable assem-
bly machine would be required to perform them.
Table 3.3 shows a breakdown of the accommodation tasks
used in the sequence specification, and Table 3.4 provides
brief definitions of the tasks. "Complex accommodation"
refers to relatively complicated motions using accommodation
that were hard to name. The other accommodation tasks were
simpler motions that were more specific and consequently
easier to name.
There were 36 tools, jigs, and fixtures needed for the
prccess, approximately one tool or fixture per part. Many
of the tools were special shapes that allowed accurate loca-
tion and gripping of parts. The tools used fell into three
general categories.
The first category contained tools with grasping sur-
faces that were designed to grasp parts in a particular way.
These grasping surfaces were designed to locate the part
accurately in the gripper or hand because the assembly pro-
cess will be simplified if the part is held accurately.
A second tool category was one of special, rigid, one-
piece jigs designed to reduce the degrees of freedom of
assembly. These tools were "invented" when a subassembly
of loosely connected parts had to be fitted to the main as-
sembly. This tool would hold the various connected parts
62
Table 3.3 Breakdown of "Accommodation" Task
Steps for Washer Gearcase (34 parts)
Task
Complex
Accornoda te
Insert
Rotate
Depress
Search motion
Slide
Seat
Move
Remove
Total
Number
of Steps
8
11
3
1
2
2
1
1
2
31T
Percent of
Total.
25.8
35.5
9.7
3.2
6.5
6.5
3.2
3.2
6.5
100.0
Operations
per Part
.23
.32
.09
.03
.06
.06
.03
.03
.06
.91
63
Table 3.4
Complex
Accommodate:
Insert:
Rotate:
Depress:
Search motion:
Slide:
Seat:
Move:
Remove:
Accommodation Task Definitions
Accommodation executed during a
complex motion. No convenient name
to describe motion.
Pushing a shaft-or-peg-like part into
a hole. Nominal trajectory is a
straight line.
Rotation of part about an axis with
accommodation.
Deflect a part in its compliant direc-
tion.
Move along surface while maintaining
contact force normal to it.
Move part along grooved or channeled
surface in direction of channel.
Place very wide peg-like part in very
shallow hole.
Insertion or similar accommodation
executed over very long trajectory.
Withdraw a peglike part or tool from
a hole.
I
64
rigid so that the assembly would become easier for a one-
armed assembly machine.
The third tool category was currently available auto-
matic feeding tools. These tools include feeding mechanisms
which automatically supply the tool with the parts. An ex-
ample is a power screwdriver with automatic feeding of the
screw fasteners.
Based on the experience of this case study, the same
general procedure is used for the assembly of each part, as-
suming a special tool must be used for each part. This pro-
cedure is:
1) Assembler moves to location of tool storage site.
2) Assembler engages tool.
3) Assembler carries tool to part storage or pre-
sentation site.
4) Tool engages part.
5) Assembler carries tool with part to assembly site.
6) Assembler with tool assembles part to subassembly.
7) Tool releases part.
8) Assembler carries tool to tool storage site.
9)- Assembler releases tool.
The motions of the assembler can be divided into two types:
gross and fine. During a gross motion the assembler arm
travels from one location to another, usually without being
in contact with the product being assembled. For example,
a gross motion occurs in step 3 above. During a fine motion
65
the assembler arm makes small movements in a localized area
and is usually in contact with either the product or the
parts feeding unit. For example, fine motions occur when
a part is actually being assembled to the product unit or
when a part is being grasped initially. Step 6 above re-
quires a fine motion.
Using a different tool for each part represents one ex-
treme in the specialization of tools for assembly. The
other extreme is to specify as few tools as possible, or
even to require the use of only one general purpose tool.
This general purpose tool would need to be quite complex in
order to satisfy the requirement for versatility, and there-
fore, it would probably be more expensive than any of the
other tools used for only one part. However, if it were not
necessary to change tools for every part, then a great deal
of time can be saved. Then, the general procedure for as-
sembling a part would look like this:
1) Assembler with gripper makes a gross motion to
part storage or presentation site.
2) Assembler with gripper engages part.
3) Assembler with gripper carries part to assembly
site in gross motion.
4) Assembler with gripper assembles part to subassem-
bly in a fine motion operation.
5) Gripper releases part.
The extra expense and complexity of a general purpose tool
66
may or may not be rewarded by the time saved. This is only
one of many technical issues which can be resolved only by
the ultimate economic test.
Summary
The assembly sequence is an ordered set of steps, each
of which is the execution of an assembly task. Two inter-
esting facts concerning these tasks are:
1) Several tasks are similar in their execution; they use
contact force to modify their motion during assembly.
Such tasks are designated "accommodation" tasks.
2) Certain tasks, such as "position," are necessary for the
assembly of each part, and, therefore, are a necessary
function for any programmable assembler.
A range of options exists in the use of assembly tools,
with the following two extremes: a special tool can be de-
signed for each individual part assembly, or a universal
part gripper which can perform each assembly step for each
part can be designed. The first extreme would require as
many as four extra steps in the assembly sequence for a
single part, but the individual tool cost would probably be
lower than the cost of the universal part gripper.
There are two types of assembly motions: gross and
fine. The gross motions are "traveling" motions, such as
a motion used for the assembly task "position." The fine
67 
motions are used, for example, during the actual assembly 
of the part to the product unit. 
The concepts of assembly tasks and tools are important 
because they play a part in the economic evaluation of a 
programmable assembly system. Gross and fine motions are 
necessary functions in assembly, and each requires a certain 
amount of time to be performed by the assembly equipment. 
Task execution time will influence production rates which, 
in turn, influence the economic evaluation. Tools, whether 
general purpose or specialized, cost money and will also in­
fluence execution time; hence, the fools also will affect 
the economic evaluation. In the next chapter a closer ex­
amination of these and other characteristics of programmable 
assembly systems that will influence the economics of their 
application is begun. 
4. EMERGING PROGRAMMABLE ASSEMBLY TECHNOLOGY
In this chapter the application of programmability to 
assembly technology will be discussed. First, the basic 
definitions and concepts of a programmable assembly syscem 
as they are applied in this research are presented. The 
remainder of the chapter discusses the economic advantages 
that are possible with programmable assembly. 
Since programmable assembly iE not, in fact, a prac­
ticed reality, it should be kept in mind that these advan-
68
tages are projected advantages, and their truth will be
proven or disproven only after programmable assembly is
actually put into use.
4.1 Basis Concepts of Programmable Assembly Systems
The words "programmable assembly" have been used in
this thesis to refer to the general concept of assembly
equipment that can be programmed to execute a sequence of
assembly tasks. In this section the specific concepts of
programmable assembly as they are applied in this research
are presented.
It is important to define specifically the terms pro-
grammable assembler, programmable assembly system, program-
mable assembly station, and programmability and to discuss
their interrelations.
Programmable Assembler
A programmable assembler is a device which assembles
products and which consists of 1) a motion device capable
of positioning a part in many different positions and 2) a
control unit that directs the motions of the motion device
and which may be programmed. The motion device may resemble
a remote manipulator, but that is not necessary. One con-
ceptualization of the motion device of a programmable as-
sembler is shown in Figure 4.1. The motion device hardware
consists of an end effector (part gripper or tool) and po-
I-
69
Figure 4.1u Example Design for Programmable
Assembler Station
Programmable Assembler
Motion Device
WorkArea
Pallet or Conveyor Feeding
LII
F m- ,IL7-
ENIMMEMOMMMM
70 
sitioning equipment (the links and axes) to move and orient 
the end effector. 
The programmable control unit may be a minicomputer or 
microprocessor, or it may be a device of less sophistication. 
The control unit must be capable of storing enough informa­
tion to execute the necessary tasks. The degree of sophis­
tication required of the programmable control unit depends 
on the capabilities of the motion device and the require­
ments of the application of the assembler. 
A programmable assembler includes not only the program­
mable control unit and the motion device, but also sensory 
equipment that is required for the completion of the assem­
bly task. Position sensors located on the motion device 
provide information about the location of the part carried 
by the assembler. These sensors are also used in the servo 
control of the motion device. Force sensors may be included 
to monitor contact forces between parts during assembly. 
Other sensors may be used in more sophisticated systems. 
For example, visual sensors may be used to locate parts and 
assembly sites, or tactile sensors located in part grippers 
may be used to identify just where the part is being held 
in the gripper. 
Programmable Assembly System 
A programmable assembly system is a collection of pro­
grammable assemblers working together on the assembly of a 
product. The system includes not only a set of assemblers 
71
but also a conveying system which moves the in-process as-
semblies from one assembler to the next; and a set of parts
feeding equipment, which presents parts to the assemblers
in known orientation and position.
Programmable Assembly Station
A programmable assembly station consists of a program-
mable assembler and the portion of the conveying system as-
sociated with that assembler.
Programmabi1ity
"Programmability" as used here is the ability of a de-
vice to be taught different tasks. This is in contrast to
the methods of conventional assembly technology in which a
task is defined by the geometry of the hardware and is not
easily changed. This kind of programmability does not re-
quire a computer, but the use of a minicomputer or micro-
processor is an easy way to implement it in assembly tech-
nology.
4.2 Economic Advantages of Programmable Assembly
As reported in Chapter 2, presently employed assembly
technology consists of manual assembly and transfer machine
assembly. Each of these methods has its own strong points;
circumstances exist where one method is clearly preferred
over the other. What are these circumstances for program-
mable assembly? In particular, in which cases will program-
72
mable assembly prove to be economically superior to manual
assembly and transfer machine assembly and why? This sec-
tion discusses in general terms some of the assembly situa-
tions where programmable assembly is seen to be potentially
advantageous. The advantages of programmable assembly are
discussed for multipart assembly, multiproduct assembly,
and adaptive assembly. The possible reduction in engineer-
ing time associated with setting up a programmable system
instead of a transfer assembly machine system is also dis-
cussed.
4.2.1 Multipart Assembly
The chief economic measure by which different assembly
methods are compared is the assembly cost per unit of prod-
uct. When capital equipment is built to assemble a product,
the assembly cost per unit is proportional to the cost of
the capital equipment divided by the number of units made
on the equipment. (Modeling and calculating costs will be
discussed in Chapter 6). The assembly cost per unit can be
reduced either by reducing the cost of the equipment or by
increasing the number of product units that are assembled
on the equipment.
A distinction is drawn here between the terms product
and product unit and the terms part and part unit. A prod-
uct is a set of identical product units. Hence, a pump is
73
an example of a product, and there are many units of the
pump made per year. Similarly, a part is a set of identical
part units. For example, a bowl feeder is designed to handle
a single part, but it may have a certain feeding rate of so
many part units per minute. Finally, the term volume, or
annual production volume, is used to mean the number of prod-
uct units that are assembled in one year.
Because a programmable assembler can execute more than
one assembly task, it can assemble a number of different
parts. This multipart assembly capability of a programmable
assembly station is in direct contrast with the transfer as-
sembly machine station where one part at most is assembled
per station (some stations may be used for nonassembly func-
tions). A single programmable station may be more complex
and expensive than a single trdnsfer machine station, but the
fact that fewer programmable stations may be required for a
system to assemble a given product raises the prospect of an
assembly system whose original cost is less than that of the
corresponding transfer machine. This comparison is illustra-
ted in Figure 4.2. However, as the number of parts assembled
per station increases, the maximum production rate of a pro-
grammable system decreases. This means that a programmable
system in which each assembler performs multipart assembly
can be designed with the appropriate number of stations for
the needed production volume. If the cost of programmable
stations is comparable to that of transfer machine stations,
74
Figure 4.2. Multipart Assembly
Assumes product with six parts
Programmable Systems
Two Assemblers
Pal
Six Sets of Parts Feeding Equipa
let Stream
tent
Transfer Machine Systems
Six Transfer Stations and Six Sets of Parts
Feeding Equipment Transfer Station
0 0 %001 0 
-0
r ] C]Pallet Stream
Palle t Str eam
75
then, in general, programmable systems will be economically
more attractive than transfer machines for lower production
volumes.
4.2.2 Multiproduct Assembly
We have seen that the versatility of a programmable as-
sembler allows it to assemble more than one part of a product
and that this can lead to unit assembly cost savings by re-
ducing the number of assembly stations required. This ver-
satility can also be used to spread the cost of the system
over many product units in another way. One programmable
assembly system can be designed to assemble the parts of
different products.
For multiproduct assembly, versatility is required not
only for the assemblers, but also for the other parts of the
system, i.e., the conveying system and the parts feeding
equipment. For example, programmable assembly systems may be
designed to assemble product families -- groups of products
that have common or related parts and assembly processes.
One product may have a "deluxe model" which requires the as-
sembly of extra parts, and this would require versatility in
the conveying system so that the deluxe model product unit
could be routed to extra assemblers. Or, one product may
differ from another simply by the size of one of its parts.
This would require versatility in one set of parts feeding
76
equipment so that it could handle two different size parts.
The degree of specialization or generalization of such
programmable assembly systems in specific cases will be the
result of a trade-off decision between the expense of the
added assembly generality and the unit assembly cost savings
this generality introduces as a result of the application of
the system to a larger number of product units.
4.2.3 Adaptive Assembly
Adaptive assembly is the use of a sensor system to mon-
itor and modify the progress of the assembly task. Adaptive
assembly requires one or more sensors which collect force,
touch, or image information during the assembly and a proces-
sor which can use this information to modify the fine assembly
motions. Adaptive assembly may be used in combination with a
programmable assembly system, and it has many advantages.
Much of the downtime of the present transfer machines is
associated with clearing jams of parts in the assembly mech-
anism caused by variations in part dimensions and quality. A_
programmable assembler with adaptive assembly can detect the
onset of certain kinds of jams and could immediately repeat
the assembly operation either with the same part or with a
new one. Because the system could automatically recover from
assembly jams, there is a corresponding reduction in downtime.
Quick recovery from potential jams is only one of the
77
uses for adaptive assembly. Force and position readings ob-
tained from the sensors attached to the assembler can be used
in fine motion assembly tasks. In other words, the assembler
station could use the sensor information to feel its way
through the assembly process. This can be particularly help-
ful in two cases: first, when the part dimensions have large
variation and secondly, when the part tolerance is very small.
Generally, present assembly machines work best when there is
relatively little part dimensional variation and the part
clearance is greater than .005 in. Adaptive assembly can re-
duce the required quality and expense of the supporting equip-
ment. For example, transfer machines must be made very ac-
curately in order to reduce the chances of jamming the parts
during assembly. The dimensional variation that the machine
must overcome results from both the parts and the machine it-
self. Transfer machines are made very accurately to reduce
some of this variation. Programmable adaptable assembly can
be specifically designed to correct for variations in the
part positions and dimensions as they appear to the assem-
bler from one assembly operation to the next. Using adapt-
able assembly to deal with variations in part dimension and
tooling dimension can allow looser standards for both the
parts and the supportive machine system tooling, such as the
conveyors and pailets. These lower standards mean that
cheaper system tooling can be used, and part manufacturing
costs may be reduced.
78
Finally, by taking readings over a series of units, pro-
duction data can be developed on the value and drift rate of
important dimensions, the number of faulty parts, the average
assembly rate, and other important production variables. This
data can then be used to improve the system and make it more
economic. At present almost no data, of even the most rudi-
mentary kind, is available to assess assembly processes and
machine performance.
4.2.4 Reduction of Engineering Time
The fact that the programmable assembler is programmable
means that the trajectory of its motions is controlled by
easily changed data in the processor memory. This simplifies
the engineering problems in developing a system to assemble
a product and will result in a cost savings in building the
system.
The programmable assembler can be used as a standard
component in the construction of an assembly system but in a
wider sense than the "standard" components of a transfer sys-
tem. The standard component in the construction of a trans-
fer machine system can perform only a limited set of tasks,
and it must be mounted accurately with respect to other
equipment on the system (such as the pallet position). A
programmable assembler can perform a much wider range of
tasks and motions, and these motions need not be accurately
The basic concepts of programmable assembly systems are
79
specified until after the system is assembled. This relieves
many of the requirements for accurate relative positioning
of the components and the corresponding design and machine
shop time. The wide applicability and ease of incorporation
of a programmable assembler raise the assembler salvage value
because it can be easily converted to use in a new system.
Programmable assembly could reduce the costs of debug-
ging. In the development of a transfer machine, the motions
of the assembler equipment are determined by the physical
geometry of the hardware. It is much more difficult to ad-
just and modify these motions during the debugging process
than it is to modify the motions of a programmable assembler.
This means that the debugging time for the programmable sys-
tem is greatly shortened with a corresponding decrease in
this portion of the cost of the system. This can represent
a considerable savings since, as reported in Chapter 2, the
cost of debugging the system can be almost half the total
price of the transfer machine. If the programmability of the
system includes adaptive asse:nbly, then the information from
the force sensors can be used to speed the debugging process
by helping to identify the troublesome assembly tasks. This
will also help to reduce the debugging time and cost.
4.3 Summary
80
important ideas which are used in the modeling of later chap-
ters:
1) A programmable assembler consists of a motion
device and a control unit.
2) A programmable assembly system is a collection
of programmable assemblers working together on the
assembly of a product and includes a conveying sys-
tem and a set of parts feeding equipment.
3) A programmable assembly station consists of
the programmable assembler and a portion of the
conveying system.
4) Programmability is the ability of a device to
be taught different tasks.
The potential advantages of programmable assembly in-
clude multipart assembly, multiproduct assembly, adaptive
assembly, and a reduction in engineering time for the set-
up of the system. The versatility of the programmable
assembler leads to its ability to assemble more than one
part, while the versatility of the programmable assembly
system leads to its ability to assemble more than one prod-
uct. Adaptive assembly may be used in combination with pro-
grammable assembly and will add advantages, such as the
ability to clear certain jams, the ability of the assembler
to "feel" its way through the assembly process, and a reduc-
tion in equipment expense. Because a programmable assembly
system does not require accurate.positioning of the assem-
81
blers in many cases and because the assembly motions and
tasks are easy to change, the system will require less en-
gineering time for setup than a similar transfer machine
assembly system.
Next, in Chapter 5, the modeling process begins with
an examination of the characteristics and requirements for
programmable assemblers and assembly systems. Then, certain
of the economic advantages of programmable assembly that have
been discussed in this chapter will be quantified in the
economic model to be developed in Chapter 6.
5. CONFIGURATIONS OF PROGRAMMABLE ASSEMBLY TECHNOLOGY
In Chapter 4 the economic advantages of programmable
assembly were presented in general terms. In Chapter 6 the
economic advantages of programmable assembly are investigated
from a different, more quantitative, point of view: Economic
models of programmable assembly systems, transfer machine
systems, and manual assembly are derived and compared. This
chapter presents the characteristics of programmable assembly
systems upon which the modelinq of Chapter 6 is based.
The programmable assembler is the "center" of the pro-
grammable assembly system. This chapter begins with a dis-
cussion of programmable assembler configurations: What are
some of the possible designs of programmable assemblers and
what are their characteristics?
82
The second section of the chapter is concerned with the
possible configurations of prcgrammable assembly systems.
The principal components of a programmable assembly system
are programmable assemblers, a conveying system, and a set
of parts feeding equipment. The possible types of arrange-
ments for the programmable assemblers in the system and the
characteristics of each arrangement are discussed.
The economic model developed in Chapter 6 for program-
mable assembly systems depends partially on the "efficiency"
of the system configuration.
The concept of system efficiency is discussed in the
third section of the chapter.
5.1 Programmable Assembler Configurations
The specific configuration of the programmable assem-
bler is now considered in greater detail. How versatile
should a programmable assembler be? Should every program-
mable assembler be able to position a part in any arbitrary
location? This section shows that there can be a wide range
of versatility for an assembler (in particular for the mo-
tion device), and that due to the existence of principal
assembly axes on many products the less versatile (and there-
fore less costly) assemblers may have many applications.
81
blers in many cases and because the assembly motions and
tasks are easy to change, the system will require less en-
gineering time for setup than a similar transfer machine
assembly system.
Next, in Chapter 5, the modeling process begins with
an examination of the characteristics and requirements for
programmable assemblers and assembly systems. Then, certain
of the economic advantages of programmable assembly that have
been discussed in this chapter will be quantified in the
economic model to be developed in Chapter 6.
5. CONFIGURATIONS OF PROGRAMMABLE ASSEMBLY TECHNOLOGY
In Chapter 4 the economic advantages of programmable
assembly were presented in general terms. In Chapter 6 the
economic advantages of programmable assembly are investigated
from a different, more quantitative, point of view: Economic
models of programmable assembly systems, transfer machine
systems, and manual assembly are derived and compared. This
chapter presents the characteristics of programmable assembly
systems upon which the modeling of Chapter 6 is based.
The programmable assembler is the "center" of the pro-
grammable assembly system. This chapter begins with a dis-
cussion of programmable assembler configurations: What are
some of the possible designs of programmable assemblers and
what are their characteristics?
83
5.1.1 Degrees of Freedom of Motion Device
A programmable assembler device must have the ability
to move a part unit through space over a range of motions.
The number of degrees of freedom of this motion is an impor-
tant measure of the versatility of the assembler.
Figure 5.1 shows a set of potential assembler motion de-
vice configurations illustrating the concept of the number
of degrees of freedom. (They are sketched so that the loca-
tion and action of each degree of freedom is plainly visible.)
A single degree of freedom device has motion along a path in
space or rotation about a single axis. A two degree of free-
dom device may be designed to move in two independent direc-
tions (and so move over a surface in space), or it may be
designed to move along a path and rotate about an axis, or
it may be designed to rotate about two independent axes. All
two degree of freedom devices are not equivalent or even sim-
ilar. One possible three degree of freedom device might move
a part unit to any point in its working volume but not con-
trol the angular orientation of that part unit at that point.
The position of a part can be completely described by
six numbers: for example, three numbers indicating its dis-
placement in three dimensional space and three numbers indi-
cating its angular orientation about the three major axes.
Therefore, to position an object to an arbitrary location and
orientation an assembler motion device would require six in-
84
Figure 5.1. Assemblers with Various Degrees of Freedom
(a) 1 dof
(d)
( 3do
(g) 4 dot
(b) 2 dof
(e) 3 dof
& 5 dof
2
Work
Piece
(j6dot
42
Work
Piece
(C) 3 dot
(t) 4 dot
6 dot
00,2
85
dependent degrees of freedom.
However, in order to control part assembly positioning
it is not necessary to hold the basic assembly fixed and
to position the part with six degrees of freedom. The assem-
bler motion device may actually consist of two motion de-
vices: one to hold the product unit and one to position the
part. For arbitrary relative positioning of part and prod-
uct unit the two motion devices must have six degrees of
freedom between them. For example, an assembler may have
its degrees of freedom divided as in assembler (j) of Fig-
ure 5.1 where three displacements and one rotation are con-
trolled by the assembler mechanism that carries the part and
the two remaining rotations are controlled by the table that
holds the product assembly.
More degrees of freedom for the assembler necessitate
more complex and costly equipment. Consequently, when de-
signing a programmable assembler or assembly system, it is
important to determine the minimum number of degrees of free-
dom required to accomplish the necessary assembly tasks.
5.1.-2 Principal Assembly Directions and Axes
Many products have principal axes along which many of
their parts- are assembled. These axial alignments occur
partly for functional reasons and partly because manufactur-
ing processes tend to create them. Fdr example, the use of
86
simple three axis milling machines tends to create parts that
have three principal directions at right angles to each other.
Turning and drilling equipment tends to create parts that
interface with axial symmetry.
We now define axis and direction with respect to a prod-
uct. Imagine the product attached to a fixed reference frame.
An axis is defined as a directed straight line passing through
the product (see Figure 5.2). The direction of an axis is
simply the angular orientation of the line in space without
regard to its physical displacement with respect to the co-
ordinate frame. Thus, several axes may have common direc-
tions. An axis of assembly is an axis along which a part is
moved to assemble it to the product.
The actual assembly process may involve general large
scale motion along the axis of assembly plus much smaller ac-
commodation motions in other directions. An assembler must
have the appropriate degrees of freedom to move the part
along the principal assembly axes. The small accommodation
motions must also be made, but they may or may not be made
with a controlled degree of freedom. For example, if the
part is held with a certain compliance in the part gripper,
then the small accommodation motions may be made passively
under favorable conditions.
Kondoleon (19) has found for a small set of products
consisting of rigid machined or molded plastic parts that
roughly two thirds of the parts of these products are assem-
87
Figure 5.2s Product Assembly Axes and Directions
Direction I
Assembly Assembly
Axis I Axis 2
-<oo
Assembly
Axis 4
0
Direction 2
Assembly
Axis 3
Assembly
Axis 5
Direction 3
cD
I .MW
A. A
88
bled in one principal direction and that over 80 percent of
the parts are assembled in only two principal directions.
Thus, even though a station in a given system may be required
to add many parts to a product unit, only a few product axes
may be involved, and so that station may need only a few de-
grees of freedom. This is important since an assembler with
a reduced number of degrees of freedom will certainly be
cheaper than one with more degrees of freedom.
For example, for the product illustrated in Figure 5.2,
the four axis device (a) illustrated in Figure 5.1 would be
adequate for the assembly of the bolts along assembly axes
1 and 2 in assembly direction 1. The device could reach to
a bolt feeder, pick up a bolt, assemble it along assembly
axis 1, reach for another bolt and assemble it along assembly
axis 2. This device would not be able to assemble the bolts
along assembly axes 3, 4, or 5.
The three degree of freedom assembler (c) in Figure 5.1
could assemble the bolts along axes 1 and 2 if the bolts were
fed directly to the part gripper through a tube (a common
fastener feeding method) or if the bolt feeding site were in
the same plane as the assembly axes. This device also could
not assemble the bolts along assembly axes 3, 4, or 5 because
of its restricted set of degrees of freedom. Assembler (f)
with four degrees of freedom has the right degrees of freedom
to assemble all bolts along all five assembly axes. The six
degree of freedom assemblers (i) and (j) could also assemble
89
the entire product because their degrees of freedom allow
arbitrary motion.
This organization of the assembly of a product into
principal assembly axes can affect the kind of assembler re-
quired in a given system configuration. For example, for a
system configuration in which one assembler must assemble
all the parts of the product in all the principal assembly
directions, the single assembler may need six degrees of
freedom. Consider another system configuration in which sev-
eral assemblers each assemble a few parts of the product so
that together they assemble the entire product. Each assem-
bler in the second configuration may need fewer than six de-
grees of freedom if each is oriented so that it has the
proper degrees of freedom to assemble a subset of the parts
with a common axis or assembly direction.
5.2 Programmable Assembly System Configurations
In this section the possible arrangements of programmable
assemblers in the assembly system are examined. There are
three principal arrangements, or configuration modes, which
can be used: serial, parallel, and overlap. First, each
mode is described. Then, the important characteristics of
each mode are discussed. Finally, the use of combinations
of modes in an assembly system is discussed.
90
5.2.1 Principal Configuration Modes
This section describes the three principal configuration
modes for programmable assemblers: serial, parallel, and
overlap. Many simplifying assumptions are made in order to
present the modes with as little complication as possible.
In the next section the operating characteristics of the
three modes are discussed without considering the simplify-
ing assumptions used here.
The principal modes of assembler arrangement into a sys-
tem can be illustrated by a pair of assemblers working to-
gether to assemble a product (see Figure 5.3).
To simplify the comparison it will be assumed that both
assemblers in the assembly system cost the same amount and
that the time spent during the part assembly cycle is con-
stant for all parts and the same for each assembler.
The time spent by an assembler during the part assembly
cycle is called the single part assembly time. It includes
the time spent in fetching parts or tools, the grasping and
release time, and the time spent in fine motion assembly ac-
tivity. In the example of the two assemblers, the assumption
that the single part assembly time is constant for all parts
and the same for each assembler means that the part assembly
time for part A is the same as for part B and that the speed
of each assembler is the same.
It will be assumed also that the parts feeding or pre-
90
5.2.1 Principal Configuration Modes
This section describes the three principal configuration
modes for programmable assemblers: serial, parallel-, and
overlap. Many simplifying assumptions are made in order to
present the modes with as little complication as possible.
In the next section the operating characteristics of the
three modes are discussed without considering the simplify-
ing assumptions used here.
The principal modes of assembler arrangement into a sys-
tem can be illustrated by a pair of assemblers working to-
gether to assemble a product (see Figure 5.3).
To simplify the comparison it will be assumed that both
assemblers in the assembly system cost the same amount and
that the time spent during the part assembly cycle is con-
stant for all parts and the same for each assembler.
The time spent by an assembler during the part assembly
cycle is called the single part assembly time. It includes
the time spent in fetching parts or tools, the grasping and
release time, and the time spent in fine motion assembly ac-
tivity.' In the example of the two assemblers, the assumption
that the single part assembly time is constant for all parts
and the same for each assembler means that the part assembly
time for part A is the same as for part B and that the speed
of each assembler is the same.
It will be assumed also that the parts feeding or pre-
91
Figure 5.
Serial Node.
Principal Configuration Modes
Assembler I
Part A d
Assembler 2
Index
Length
U Pert B
Parallel Mode.
Assembler I
Ce
Assembler 2
Ind
Lain
lex
trth
Part A do Part B
Overlap Mode.
Assembler I Assembler 2
Index
Length
P3 A PatB
Part A d Part B
ED 1: ID 1:3O
92
sentation equipment is so constructed and situated that two
or more assemblers can share the same parts feeding equip-
merit. The partially completed product units will be assumed
to be on pallets passing in front of the assemblers in an
indexing motion. The distance that the pallets are moved
along the stream in one index cycle will be called the index
length and will be measured in number of pallet lengths.
In the serial arrangement, both assemblers function
simultaneously but on different product units. Each assem-
bler adds a different part to the product. If two parts are
assembled by these two stations, then assembler 1 adds part A
and assembler 2 adds part B. The effective time between com-
pleted assemblies from the pair is the assembly time for one
part by one assembler. In the arrangement shown in Fig-
ure 5.3, each pallet stops at both assemblers. The index
length of the pallet stream is one pallet spacing, and the
price of the pair of assemblers is twice the price of the
individual assemblers.
In the parallel arrangement, both assemblers function
simultaneously and on different product units. However, both
assemblers add the same parts to different product units.
Once a product unit is finished at assembler 1 it does not
go to assembler 2. Each assembler works on only every other
product unit in the stream. The index length of the product
stream is two pallet spacings. The time for each individual
assembler to complete its operations on a given product unit
93
is twice the single part assembly time since it must assemble
two parts, but, because the two stations are operating in
parallel, the effective time between completed assemblies is
still equal to the single part assembly time. Notice that
the parts feeding equipment is shared between the individual
assemblers. The price of the pair of stations is twice the
price of an individual station, and, hence, the total costs
and production rates of the serial and parallel systems are
equivalent.
In the overlap arrangement, the two assemblers operate
simultaneously on the same product unit. Assembler 1 adds
part A and assembler 2 adds part B. If the geometry and
timing of their motions permit, the assembler motions are
simultaneous. Each pallet stops in front of the assembler
pair. The index length of the pallet stream is one pallet
spacing. In this case the time between completed assemblies
is equal to the part assembly time for an individual assem-
bler since the assembly motions are simultaneous. Again, the
price of this system of stations is twice the price of a
single assembler.
All three of the above arrangements are equivalent in
terms of production rate and cost in this ideal example.
This equivalence is due to the assumption that both assem-
blers are always kept busy -- there is no waiting time for
any assembler. This is due to the fact that the single part
assembly time is assumed to be equal for parts A and B and
94
equal for assemblers 1 and 2. If these assumptions are not
true (as indeed they are not, in general), differences in
the production rate and system cost for the three modes do
exist, and these are discussed in the next section.
The examples presented here of the two assembler systems
are intended simply to define the different modes clearly.
Many more issues are actually involved when the system be-
comes more complicated, and these are left to later discus-
sion.
The discussion so far has centered on the arrangement
of assemblers within a system. In some circumstances entire
programmable assembly systems may be duplicated. This may
occur if the production rate of one system is not sufficient
to meet the annual production requirements. If there are two
duplicate systems, then there are twice as many assembler
stations and twice as many sets of parts feeding equipment
as in the single system. We will consider the economics of
this duplicate system to be the same as the economics of a
single system working on one half of the production volume
of the product.
5.2.2 Operating Characteristics of the Principal Modes
Although the principal modes are equivalent in an ideal
sense, there are differences in operating characteristics in
practical systems.
95 
One important factor is that, in general, single part 
assembly times vary. The same assembler will take different 
times to assemble different parts because of variations in 
part weight, fit characteristics, and distance between part 
presentation site and assembly site. Different models of 
assemblers will take different times to assemble the same 
part because of differences in load and speed capabilities. 
If two equivalent assemblers are operating in a serial 
mode, and if the part assembly times differ for the two dif­
ferent parts, then the longer assembly time will dominate. 
The slower station will pace the pair because the faster sta­
tion must wait for the completion of the slower one. The 
waiting time of the faster station represents unusable cap­
acity. 
If the same two stations were placed in parallel, so 
that each station assembled both parts A and B, then there 
need not be any waiting time. As soon as either assembler 
is finished with part A it may proceed to part B. Both as­
semblers will finish at about the same time because they have 
identical tasks to perform. Figure 5.4 illustrates this ef­
fect. Under these conditions, the parallel arrangement al­
lows a higher production rate. 
The applicability of the parallel arrangement is de­
pendent upon the ability of the assemblers to assemble more 
than one part in sequence. If the parts that must be assem­
bled are such that special tools must be used for each of 
96
Figure 5.4m Serial versus Parallel Modes
Serial Mode m
C E C I
Part A j d Part B
Time
4 A Time1B 
Time
-
Index - - Wait
A Time B Time
- Index - pWait
A Time > B Time
Product Interval
= A Time
Parallel Modem
o o:3
Part A d Part B
A Time A
B Time B
- Index -
A Time A
B Time B
- - Index 
-
A Time > B Time
Time
Time
Time
Time
Product Interval
SA TIme + B Time
2
I
Time
1I
I
97
them, then the parallel arrangement would suffer because of
the extra time the assemblers must devote to the tool chang-
ing. In the serial arrangement where each assembler must
handle a smaller variety of parts, the amount of tool chang-
ing would be reduced.
In the parallel arrangement the need to assemble a
greater number of parts at one station may require more com-
plex and expensive assemblers. For example, extra degrees
of freedom may be required in the assembler motion device.
In the example given here only two assemblers operate
in parallel, and the two share the same parts feeding equip-
ment. As the number of assemblers operating in parallel in-
creases, the requirement for shared parts feeding equipment
becomes more difficult to satisfy. In order to have three
or four assemblers operating in parallel, it would probably
be necessary to modify portions of the parts feeding equip-
ment, at extra expense. For five or more assemblers it would
probably be necessary to duplicate the feeding equipment of
the parts, at even greater added expense.
In the overlap mode, two or more assemblers add parts
to a single product unit simultaneously. Under ideal condi-
tions this mode could be as efficient a use of individual
assemblers as the.serial or parallel modes. However, it is
likely that a large fraction of waiting time would occur in
this arrangement because of the sequential nature of assembly
and because geometric interference will prevent true simul-
98
taneous operation of the assemblers.
However, an advantage of the overlap arrangement is that
it allows the execution of two-handed assembly tasks. Typi-
cally, parts that require two-handed assembly are not stable
in their final assembled position until succeeding parts or
fasteners are added. For example, a bolt will not hang un-
held upside-down in a hole waiting for a nut to be attached.
The unstable part must be held in position with one assembler
while the other adds the next part or fastener. Serial and
parallel modes are generally restricted to single-handed
operation.
An assembly system may be constructed according to one.
of the principal configuration modes or a combination of them.
Each mode has its own advantages and disadvantages. These
were outlined generally above, but which of these are most
important in the design of a particular assembly system will
depend on the individual constraints of the application.
These are discussed more completely in the next section.
5.2.3 Combinations of the Modes
An entire system need not be completely of the serial,
parallel, or overlap type. Combinations of these modes may
be used throughout the assembly system. The mode actually
used at any particular point in the system will depend on
special considerations peculiar to the part, the product,
99
and the production volume.
The system configuration may be designed to take advan-
tage of part subsets. As noted in Section 5.1.2, product
parts are often oriented in a few specific directions, and
this is one example of how the parts of a product may be
grouped into natural subsets. Another natural subset may
occur when several of the parts are identica], such as fas-
teners.
It may prove to be convenient to have an entire subset
of parts assembled by the same assembler. However, 'f the
subset is a large fraction of the total number of p ts, it
may prove most efficient in terms of the balance of the sys-
tem to have parallel assemblers handling the large subsets
and single assemblers handling the subsets with fewer parts.
Such a system would be parallel at some points and serial at
others.
If some of the tasks are two-handed -- requiring two
assemblers simultaneously -- then certain portions of the
system may be configured in the overlap mode and the two-
handed tasks assigned there. The potential configurations
of even a few assemblers are many.
5.3 System Efficiencies
A designer who wishes to build a programmable assembly
system wishes to reduce the cost of assembly per unit as
100
much as possible. Therefore, he will want to build as in-
expensive a system as he can, which means using a minimum
number of programmable assemblers. However, he must also
fulfill the production requirements of the product to be wX
assembled, and the fewer the programmable assemblers in a
system, the lower the maximum production rate of that system.
This is because each assembler must assemble more parts on
the average so that the average time between completed as-
semblies is longer. Since the available production time is
limited (for a given number of working shifts and working
days per year), the total annual production volume of a given
system configuration is also limited. The fewer the stations
in the system, the longer the average product assembly time,
and the lower the maximum production volume.
In order to estimate the cost of programmable assembly,
it is important to be able to estimate the number of program-
mable assemblers required in a system that is designed for a
given product. The net station efficiency of a system, which
will be defined in this section, can be used to determine the
number of assemblers required by the system and, therefore,
to determine the capital equipment cost of that system. The
net station efficiency is found by using the configuration
efficiency and the utilization efficiency of the system.
These terms will be defined precisely in this section, but,
briefly, the configuration efficiency of the system is a
measure of how well the system is balanced. It is low if
101
an assembler spends a lot of time waiting for other assem-
blers or if assemblers are performing nonassembly tasks. The
utilization efficiency is a measure of the use of the system.
It compares the actual production volume with the potential
production volume of the system.
First, the concept of assembly station capacity, which
is necessary in the definition of configuration efficiency,
is discussed. Then, the configuration, utilization, and net
system efficiencies are defined; and the expression for find-
ing the number of assemblers needed is developed. Finally,
an example is presented showing the calculations of the ef-
ficiencies.
5.3.1 Assembly Station Capacity
Assembly time is the time spent grasping parts and moving
them to the assembly site, time spent retrieving and storing
tools, and time spent during assembly fine motion.
The discussion in the previous section concerning assem-
bly system configurations showed that some of the time of an
assembler may be nonassembly time -- time spent waiting for
another assembler to complete an assembly task. There is a
second way for an assembler to have nonassembly time; when -
an assembler is assigned a nonassembly task, such as trans-
porting a part from one point to another point without as-
sembling the part, the time spent is nonassembly time because
102
it was not spent on an assembly task.
The capacity of an assembler, CAP, is defined as the
number of parts that it can assemble during a period of time
equal to the yearly operating time of the assembly system in
which it will be installed. The assembler capacity is com-
puted assuming that it is operating by itself before it is
installed in the system and does not have to wait idlely on
any other equipment (as it may have to do when it is in-
stalled). Hence, the assembler capacity represents what the
assembler could do if it were not limited in any way by the
configuration or line balance of the system.
The amount of yearly operating time for the assembly
system will depend on the number of shifts worked, the num-
ber of working days in the year and the amount of downtime
for the system. Therefore, the capacity of assembly sta-
tion i, CAP., is the number of part assembly tasks that sta-
tion i could accomplish in one year in the allowed working
time assuming that the working time of station i consists
entirely of assembly time (no nonassembly tasks and no wait-
ing). The sum of the assembly station capacities is Y CAP.
i I
The capacity of a single station i can be expressed in
terms of working seconds in the year (the yearly operating
time of the system in seconds) and the single part assembly
time of the ith station as
103
CAP. NSPY (5.1)1 PARTTIME.
where CAP. = number of parts that can be assembled
annually by the ith station
NSPY = number of working seconds per year
(yearly operating time of the systea
in seconds)
.th
PARTTIME . = single part assembly time for 1
assembler as defined in section 5.2
(A list of variable definitions is contained in Appendix 1.)
NSPY can be expressed analytically as follows:
NSPY = UT*DY*HD*3600 (5.2)
where UT = uptime fraction
DY = number of days worked per year
HD = number of hours worked per day
The uptime fraction is simply one minus the downtime fraction;
it is the fraction of the time that the system should be pro-
ducing that it actually is producing. If the uptime fraction
is .8, there are 250 days worked per year, and 16 hours worked
per day (2 shifts), then the value of NSPY is 1.152 x 107
sec/yr.
5.3.2 Configuration Efficiency
The configuration efficiency is defined as the potential
number of parts that the system could assemble per year di-
104
vided by the sum of the assembly station capacities.
NPART * MAXVOL (5.3)
CEF = ,CAP.
where CAP = configuration efficiency
NPART = number of parts in the product
MAXVOL = potential production volume of the
system (number of product units per year)
The potential production volume of the system is the
number of product units that can be assembled during the
yearly operating time of the assembly system. It is usually
determined by a particular pacing station or sequence of
such stations because the other stations must spend some
time waiting on the pacing station to complete its tasks.
The configuration efficiency is a measure of the amount
of nonassembly time that the assemblers are forced to spend
as a result of the assembly system configuration. This will
be illustrated by example in section 5.3.4.
For the special case in which the single part assembly
time for all the assemblers in the system is the same, the
configuration efficiency can be shown to be equal to the
total time the assemblers are actually performing assembly
operations during one index period divided by the total assem-
bler time available in that index period as follows:
The capacity of a single station is:
NSPY (5.4)
CAP.= PARTTIIME
105
Now, the sum of the assembly station capacities can be
expressed as follows:
ECAP =NSTA * NSPY (5.5)
i1 PARTTIME
where NSTA = number of programmable stations in the
system.
The index time for one product unit in terms of the num-
ber of working seconds per year and the maximum production
volume that the system can achieve during those working
seconds is
INDEXTIME = NSPY (5.6)MAX VOL
where INDEXTIME = average time between completed
product units (in seconds)
Notice that the assumption is made here that the index
time corresponds to the maximum production. rate. It is
assumed that the system will operate at its maximum pro-
duction rate even when less than the maximum production
volume is required. Then, to achieve reduced production
volume, the system will be operated for a reduced amount
of time during the year.
Equations 5.3, 5.5, and 5.6 can be combined together
to form an alternate expression for the configuration
efficiency for the case of equal single part assembly
times.
=-NPART * PARTTIME
CEF =NSTA * INDEXTIME (5.7)
106
Notice that the numerator of the expressian--in.
equation 5.7 is equal to the number of station-seconds
that must be devoted to the actual assembly motions for
a single product unit, whereas the denominator is equal to
the number of station-seconds tied up in the index period
during which one product unit is made. Hence, the config-
uration efficiency represents that fraction of the index
period that is actually spent in assembly task execution.
5.3.3 Utilization Efficiency
The utilization efficiency of an assembly system is
defined as the ratio of the actual annual production volume
divided by the potential annual production volume.
PUEF = VOL (5.8)
MAXVOL
where PUEF = utilization efficiency of the programmable
system
VOL = actual production volume of the product.
Essentially, the utilization efficiency is the fraction of
the capability of the system that is actually being used.
5.3.4 Net Station Efficiency
Finally, the net station efficiency is defined as
follows:
where 
NSEF = 
NPAR'l' *
�CAP. 
i l. 
107 
VOL 
(5.9) 
NSEF = net station efficiency of the system. 
It can be seen by comparing equation 5.9 to equations 
5.3 and 5.B that the net station efficiency is also equal 
to the product of the utilization efficiency and the con­
figuration efficiency. 
NSEF = PUEF * CEF (5.10) 
The net station efficiency includes not only the effects of 
the imbalance b8tween the stations but also the degree of 
use of the system: How closely does the potential produc­
tion volume of the system match the production voJ.ume re­
quirements of the product? In the special case of identi­
cal assemblers used in a system, the net station efficiency 
is the ratio of the number of stations needed under "ideal 
conditions" to the number of stations actually used. Ideal 
conditions consist of perfect configuration balance (config­
uration efficiency = 1.0) and equality between the potential 
production volume and the production volume requirements 
(utilization efficiency = 1.0). 
For any particular assembly system design, the net sta­
tion efficiency cannot be specified or estimated in advance. 
The system must first be designed and then the net station 
efficiency calculated. However, in later modeling it will 
be necessary to be able to estimate the number of stations 
required in a typical system for a product with a specified 
108
production volume. In this case a net station efficiency
must be estimated that is representative of the range of
net station efficiencies that would occur in the actual
systems designed for products with that production volume.
Combining equations 5.5 and 5.9 gives
NSTA = VOL*NPART*PARTTIME (5.11)
NSPY*NSEF
This equation can be rewritten in terms of the configuration
efficiency and the utilization efficiency.
NSTA = VOL*NPART*PARTTIME (5.12)
NSPY*PUEF*CEF
Thus the number of assembly stations needed in an assembly
system can be estimated from the production volume of the
product, the number of parts in the product, the single
part assembly time, and estimates of the configuration and
utilization efficiencies.
5.3.5 Example Calculation of System Efficiencies
To show how configuration, utilization, and net
station efficiencies would be calculated for a simple
system, consider the pair of assemblers illustrated in
Figure 5.5. They are to be used in a system to manufac-
ture a product with a total of eight parts. This product
has two principal directions of assembly with five of the
parts assembled in one direction and threa assembled in the
I109
figure 5.5
let can*#
Example Configuration Efficiency Calculation
Station 1
5 Parts
EaJ
Station 2
3 Parts
C1[
Station I
Tim Part I
2
31
5
Station 2
8a
1wait
Assembly
Interval
0 5 Units
Configuration Efficiency - 0.8
2nd
Station I
1 Parts
C:0
Station 2
4 Parts
s Sf
nia
Station I
Time Part
2
3
'Im
Station 2
Turn
verj
7
81
17
AsaenblInterral
m 4 Units
Configuration Efficiency 1.0
r -
110
other. The assemblers both have a single part assembly
time equal to PARTTIME.
Assume- that each assembler is aligned with a princi-
pal direction of assembly. The first assembler will have
five parts to assemble and the second will have three.
Since the first assembler will pace the system, its rate
will determine the system rate and capacity.
MAXVOL - NSPYMAXVOL =5 *NPARTTIME
Here it is assumed that the first assembler spends all of
its time in assembly motions--there are no nonassembly mo-
tions and no waiting time.
The sum of assembly station capacities for the pair
of assemblers is just twice their individual capacity.
2CAP.. =2 * NSPY
, =PARTTIME 
-
The configuration efficiency is, according to equation 5.3,
CEF = 8 * NSPY * PARTTIME _
5 PARTTIME 2 * NSPY
The utilization efficiency depends on the actual
volume demanded in the market. If the actual volume VOL
produced were 750.,000 but the potential production volume
MAXVOL were 1,000,000, then the utilization efficiency
PUEF would be .75
111
The, net station efficiency of this arrangement is,
according to equation 5.10, the product of the configura-
tion and utilization efficiences.
NSEF = .8 * .75 = .6
To continue the example, we now attempt to improve the
configuration efficiency of the system by adding a device
to the second assembler station to rotate the work pallet
so that both principal directions are accessible from the
second assembler. (It is assumed that the rotation is
accomplished while the assemblers are reaching for tools
or parts.) Now, four parts can be assembled at each assem-
bler. Since each assembler is being used constantly for
assembly tasks only in this new arrangement, the configura-
tion efficiency is now equal to one. Both stations are
now equal and limiting, and the potential production vol-
ume of the system has been increased.
MAXVOL - NSPY
4 * PARTTIME
This represents a 25 percent increase in the potential
production volume of the system; that is, from 1,000,000
to 1,250,000. If the actual production volume of the
112 
system does not change, there is a reduction in the 
utilization efficiency of the system. 
PUEF = 750,000 = • 6
1,250,000 
The net station efficiency of this arrangement is 
NSEF = 1. * .6 = .6 
This example illustrates that improving the balance 
of the system (i.e., the configuration efficiency) will 
not improve the overall net station efficiency if there 
is no reduction in the nwnber of assemblers. The second 
configuration of the example was a much better balanced 
system, and because of its higher production rate, it will 
be able to satisfy the annual production requirements in 
less operation time. This means that other expenses asso­
ciated with the length of its annual operation time (such 
as labor and maintenance) will be less. However, since 
the cost of the assembly system is the same as in the first 
configuration, that portion of the unit cost of assembly 
attributable to the capital investment in the system remains 
the same. (In fact, the capital investment cost will go up 
due to the cost of the reorientation device at the second 
station.) 
Another alternative is available if there is another 
assembler on the market with longer assembly time and lower 
price. If a system constructed with a lower cost-longer 
time assembler and a rotation device can meet the production 
• 
� .-
I 
113
requirements, then the balancing of the system does lead
to reduced unit assembly cost.
5.4 Summary
This chapter presented the characteristics of pro-
grammable assembly which are necessary as a basis for the
modeling done in Chapter 6.
The configuration of a programmable assembler refers
to the degrees of freedom of the motion device and the way
in which they are implemented. In general, six degrees of
freedom are required to position a part in an arbitrary
location. However, due to the existence of principal as-
sembly axes on a large number of products this number may
be considerably reduced for part assembly on any particular
product. In addition, the assembler motion device may ac-
tually consist of two motion devices: one to position the
product unit and one to assemble the part onto that product
unit. The total number of degrees of freedom required may
be split between the devices so that each motion device is
less complex than if all the degrees of freedom were con-
tained in one device.
The configuration of a programmable assembly system
refers to the arrangement of the assemblers and feeding
equipment in the system and also the organization of the
assembly sequence. The three principal arrangements
114
(configuration modes) for assemblers in an assembly system
are serial, parallel, and overlap.
There are advantages and disadvantages to each mode
depending on the specific circumstances involved. One
assembly system may use any combination of the modes.
When the designer plans an assembly system, he would
like to minimize the cost while still accomplishing the
targeted production volume. He therefore needs an estimate
of the minimum number of assemblers required to do that.
One way to find this is through a priori estimation of the
system efficiencies--configuration efficiency and utiliza-
tion efficiency. The configuration efficiency is a measure
of how well the system is balanced; utilization efficiency
is a measure of how well the system is matched to the re-
quired production volume. Their product is the net station
efficiency. By making estimates of these efficiencies, the
designer of a system can combine them with other factors he
knows--the number of parts in the product, the single part
assembly time, and the production volume--to obtain an es-
timate of the number of assembly stations he will need,
and, consequently, the number of parts assembled at each
station. This serves as a starting point in the system,
design process. The designer can then begin to design a
system with approximately that number of assemblers in the
combination of configuration modes which best fits the
particular product assembly sequence.
115
6. SIMPLE ECONOMIC MODELS OF ALTERNATE ASSEMBLY METHODS
In this chapter simple economic models of alternate
assembly methods are developed. The purpose of these
models is to gain an understanding of the programmable
assembler characteristics that play a major role in the
economics so that more effective assemblers can be de-
signed. It is also a goal of this modeling to determine
some criteria for indicating the circumstances in which
programmable assembly is most applicable.
In the first section of this chapter very simple
models of the major alternate assembly methods-- manual,
transfer, and programmable--will be developed. While
these models are much too simple to provide an accurate
estimate of the cost of assembly in any specific situation,
the form of the equations does provide some insight into
the circumstances under which each of the alternate methods
is best used and also suggests a criterion for the design
of individual programmable assembler stations. It is im-
portant to note that it is the cost to the user of the
programmable system that is being modeled.
In the second section two hybrid combinations of the
major methods a e considered. In one the assembly opera-
tions are divided between manual stations and transfer
stations and in the other between programmable stations
and transfer stations. Again, the form of the equations
116
leads to some understanding of the circumstances under which
the hybrid systems are most applicable.
Finally, in the third section, the simple models pre-
viously developed are improved somewhat in their accuracy
at the cost of increased complexity of the equations.
Labor costs are added to the models of transfer machine
and programmable system assembly, and equipment costs are
added to the model for manual assembly. An example is
used to compare these rrore complex equations to the equa-
tions of the simple model to see if there are any signifi-
cant differences. Certain differences will appear, but the
basic results will still hold.
6.1 Simple Alternate Economic Models
6.1.1 Modeling Manual Assembly Costs
The manual assembly cost per unit will be modeled
as follows:
MCPU = MATP * LABCST * NPART (6.1)
where MCPU = manual assembly cost per unit, $/unit
MATP = manual assembly time per part, sec
LABCST = cost rate of labor, $/sec
The concept is that the manual assembly time, and therefore
cost per unit, is proportional to the number of parts.
Furthermore, the manual assembly cost per unit is indepen-
dent of the annual volume. To increase his production vol-
ume, the manufacturer pays for more worker time. The manual
assembly time per part MATP refers to the average time be-
117
tween the start of the assembly of one part to the start
of the assembly of the next. Hence, the manual assembly
time per part includes any slack time between part assem--
blies.
6.1.2 Modeling Transfer Machine Assembly Costs
The system cost for the transfer machine configura-
tion is modeled as proportional to the number of parts it
assembles; that is
TSCST = NPART * TMCPP (6.2)
where TSCST = system cost for transfer machine
TMCPP = transfer machine cost per part
This is reasonable because transfer machines are organized
so that a given portion- of the equipment is dedicated to
the assembly of one part only. The transfer machine cost
per part, TMCPP, is dependent on the size of the part and
the type of machine, as was discussed in Chapter 2.
We now must translate the original investment cost of
the transfer machine into a unit assembly cost. This
means that somehow the cost of the machine must be allocated
to the units that it produces. We will use an allocation
model that can be related to the discounted cash flow (DCF),
or return on investment (ROI), method of evaluating capital
investments. For descriptions of this and other capital in-
vestment-evaluation methods see Swalm (20) and Van Horne (21).
118
We will not derive the DCF method here. Only the
important points of the method as they pertain to this
modeling will be discussed.
The discounted cash flow method is used to compute a
return on investment (ROI) for a specific project involving
capital investment. It requires that a projection be made
of the cash payments and receipts (the "cash flows") of
a project over the life of the project. The ROI iLself is
the "interest rate" that these cash flows appear to have
over the life of the project.
Every firm has a required minimum return on investment
for its projects. This minimum return on investment is
partially set by company policy and partially set by the
ease with which the company can borrow money to finance its
projects. When a firr has a selection of potential projects
from which to choose, only those projects with ROI's above
the minimum return on investment will be :onsidered.
The DCF method is most commonly used to examine re-
placement projects. For example, if a firm were consider-
ing replacing a manual assembly li.e with a transfer as-
sembly machine, then the cash flow projection upon which
the ROI would be calculated would represent the differences
of the absolute cash flows of the manual and transfer ma-
chine alternatives over the life of the transfer machine.
The ROI calculation then depends as much on the absolute
cash flows of the manual assembly method as on the
cash flows of the transfer machine method. Hence, the
119 L
same new assembly method when used to replace different
old methods will result in different ROI's.
The use of the ROI does not result in measurement of
either the new assembly method or the old assembly method
themselves; the value of the ROI only describes the com-
parison of the two. The evaluation method used in this
thesis is first to compute an assembly cost per unit
product for each method of assembly and then to compare
these costs. The unit assembly cost for one assembly
method is not functionally related to the unit assembly
cost of another method. This approach simplifies the com-
parison between alternate assembly methods, especially
when more than two alternate methods are involved,
For assembly methods involving capital investment, the
cost of assembly per unit product will be based on the min-
imum required return on investment of the firm. When the unit
assembly cost is defined in this way then the requirement
that a replacement project ROI be above the minimum ROI
is the same as the requirement that the unit assembly cost
of the replacement method be less than the unit assembly
cost of the old method.
For example, consider the replacement problem in which
a firm is contemplating replacing a manual assembly line
with a transfer assembly machine. If the manual unit as-
sembly cost is equal to the transfer machine unit assembly
cost calculated using the minimum rate of return, then this
120
is the same as saying that the ROI of the replacement
project is equal to the minimum rate of return. The firm
would be indifferent to the two assembly methods. But, if
the transfer machine assembly cost per unit so defined is
less than the manual unit assembly cost, then the replace-
ment ROI is actually greater than the minimum rate of re-
turn. Then, the firm will prefer the transfer machine
method.
We now seek to derive a unit assembly cost for the
transfer machine based on the minimum return on investment
of the firm. We will use the "after tax rate of return"
approximation to the ROI.
CAT
R =CA (6.3)
where R = after tax rate of return
CAT = net annual cash flow after taxes
I = initial investment
This approximation to the ROI is a commonly used one. For
all but the simplest problems, there is no simple expiession
for the ROI. In almost all practical cases, the value of
the ROI is difficult to calculate, and usually a computer
is used to obtain a solution. It is important to this ana-
lysis that a simple expression for ROI (even though only ap-
proximate) be used, and the after tax rate of return suits
this purpose. See Appendix 2 for an example illustrating
the accuracy of the approximation.
(
121
We now assign a unit assembly cost for each unit of
product made and will derive an expression for this cost.
The cash flow after taxes will be modeled as
CAT = TCPU * VOL - TAX (6.4)
where TCPU = unit assembly cost for the transfer
assembly machine
VOL = actual annual production volume
TAX = taxes on income allocated to the transfer
machine
The first term above, TCPU*VOL, represents the gross an-
nual "wages" of the assembly machine; that is, the cost it
must charge for each unit times the total annual production
volume.
The taxes, TAX, are computed on the annual income after
a depreciation deduction is subtracted. If a straight line
depreciation method is assumed, then we may model the tax as
TAX = T*(TCPU*VOL-DPTM*TSCST) (6.5)
where T = tax rate
DPTM = annual depreciation rate for
the transfer machine
TSCST = original investment cost of the transfer
machine.
Substituting equation (6.5) into equation (6.4) gives
CAT = (1-T)*TCPU*VOL+T*DPTM*TSCST (6.6)
Now, by analogy with equation (6.3) using the minimum rate
122
of return R, we have
R = (1-T)*TCPU*VOL + T*DPTM*TSCST (6.7)
TSCST
Solving for TCPU gives
TCPU = TSCST*(RT*DPTM) (6.8)TCTVOL*(l-T)
Finally, substituting for the value of the transfer machine
from equation (6.2) gives
TCPU = TMCPP*NPART*(RTDPTM) (6.9)VOL* (l-T)
6.1.3 Modeling Programmable Assembly Costs
A programmable assembly system will be assumed to con-
sist of two types of component equipment: programmable
assembly stations and their associated equipment; and parts
feeding tooling and its associated equipment. Because they
are programmable, the assembler stations can be used for
many different kinds of parts. Any given set of parts
feeding equipment usually is specially made for a specific
product; then, within cartain limits, the design of the
feeding equipment is relatively unaffected by the number
and configuration of the programmable stations. If ten
parts must be assembled, then ten sets of parts feeding
equipment are required, one for each part, regardless of
the number of assemblers in th system. However, the num-
ber of assembler stations used in the programmable system
may vary depending on the number of parts assembled at each
123
station.
There may be cases where several identical program-
mable assembly systems might be used for the assembly of
one product. The economics of such duplicate systems are
not considered explicitly in this modeling. A simple method
of extending the modeling derived here to duplicate systems
will be discussed later.
Figure 6.1 illustrates how the configuration of pro-
grammable assembly systems may vary. A system for assem-
bling ten parts into a product will need to have ten sets
of parts feeding or presentation equipment, each set
specific to a particular part, no matter what the assembler
configuration. However, the system will have ten stations
if one part is assembled at each station, five if two parts
are assembled at each station, or two stations if five parts
are assembled at each station.
We may model the total cost of a system as follows:
PSCST = NSTA * STAP + NPART * TOLPP (6.10)
where PSCST = programmable system cost
NSTA = number of assembly stations
STAP = single station price
TOLPP = price of parts feeding tooling per part.
The important simplifying assumptions behind this model
are that all the programmable assembly stations are assumed
to have equal cost. Also, the sets of parts tooling and
presentation equipment are assumed to have equal cost.
124
Figure 6.is Simple Variation of System Configuration
for Assembly of One Product
10 Assemblers
n 0 0 000 0 0 0 0d dd d dd d d did
5 Assemblers
D D 0D 0 0b
cb dbdb dco
Interval
between
completed
products
a PARTTIME
Interval
between
completed
product.
- 2 i PARTTIME
2 Assemblers
Q /P QZO9
c56
Interval
be tween
completed
products
a5 x PARTTINE
Assumes a
Product has 10 parts
All assemblers are identical
Single part assembly time, PARTTINE. is the same
for all parts and all assemblers
Each assembler assembles the same number of parts
O |
E'D
125
Clearly, in a realistic system this is not the case, but if
average numbers are used for the price of a station and for
a set of parts feeding tooling, then an average estimate of
the cost of the programmable system will result,
The station price per part includes all the costs to
the user of the programmable system associated with the par-
ticular station. This includes the cost of the program-
mable assembler itself, all dedicated processors and sen-
sors, and an appropriate portion of the conveying device
or index table between stations associated with that sta-
tion. The station price also includes the engineering cost
of integrating that station into the system.
The parts feeding tooling price per part includes the
cost of the basic feeding mechanisms--bowl, bowl feeders,
hoppers, magazines, or eggorate table--feed tracks or qhutes,
and placement or escapement devices that bring the parts LO
the assembly stations or the conveying mechanism that links
them together. The parts feeding tooling considered here
may range from relatively sophisticated bowl feeders to a
simple table where parts in eggcrates are placed within
reach of the assembler. The assembler controller can be
given the information describing the eggcrate pattern so
that the assembler can pick parts directly from the egg-
crate. One possible feeding method would involve the parts
presentation equipment "handing off" the part to the assem-
bler directly. Another method might involve placing the
126
oriented part in some sort of pallet from which the sta-
tion assembler picks the part. For a special pallet system
the pallets should be considered part of the tooling cost
but the pallet conveying or index system should be part of
the station costs.
By analogy to the method of allocating the capital
investment of the transfer machine to the unit assembly
cost, equation (6.9), the programmable assembly cost per
unit will be modeled as follows:
PCPU = NSTA*STAP* (R-T*DPPA)+NPART*TOLPP* (R-T*DPTL)
VOL*(l-T) (6.11)
where PCPU = programmable system cost per unit
DPPA = annual straight line depreciation rate
for the programmable assembler stations
DPTL = annual straight line depreciation rate for
the parts feeding tooling
T = tax rate.
Here we have assumed separate straight line depreciation
rates for the parts feeding tooling and the reusable pro-
grammable assemblers.
We now address the problem of specifying the number of
assembler stations for the programmable system. We wish to
design the minimum cost system that meets the production
requirements. Therefore, it is important to use the minimum
number of assemblers. (Since we are working under the as-
sumption of a single programmable system to satisfy the
127
entire production requirements, then we are already
using a minimum number of sets of parts feeding equipment.)
In Chapter 5, equation (5.121.was derived to estimate
the number of stations required in a system based on the
capacity of the stations; that is,
NSTA = VOL*NPART*PARTTIME (5.12)NSPY*CEF*PUEF
where CEF = configuration efficiency
PUEF = programmable utilization efficiency
Now, equation (5.12) is substituted into equation (6.11)
for the programmable unit assembly cost to obtain
-=NPART FSTAP*PARTTIME* (R-T*DPPA)(1-T) *1 NSPY*CEF*PUEF
+TOLPP*(R-T*DPTL)
VOL (6.12)
In this equation the number of stations is no longer
fixed but is free to adjust to different volume require-
ments or assembler capacities. It allows one to estimate
the programmable unit assembly cost from a knowledge of
the production volume and number of parts in a product,
the assembler part assembly time, and assumed values for
the configuration and utilization efficiencies. It assumes
that a single system is constructed to produce the entire
production volume of the product.
6.1.4 A Comparative Example
The simple models of the manual, transfer, and pro-
128
grammable methods show that the unit assembly cost for
each of these methods is proportional to the number of
parts in the product. This means that the number of parts
does not effect the relative cost of assembly per unit be-
tween the three methods. The important product variable
is the volume.
An example plot of cost of assembly per unit against
annual volume is shown in Figure 6.2. For the purposes
of illustration the following values of the parameters
have been assumed.
NPART = 10 parts
STAP = $30,000
PARTTIME = 3 sec
R = .25
DPPA = .125 (8 year life) U
TOLPP = $7500
DPTL = .25 (4 year life)
TMCPP = $30,000
DPTM = .1 (10 year life)
MATP = 7 sec
LABCST = .0020833 $/sec (= $7.50 $/hr)
NSPY = 1.152 x 10 sec/year
CEF = .8
PUEF = .95
The above are simply round figures that are meant to
be plausible, not definitive. Better data could be obtained
129
Figure 6.2. Comparison of Assembly Costs as a Function
of Annual Volume
Assumes hypothetical product with 10 parts
1 111111 I
Transfer Machine
Programmable
Savings Region
I 1 Manual -
1.0
.1
C
:5
'r4
c
uit
I m I I a I I nII
mmmlm I I 4 --1 I I i . I I I 10 . - 5 - - a L -- _
0.2 0.5 1.0
I I I I I I N
2.0 5.0 10.0
Annual Production Volume (millions)
rma trd-srf-e. r " 1 11' Fri Z; [Ir
'11 .A ro "J
lot g. Cbo Ape-,, -It's - J. J,- 0
15 2, 4 4 ) le, . F4L @ e13,b
c oc a ca
NMI
ds
amw
ra
MEW
Progr bl"s 
AI
0.01
owI
or EF w v w m w -
Arl
130
for more specific examples. However, for more accurate
answers a very detailed cost model is required. The
figures are meant to represent plausible values for an
assembly system assembling products limited to 8 inches
in size. The station price of $30,000 and part assembly
time of 3 seconds are rough figures meant to represent-a
small assembler (about one foot reach and lift) with dedi-
cated processor and mounted on a conveyor section. The
station price must include the engineering cost of incor-
porating the station into the system. The transfer machine
price per part of $30,000 is a round figure representative
of transfer machine assembly systems for this product size
range. The parts feeding tooling price per part of $7500
for the programmable system represents a rough estimate
based on the price of feeding tooling equipment for the
corresponding transfer machine ($2600 to $5500) plus an
additional engineering expense for integrating the tooling
to the system.
The configuration efficiency has been set at .8
Kondoleon (19) has found by a series of simple paper studies
on assembly system layouts for real products that configur-
ation efficiencies ranged from about .7 to .9 for a simple
layout procedure he developed. An estimate of CEF equal to
.8 represents an average value. An estimate of programmable
utilization efficiency PUEF of .95 represents a management
rhw
131
decision to have only a small amount of excess capacity
in order to bring down the system cost.
The required rate of return of 25 percent after taxes
is a common value. Depreciation rates of .1 per year
(10 year life) for the transfer machine, .125 per year (8
year life) for the programmable assemblers, and .25 per
year (4 year life) for the programmable system parts feed-
ing tooling were assigned. The labor cost rate of $7.50
per hour is also representative of a range of labor cost
rates currently running from $5 to $10 per hour ($10,000
to $20,000 per year). The assumption of a manual assembly
time of 7 seconds per part is a result of observation of
certain manual assembly lines where operators assembled
roughly two parts in a fifteen second station period.
Manual assembly time per part varies considerably in prac-
tice. Often the actual operation time for the assembly does
not completely fill the station time allowed so that there
is some built-in idle time. Nevertheless, the idle time
must be included in this model.
The number of working seconds per year NSPY represents
two shift operation for 250 days per year with 80 percent
uptime fraction.
In Figure 6.2, the vertical axis represents the assem-
bly cost per unit assuming ten parts in the product. Since
the assembly cost for all three methods is proportional to
the number of parts, the vertical axis can be easily scaled
132
to any other number of parts in the product.
The intersection of the transfer machine line and the
manual line represents the boundary between economic appli-
cation of manual and transfer machine assembly if program-
mable assembly is not considered. In this case it occurs at
about 800,000 units per year. With the addition of program-
mable assembly machines, a range of production volumes that
would have been handled by manual assembly or transfer
machines is now more economically done by programmable sys-
tems. The region of cost swings is shaded and extends from
annual volume of 1.73 * 105 to 2.60 x 106. This range ex-
bends from the boundary between manual and programmable
assembly at the low end and programmable and transfer ma-
chine assembly at the high end.
This range will depend on the relative values of the
costs used in the equations, and as labor rates, capital
costs, and equipment costs change, the range will also
change. Also, even if accurate average values of the
costs were used in the equations, the resulting unit as-
sembly costs are still only average costs. The true unit
costs for all three methods would actually form a distri-
bution about the mean lines shown in Figure 6.2, Hence,,
there will be cases in the manual or transfer ranges where
programmable assembly is most economic and
vice versa. These cases will represent deviations
from the average and will therefore be less frequent.
133
The shape of the programmable unit assembly cost curve
approaches a horizontal asymptote at very high volume and
a minus 450 asymptote at very low volume. This is be-
cause the number of programmable stations will vary along
the curve according to the volume requirements. Hence, at
low volume, few stations are needed and most of the price
of the system is in the fixed cost of the parts feeding
tooling equipment. This dominance of the fixed costs makes
the cost curve parallel to that of the fixed cost transfer
machine. At higher volumes most of the cost is in the pro-
grammable assemblers because more of them are needed to meet
the production requirements. Their total cost is propor-
tional to the volume and so the unit assembly cost approach-
es a constant.
Figure 6.3 shows what happens to the unit cost curve
if +he number of stations is forced to be an integer as of
course it must be in practice. Essentially the number of
stations used in the system is taken to be the next integral
number above the value given by equation 5.12. This does
not model all of the quantization problems. For example,
this model would still assume that the number of parts assem-
bled per station could be non-integral. For example, if
10 parts were assembled by 7 stations then this model assumes
that 1 3/7 parts are assembled at each station. Rather than
attempt to deal with all the quantization effects explicit-
ly, we will describe them with the use of configuration
134
Figure 6.3s Comparison of Assembly Costs as a Function
of Annual Volume with Integral Station
Number
Assumes hypothetical product with 10 parts
1 1 P 11111 1 1 1 1 -D I 1m
Transfer Machine
Ma
Prograwtable
Number of Programmable Stations
2 4 6?8 10
10,9876 5 4 3 2 1
Numbir of Parts per Station
~1 0.2 0.5 1.0 2*0
Annual Production Volume (millions)
5.0
%1w
10.0
nual
1.o
0.1
W.4
C
C
0.011
0.
- ow - -
I I I I F-I
-pr
135
efficiencies less than one. Figure 6.3 shows graphical-
ly that the number of programmable stations will vary
with the production volume and that for the values of the
example data the station quantization effect does not
drastically alter the unit cost curve.
There is a way in which there may be more assemblers
than number of parts; that is, for the number of parts per
station to be less than one. This is the case where
parallel assemblers are used to assemble the same part.
For example, if there were a product with ten parts,
then such a system would be one which had two assemblers
for each part sharing the parts feeding equipment for
that part. Such a system would have twenty assemblers
and ten sets of parts feeding equipment and would have
twice the production rate of the system with one assem-
bler per part. For the example shown in Figure 6.3,
such a system could not compete with a transfer assemb-
ler machine. However, later in this chapter in the dis-
cussion of hybrid programmable-transfer systems, it will
be shown that parallel assemblers for single products
may be a part of competitive system designs.
Finally, it has been implicitly assumed that the
product has a fairly stable production volume require-
ment. This is a realistic assumption for some products
but not for others. The question of the life cycle of
136
a product is an important one. Often a product begins
with low volume and manual assembly. If the ultimate
production volume. of a product is expected to rise to the
transfer machine range, then it must be decided whether
it is wise to build a programmatle system when the volume
is in the programmable range and climbing.
The answer should depend on the rate of climb. If
the production volume is increasing rapidly, then the
period of time in the programmable volume range may not
be long enough to pay for the feeding equipment and the
depreciation on the assemblers. If the climb is slow,
then it makes sense to build the programmable system
when the volume is sufficient and in several years sal-
vage it and build a transfer system. However, if the
anticipated ultimate volume of the product is not high
enough to be in the transfer range but is in the program-
mable range instead, then the programmable system can be
built with greater confidence when the volume require-
ments are met.
6.1.5 Product Volume Analysis
It is possible to solve for the annual volumes rep-
resenting the boundaries between the regions economical-
ly dominated by manual, programmable, and transfer machine
assembly. For the programmable-transfer boundary we have
137
= (TMCPP* (R-T*DPTM) -TOLPP* (R-T*DPTL) ) *NSPY*CEF*PUEF
OLPT =STAP*PARTTIMF* (R-TDPPA) (6.1.3)
where VOLPT volume boundary between economic pro-
grammaile and transfer machine systems.
For the programmable-manual boundary it is
= LPM TOLPP* (R-T*DPTL)
VOLPM MATP*LABCST* (l-T) - STAP*PARTTIME* (R-T*DPPA)
NSPY*CEF*PUEF (6.14)
where VOLPM = volume boundary between economic manual
and programmable systems.
Finally, for the manual-transfer boundary, it is
TMCPP* (R-T*DPTM)
VOLMT = MATP*LABCST*(l-T) (6.15)
where VOLMT = volume boundary between economic manual
and transfer machine systems.
These volumes VOLPT and VOLPM will be called the system
volume boundaries because they refer to the limits of the
volume range in which a programmable system is economic.
Notice that the system volume boundaries are not a function
of the number of stations in a system (although the number
of stations is a function of the volume) but are a function
of the product of the individual station price and the
single part assembly time of the stations that make up the
system.
consequently, these volume boundaries apply to products
with any number of parts. More parts in, the product mean
longer transfer machines, more stations in the programmable
138
systems, and more workers in the manual lines, but the
economic production volume ranges remain the same.
In Figure 6.4 is a plot of system volume boundary
versus station price assuming asseablers with single part
assembly time PARTTIME equal to 3 sec. (The manual assem-
bly time remains at 7 seconds for this example.)- Notice
that the lower programmable-manual volume boundary in-
creases with programmable station price while the upper
programmable-transfer volume boundary decreases unt-l
finally they intersect at a station price of $98,000.
Notice that they intersect at the level of the manual-
transfer boundary.' The three boundary curves divide the
graph into programriable, transfer, and manual regions.
For single programmable station prices higher than
$98,000, any programmable system composed of a set of those
stations will be uneconomic compared to one of the other
two methods. In Figure 6.2 this corresponds to the pro-
grammable assembly cost curve being above the corner
formed by the manual and transfer machine curves. This
condition may be solved for a bound on the product of the
single station price and the single station part assembly
time. This bound is
STAP*PARTTIME [TMCPP*(R-T*DPTM)-TOLPP*(R-T*DPTL)
TMCPP* (R-T*DPTM)
* MATP*LABCST*(l-T)*NSPY*CEF*PUEF
(R-T*DPPA) (6.16)
139 
Figure 6.4, System Volume Boundaries versus Station 
Price for Assembler Part Assembly Time 
of 3 Seconds 
Progr8111111able•Transfer 
Boundary 
I 
I 
I 
I 
I 
I 
I Manual-Transfer 
l Boundary 
I 
Progr1U111able•Manual 
Boundary 
o.11.....��----1�_..JL........L--1.--1....L.J...1..1...���-'-�..L.__JL....J.-.L..JL...L..u 
10 100 1000 
Prograamable Assembly Station Price ($1000'a) 
140
This is a general solution; the assumptions concerning
the values of the parameters have been removed. If this
constraint is not satisfied for an individual assembler,
then assembly systems made from sets of thac assembler
will not be economic compared to manual or transfer
machine methods, on the average. Furthermore, the lower
the station price-time product is below this constraint,
the larger the range of economic applicability.
This is an important result because it relates
properties of an assembler to the economics of systems
composed on that assembler compared to both manual and
transfer machine methods. This single result bridges
the gap between individual assembler design and assembly
systems, it describes the effects of competition with
both manual and transfer machine assembly, and it does this
for products with different numbers of parts. Later in
this thesis STAP*PARTTIME, the "price-time product," will
be used as a measure of assembler design. The inequality
expressed in equation 6.16 forms a bounding criterion for
economically acceptable designs, and the minimization of
the price-time product will be used as an assembler design
objective.
Using the data of the example we find
STAP*PARTTIME < 2.93*10 5 $-sec (6.17)
In other words, if the product of the programmable sta-
141
tion price and the part time were greater than 2.93*105
$-sec, then the programmable system could not com-
pete with a manual line or a transfer machine or maybe
both. If stations cost $125,000 each then they would have
to assemble parts at least at the rate of one every 2.34
sec to be economic compared to manual or transfer machine
assembly or both. (Of course, it should be remembered
that the numbers used here are only plausible example
numbers and, at that, only apply to a product size range
of about eight inches. Actual values in specific situations
will vary.)
In Figure 6.5 is a plot of constant system volume
boundaries for different combinations of individual pro-
grammable station price and part assembly time for the
example. Individual station price is plotted on the ver-
tical axis and single part assembly time is plotted hori-
zontally. Any combination of station price and part assem-
bly time corresponds to a certain point in the plane. Once
the point is plotted, interpolation between the lines of
constant boundary volume will give estimates of the upper
and lower system boundary volumes. The line corresponding
to the constraint on station price - part time product,
equation (6.16), is indicated. Points above this line rep-
resent uneconomic programmable assembly. This constraint
line occurs where the programmable to manual boundary vol-
ume is equal to the programmable - transfer boundary volume.
142
Figure 6.5i Example System Volume Boundary Chart
- - - VOLPM w Programmable-Manual Volume Boundary
VOLPT - Programmable-Transfer Volume
Boundary
n.
ww
50
20
10
5F
1I
11
I
- 1 -L I I I III I iZa
2 5 to 20
I III
50 100
Assembler Single Part Assembly Time (seconds)
\no-044
e\ Upper Bound
for Economic
K \ ProgrammableO-
\Assembly
+-
4 -
- \O-
%PO N
A lp IV n o
0
.4
wI
21
142
To illustrate how to use the chart, notice that a
programmable assembly system constructed of stations
needing 5 sec.per part and costing about $24,000 each
would be economic for a range of production from 200,000
to 2,000,000 per year. Also notice that a system having
stations with 5 sec assembly time costing $100,000 each
is not economic. Remember that this analysis applies to
products with.any number of parts. Figure 6.5 contains
purely economic analysis, assuming all conbinations of
station price and part assembly time are possible. Of
course, there are engineering constraints and relationships
that relate the station price to the part assembly time,
the size of the station and its number of degrees of free-
dom, and so on. There may be lower practical bounds on
the part assembly time. A chart like Figure 6.5 can help
to assess the economic consequences of these technological
relationships.
6.2 Hybrid Alternate Models
In the previous sections we have examined the "pure"
alternate methods of assembly. There are two important
combinations of these methods that have special interest.
In the hybrid programmable-transfer system, some
parts are assembled by programmable technology and others
with transfer technology. This is of interest especially
144
where the transfer assembly technology is almost capable
of handling the assembly economically except for certain
tasks.which require programmability.
Hybrid transfer-manual assembly represents a cur-
rently common method, especially in non-synchronous index-
ing systems. In the design of a transfer-manual system for
a product, the assembly of each part is evaluated with
respect to manual or transfer machine assembly and then
the most economic method is used for that part.
Both of the hybrid approaches will be evaluated from
the viewpoint of the simple model to determine conditions
of economic applicability.
6.2.1 Modeling Hybrid Transfer-Programmable Assembly
There are three distinct sections of the hybrid
transfer-programmable assembly system as modeled here.
1. Programmable assembly stations. Each station may
assemble one or more parts to the product.
2. Transfer machine assembly stations. Each of these
stations assembles one part to the product and is
not programmable.
3. Parts feeding tooling. Each part has a set of
parts feeding tooling associated with it. The
tooling may be connected to a transfer machine
station or a programmable station. A program-
145
mable station will have tooling for as many
parts as it assembles sequentially; a transfer
machine station will have the parts feeding
tooling only for the one part associated with it.
These sections form the major components of the orig-
inal cost of the hybrid system. This cost may be modeled
as follows:
HCST = NSTA*STAP + NPPRT*TOLPP + (NPART-NPPRT)*TMCPP
(6.18)
where HCST = hybrid system cost
NSTA = number of p.ogrammable stations
STAP = programmable station price
NPPRT = number of parts assembled by Programmable
stations
TOLPP = parts feeding tooling price per part
TMCPP = transfer machine cost per part
It will be assumed that the assembly rate will be
governed by the programmable stations. This is because the
programmable station will probably have a longer single part
assembly time than a transfer station. Even a dual program-
mable station--one in which two single stations are operat-
ing in parallel--will probably have a longer effective
single part assembly time than a transfer station. The
transfer station times are quick because the motions are
short and simple and identical. Because the programmable
station will have a more complex mechanism and control
146
function to increase its versatility, it will very like-
ly take longer at any specific task than a transfer machine
station specifically designed for it.
If the programmable stations are allowed to pace
the entire system, then in some sense the transfer stations
are not working at their maximum production rate and the
system is not balanced. However, the simple model for the
unit assembly cost by transfer machine does not take into
account the production rate of the transfer machine except
to assume that it is sufficient to meet annual production
requirements. The unit assembly cost is obtained by direct-
ly charging the cost of the machine to the units actually
produced.
As far as determining the unit assembly cost (due to
the capital investment) is concerned, the actual production
volume is the only volume that matters. To know that cer-
tain stations or even the entire system could operate fast-
er does not change their contribution to the unit assembly
cost.
The unit assembly cost for a hybrid system may be di-
vided into two parts: One part of the cost comes from the
programmable stations and the other part comes from the
transfer machine stations. The hybrid system may be re-
garded as a programmable assembly system interwoven with
a transfer machine system. To compute the total unit
assembly costs we may add the unit assembly cost from
147
both parts.
HTPCPU = HPCPU + HTCPU (6.19)
where HTCPU = hybrid transfer-programmable cost
per unit
HPCPU = unit assembly cost component due to
programmable assembler stations and
associated feeding equipment
HTCPU = unit assembly cost component due to
transfer machine stations.
The unit assembly cost component due to the programmable
stations is
HPCPU = NPPRTSTAP*PARTTIME*(R-T*DPPA) + TOLPP*(R-T*DPTL)(1-T) L-NSPY*CEF*PUEF VOL J(6.20)
where HPCPU = unit assembly cost component due to
programmable assembly subsystem
Here the variables are defined as they were for the purely
programmable system.
The unit assembly cost component due to the transfer
stations is
HTCPU = TMCPP*(NPART-NPPRT) * (RT*DPTM) (6.21)
VOL* (l-T)
where HTCPU = unit assembly cost component due to
transfer machine stations.
Here, it is assumed that the number of parts assembled by
transfer machine stations is equal to the total number of
parts in the product minus the number of those parts assem-
148
bled by programmable stations. The rest of the variables
are defined as they were for the pure transfer machine
assembly system. -However, the hybrid unit assembly cost
can also be related to the unit cost for a pure program-
mable system that assembles all the parts and the unit
cost for a pure transfer machine system that assembles
all the parts by substituting equations (6.20) and (6.21)
into (6.19) and then isolating the pure programmable and
pure transfer system costs.
HCPU = NPPRT*PCPU + 1 - _____ * TCPU 6.22)
Notice that the weighting factors NPPRTand 1 - _____NPART N1 A /
are less than or equal to one and also sum to one.
Equation (6.22) can be reduced somewhat by defining a
programmability ratio; that is
HCPU = PRATIO*PCPU + (1-PRATIO) * TCPU (6.23)
where PRATIO = NPPRT/NPART = programmability ratio
(6.24)
PRATIO is the number of parts assembled at programmable
stations divided by the total number of parts. If PRATIO
= 1 then the hybrid system corresponds to a purely program-
mable one. If PRATIO = 0 then the hybrid system is a
transfer machine.
An initial examination of equation (6.23) might lead
one to conclude that a hybrid system could never be econom-
ic because either a purely programmable system or a pure
149
transfer machine system would produce a lower assembly cost.
This would be true so long as the production volume VOL in
the equations represented a single uniform product.
But if VOL represents a family of products which have
some common parts but some different parts, then a single
transfer machine may not be technically feasible for the
entire product family. Specifically it may not be possible
to build the transfer machine to handle the parts that are
different from member to member in the product family.
But this part variation between product family members
does not affect the application of the purely programmable
system. Within the limits of its programmability, it can
handle the varying parts. A hybrid system could also handle
the entire product family if programmable stations are used
to handle the parts that vary between membeirs of the pro-
duct family. The parts that are the same for all the mem-
bers of the product family could be assembled by transfer
machine stations or programmable ones, whichever is more
economical.
A plot of assembly cost per unit versus production
volume, VOL, for different methods is shown in Figure 6.6.
The numerical values correspond to the example previously
developed in section 6.14. It should be remembered that
the following values simply represent plausible numbers
for illustrative purposes only and are not necessarily
accurate estimates of the true mean values.
150
Figure 6.6. Comparison of Hybrid Transfer-Programmable
Assembly Systems
Hybrid Assembly Systems.
Programmability Ratio
0 Transfer Machine
1.0
0.5.
+31
0.2
+-0 0.1
.450
10 0.15
04
-1
0.2 0.5 1.0 2.0 5.0
Annual Production Volume (millions)
I I I 1 U1 '-
manual
Programable
Programmability o
Ratio
10.0
0 T- AF-- I I I I
151
NPART = 10
STAP = $30,000
TOLPP = $7500
TMCPP = $30,000
PARTTIME = 3 sec/part unit
LABCST = $7.50/hour = 2.0833 x 10-3 $/sec/worker
MATP = 7 sec/part unit
NSPY = 1.152*107 sec/yr (2 shifts, 250 days/yr,
uptime = .8)
DPPA = .125 per yr
DPTL = .25 per yr
DPTM = .10 per yr
T = .48
R = .25 per yr
Cost curves for manual, programmable, hybrid, and
transfer machine production are shown. For the hybrid
configuration, curves for different values of program-
mability ratio are shown. It can be seen that a region
where manual assembly is best extends up to a certain
production volume, 1.73x105 . Between this boundary
volume and a higher boundary volume at 2.60x106, the
purely programmable system is most economical. It is
even more economical than a hybrid system. This program-
mable range is the same one that would exist if the pro-
grammable system were competing with only manual and pure
transfer machine methods. The reason is that the total
152 
cost of the pure programmable system is less than the 
transfer machine cost in this range. This is primarily 
due to the fact that programmable stations are used to 
assemble more than one part, resulting in fewer total 
number of stations. If transfer machine stations were 
used to replace some of the stations of the purely program­
mable system, the total system cost would increase be­
cause more transfer machine stations would have to be 
added than the number of programmable stations replaced. 
Beyond the upper bound of the programmable range any 
hybrid system (i.e., 0 5_ PRATIO �l) is better than the 
purely programmable system. This is because the higher 
volume requirements limit the number of parts that can 
be assembled at each programmable station, bringing up the 
programmable system cost per part above the transfer machine 
cost per part. Systems with low programmability ratio are 
the most economical because they have fewer of the more 
expensive progra.mn,able stations -they are more like the 
transfer machine. 
The production volumes are high in this region where 
hybrid systems form the most economic alternative. This 
means that the programmable stations in a hybrid system 
will have relatively few parts per station. In fact, in 
certain circumstances, it may be necessary to use parallel 
stations for the programmably assembled parts in order to 
meet the production requirements. 
153
For lower assembly costs, as much of the hybrid system
as possible should consist of transfer machine technology
in this volume range. In fact, if a transfer machine can
be built to handle the product, it will be the most econom-
ical alternative. It is the characteristics of the pro-
duct or product family that will determine whether a trans-
fer machine is technically feasible, or whether program-
mability is required and how much.
The required degree of programmability of the appro-
priate hybrid system would depend on the variation between
members of the product family. If only a small fraction of
the parts actually vary between members then only a small
degree of programmability is needed because only certain
assembly operations need it.
The potential cost saving resulting from hybrid and
purely programmable systems for product families is illus-
trated by an example shown in Figure 6.7. The system
parameters for this example are the same as for Figure 6.6.
The example product family has four members, each with an-
nual volume of 1.x106 . The number of parts in the product
is ten, and the programmability ratio of the product family
is assumed to be .5, that is, one-half of the parts in the
product differ in their assembly operations between the
four members.
The dashed lines in Figure 6.7 point out the assembly
costs of different assembly methods for this example. These
154 
Pigure 6.7, Bxaaple ot Savings of Hybrid 
'l'ranafer-Prograaaable System on Product 
P'aaily 
Aasuaea hypothetical product with 10 parts 
Hybrid (PRATIO-o5) 
Transfer Machine 
(PRATIO • 0)
Manual 
1--������'"'c---'�r-��----'IC.-.�,--��---1.145 
_____ _j ____ .111 
� 0.1 II I 
� 0.05 
II 
II " 
� 
� 
,pf 
c 0.02 
Progra11Rabl1t 
(PRJ.TIO • 1.0) 
Member 
1 X 
Volume I
106� 
I 
I 
I 
I 
->...:>-..-- -1- --- .055 
Jl'a111lly Volume I
4 X 106 ,z.pl 
I 
I 
- .042
-- -- o0J5 
o.otL-��-L.�.,L__J__J__...L..L.JL...LIL--��-'-��_,__._ ........................ 
o.t 0.2 1,0 2.0 ,;.o 10.0 
Annual Production Volume (millions) 
Product family has tour members, each with 
annual volume• t x 106 • Progr9.lllll&billty ratio 
aaaumed equal to 0.5. 
L 
II 
f-• 
i 
• 
-
--
155
costs are:
Manual assembly .]45 S/unit
Four pure transfer machines, .111 $/unit
one for each member
Four pure programmable systems, .055 $/unit
one for each member
One pure programmable system .042 $/unit
for all members
One hybrid system, PRATIO = .5, .035 $/unit
for all members
These costs represent only those due to the capital
equipment investment in the assembly machinery or the
pure labor rate in manual assembly. In a real system
that assembles more than one product in a product family,
there will be costs associated with the changeover process
when production of one member is halted and another begun.
The labor cost of production workers who must tend the
machines and are idle during changeover and the labor cost
of the workers who effect the changeover are some of the
changeover costs. Since the capital equipment does not
change with every changeover, and since the annual produc-
tion volume does not change with the changeover, that com-
ponent of assembly unit cost due to the capital investment
is not affected by the individual changeover process.
(Since changeover time is a non-productive time, it might
be considered a form of "non-assembly time." Therefore,
I ,
156
its effects on system design may be approximated by reduced
configuration efficiency as described in section 5.3.) For
all five of the systems tabulated above, there will be change-
over costs. Typically the changeover costs should be least for
the manual assembly, greatest for the transfer machine assem-
bly, and intermediate for the programmable and hybrid systems.
The annual changeover costs will depend heavily on other fac-
tors not considered yet such as the number of changeovers
per year. To evaluate the effect of changeover costs would
require a much more detailed examination and so will not be
treated in this simple model.
To estimate the potential savings for hybrid and pro-
grammable systems, it is necessary to know or estimate the
present assembly cost. In the case of the example, assuming
programmability were not available, the obvious choice is
four transfer machines since this alternative is cheaper
than manual assembly. With programmability, the obvious
choice is the hybrid system. The savings of the hybrid
over the four transfer machines is .076 $/unit, or 68 percent.
If the product family had been fragmented into more than ten
members so that each member had less than .6x106 annual volume,
then manual assembly would have been the obvious non-program-
mable choice. Then the savings with the hybrid system would
be .11 $/unit, or 76 percent. (This assumes PRATIO = .5 as
before.)
157
Under the assumption of the simple model the source
of cost savings for hybrid programmable-transfer systems
is different than for pure programmable systems. In the
volume range where it is most economic, the hybrid system
represents a greater initial investment than a transfer
machine, but it obtains unit assembly cost savings by
extending the applicability of the assembly system over a
larger volume of production than a simple transfer machine
would be technologically capable of. The appropriate pro-
duction volume is the volume of the product family and not
of just a uniform product.
6..2.2 Modeling Hybrid Transfer-Manual Assembly
Another important hybrid assembly method is the com-
bination of manual assembly and transfer machine assembly.
This combination can be modeled by the same method that was
used in the modeling of the hybrid transfer-programmable
assembly. The parts of the product are divided into those
that are assembled manually and those that are assembled by
transfer machine stations. The cost of assembly for each
subset is computed and added together to obtain the total
cost of assembly per unit.
The cost of the transfer machine stations can be
modeled as
where 
158 
TSTCST = NPT * TMCPP (6.25) 
TSTCST = total cost of the transfer stations 
NPT = number of parts assembled by transfer 
stations. 
The assembly cost per unit for the subset of parts assem­
bled by the transfer machine stations is obtai�ed by ana­
logy with equation (6.9) of section 6.12. 
where 
TSCPU = NPT*TMC.PP* ( R-
T*DPTM) 
VOL1(1-T) 
( 6 • ;;
TSCPU = the unit assembly cost for the parts 
assembled by the transfer stations 
The manual cost per unit is simply the manual cost 
of assembly for the remaining parts in the product. 
where 
MSCPU = MATP * LABCST * (NPART - NPT) (6 .27)
MSCPU = unit assembly cost for the parts assembled 
manually. 
The total unit assembly cost for the hybrid system is 
the sum of the manual and transfer station costs. 
where 
HTMCPU = MSCPU + TSTCPU (6 .28)
HTMCPU = unit aRsembly cost for the hybrid 
transfer-manual system. 
We now seek to relate the unit assembly cost of the 
hybrid transfer-manual system to the unit assembly costs 
for a pure programmabls system and a pure transfer system 
operating at the same production volume. 
First, it is convenient to define a transfer ratio 
159
as the number of parts assembled by the transfer stations
divided by the total number of parts in the product.
TRATIO = 1PT (6.29)
NPART
where TRATIO = transfer ratio
We now combine equations for the manual and transfer
machine unit costs with the definition of the transfer
ratio to obtain an expression for the unit assembly cost
for the hybrid transfer-manual system.
HTMCPU = NPART* (TRATIO*TCPU+ (I.-TRATIO) *MCPU)
(6.30)
whexe TCPU = unit assembly cost for a transfer.machine
operating at the desired production vol-
ume
MCPU = unit assembly cost for a manual assembly
line operating at the desired production
volume.
Figure 6.8 shows an example of curves of unit assembly
cost plotted against production volume for the variable
values used in the examples of the previous sections. The
values are merely plausible estimates of the typical
values. The model is not sufficiently detailed to predict
costs in individual cases.
The curves indicate that there is a critical value
of production volume. For products with volumes below
this value, pure manual assembly is the cheapest method,
160
Figure 6.8 Comparison of Hybrid Transfer-Manual
Assembly Systems
Hybrid Transfer-Manual s
. Transfer Ratio
Transfer Machine
0.0 X
Manual
1.0
0.5
0.2
rt
0.1
0.
rq 0.05
0.02
+
C
I I I 1I i ii 1
0.5 1.0 2.0 5.0 10.0
Annual Production Volume (millions)
I I I I I1
I 5
0.0
- *025-
0-50_
Programmable
Critical Volume
(VOLMT) TZar1 fTrans
Ratio
I.
0.01
0.1 0.2
3 a m S I - I I -I -I L
I
1
161
even cheaper than the hybrid transfer-manual method.
Above this critical value, a pure transfer machine is the
most economic -alternative. This critical value is the
manual-transfer volume boundary derived in section 6.1.5:
TMCPP* (R-T*DPTM)
VOLMT = MATP*LABCST*(1-T) (6.31)
where VOLMT = volume boundary between economic manual
and transfer machine systems.
For the example values of the parameters,
VOLMT = .799xl06  product units/year (6.32)
Since for any production volume under consideration
either pure manual assembly or pure transfer machine assem-
bly seems most economic, then it appears that hybrid trans-
fer-manual assembly would never be most economic. But,
this conclusion depends on certain assumptions of uniform-
ity that are inherent in this "average" model; for example,
that a transfer machine actually can be built to assemble
any product, that the manual assembly cost per part is the
same for all parts, and that the transfer machine cost per
part is also the same for all parts.
However, assembly tasks vary in their susceptibility
to transfer machine assembly. Some tasks are either im-
possible to do by transfer machine methods or would re-
quire very expensive equipment. With a knowledge of
transfer machine technology and an examination of the
product, one could estimate the minimum number of parts
162
that should be assembled by hand and the corresponding
maximum number of parts that could be assembled by the
transfer machine.stations. This defines a practical up-
per limit on the transfer ratio TRATIO of the transfer-
manual system. If we now examine Figure 6.8 we see that
for products with production volumes less than the criti-
cal value, manual assembly remains the most economic al-
ternative. This is because manual assembly of any of the
parts, including the ones that could be assembled by a
transfer machine station, is the cheapest method. For
products with production volumes greater than the critical
value, the hybrid transfer-manual system with the highest
feasible transfer ratio is the most economic alternative.
This result is true for classes of products with the same
transfer ratio; that is, the model predicts that products
with a given transfer ratio, say .5, will, on the average,
be assembled most economically by pure manual methods for
production volumes less than the critical volume VOLMT.
For production volumes above the critical value, hybrid
systems with transfer ratio equal to .5 are the most eco-
nomic, on the average.
In practice other factors will influence the design
of individual transfer-manual systems. The modeling pre-
sented here is intended to describe average costs and to
identify general classes of applications. Individual
system designs will deviate one way or another from the
I163
average depending on the particular circumstances.
6.3 Improved Simple Economic Models
The simple economic models developed in the pre-
ceding sections have been especially useful in that they
have led to the identification of the price-time product
as a measure of assembler economic performance. Con-
straints and system economic volume boundaries have been
analyzed and expressed in terms of this measure. The
concept of the assembler price-time product will be devel-
oped more fully in the next chapter.
In the following section certain improvements are
made to the simple economic model. Many improvements
could have been made, but the ones made here represent
what the author feels are the most important additions
that sacrifice a minimum of model simplicity. These im-
proved models will be used to repeat quickly the volume
and constraint analysis of section 6.1.5 to see if signi-
ficant changes in the form of the equations will result
and to see if significant numerical differences occur in
the results of the example model. The improved model will
give results which are somewhat less favorable to program-
mable assembly but which on the whole reinforce the-results
of the simple model.
164
6.3.1 Manual Assembly with Equipment Costs
Only rarely will people be used to assemble a product
with no tools or support equipment. Consequently, the unit
assembly, cost formula for manual assembly from the simple
model gives an estimate lower than the actual assembly
costs. We now add the cost of the manual assembly equip-
ment to the basic manual assembly labor cost.
This improved model of the manual assembly cost per
unit is meant only to provide a more accurate estimate
of the true unit assembly cost by including the effects of
the equipment that is used. It does not refer to improved
manual assembly performance because of the addition of
better equipment.
It will be assumed that the cost of the manual assem-
bly equipment is roughly proportional on the average to
the number of parts in the product. This is plausible
because the support equipment is likely to be different
for each part and probably can be used as rapidly as the
operator can use it. The manual equipment cost is modeled
as follows:
MECST = MECPP * NPART (6.33)
where MECST = total manual equipment cost
MECPP = manual equipment cost per part
To allocate the equipment cost to the production units
the same rate of return is used that was applied in the
simple model to the programmable and transfer machine
165
systems.
zcpu = EP(R-T*DPME) (6.34)MECPP*NPART+VOL*(l-T)
where MECPU = manual equipment cost per unit
R = required rate of return
T = tax rate
DPME = annual straight line depreciation rate
for the manual equipment.
Now, the manual equipment cost per unit, equation(6.34),
is combined with the manual labor cost per unit, equation
(6.1), to obtain the improved estimate of the manual unit
assembly cost.
MCPUI = NPART* MATP *LABCST+MC*(R-T*DPME)CIVOL*(lT) (6.35)
where MCPUI = manual unit assembly cost, improved
model.
Notice that the unit assembly cost is still proportional
to the number of parts in the product, but now the manual
cost is not independent of volume. A comparative example
will be presented in a subsequent section.
6.3.2 Transfer Assembly with Labor Costs
No transfer machine can run entirely by itself.
It must be tended, perhaps only occasionally, by one or
more workers. In the case of transfer assembly machines,
166
these workers are responsible for supplying some or all
of the parts to the feeding equipment on the machine.
They must also clear the jams in the feeding equipment
and the actual assembly equipment.
The number of workers assigned to a transfer machine
varies widely and does not depend solely on the character-
istics of the machine. Sometimes the local work agreements
will influence the assignment. The stockman who refills
feeding devices may be a different worker from the one that
actually performs assembly or operates assembly equipment.
Also, there is a tendency to have at least one whole worker
assigned to a new type of machine. Hence, one new assembly
machine may have one whole worker assigned to it even though
it requires only a half or a quarter of a worker's atten-
tion (i.e., only one job of a worker who has more than one
job). But, if more similar machines are added, that same
single worker will tend them all until he reaches a true
load limit (or a work rule limit). This may have the ef-
fect of using more labor than necessary at small assembly
system installations. For the purposes of this model it
will be assumed that the number of workers required is
proportional on the average to the number of parts in the
product.
NWRKR = NPART * NWPP (6.36)
where NWRKR = number of workers assigned
NWPP = number of workers assigned per part
167
The total annual labor cost depends on the number of
hours that the system transfer machine must be run in or-
der to meet the required annual production volume. This
time must take into account the effect of downtime. The
first step is to model the total annual operational time.
TTIME*VOL
TOPT = (6.37)UT
where TOPT = total annual transfer machine operational
time, sec
TTIME = average time between the production of
single product units, sec
UT = uptime ratio of the transfer machine
Here, TTIME represents the average time between the assem-
bly of single product units on a transfer machine, and so
it corresponds to the INDEXTIME variable used in section
5.3.2 to describe the time between product units on the
programmable system.
For the purposes of this model, the same uptime ratio
will be assumed for the programmable and transfer machine
systems. (This assumption is a matter of convenience. The
programmable system should have greater uptime than the
transfer machine as discussed in section 4.2.3).
The annual labor cost is obtained by multiplying
the total operational time by the number of workers and
the labor cost rate per worker per second, LABCST.
ATLCST = NPART*NWPP*TTIME*VOL*LABCST(6.33)UT
168
where ATLCST = annual labor cost for transfer machine
operation.
This annual cost must be allocated over the annual pro-
duction volume of the product.
TLCPU = ATLCST (6.39)VOL
where TLCPU = transfer machine labor cost per unit.
Equation (6.39) may be combined with equation (6.38) to
obtain
TLCPU = NPART * NWPP * TTIME * LABCST (6.40)UT
Finally, the improved estimate of the transfer machine
cost per unit is obtained by adding the unit cost due to
the equipment investment from the simple model, equation
t6.9), to the labor cost per unit, equation (6.40) above.
TCUI= PAT*TMCPP* (R-T*DP M) NWPP*TT IME*LABCSTTCPUI = NPART*[T{VOL*P(T-T)UT L S 6.41)
where TCPUI = imprOved estimate of the unit assembly
cost for the transfer machine.
This improved estimate of the transfer machine unit assem-
bly cost is still proportional to the number of parts in
the product. An illustrative example will be presented
in a subsequent section.
Programmable Assembly with Labor Costs6. 3. 3
169
Just as in the case of the transfer assembly machine,
no programmable assembly system will be able to operate
without human.intervention. The workers that tend the
programmable system will be performing many of the same
functions as the workers that tend the transfer machine
system. They will be clearing jams in the parts feeding
equipment and also will be supplying some or all of the
parts to the parts feeding equipment. Because of the pro-
grammability, the assemblers should have the ability to
sense certain jams at the assembly site before signifi-
cant damage is done and take appropriate clearing action
on their own in many cases. This will act to reduce the
total downtime.
In order to model the labor cost in operating a
programmable assembly system, it will be assumed that the
attending workers will be paid during both uptime and
downtime just as in the case of the transfer machine
system. Recall from Chapter 5 that the programmable util-
ization efficiency PUEF is the amount of time (including
downtime) that a system requires to meet the production
volume divided by the total amount of time that the system
has available in the year. The programmable utilization
efficiency can be used to model the total annual opera-
tional time for the programmable system.
POPT = DY * HD * 3600 * PUEF (6.22)
170
where POPT = total yearly operational time for the
programmable system
DY = number of working days in the year
HD = number of working hours in the day
PUEF = programmable utilization efficiency
This equation may be simplified by using the variable
NSPY representing the effective number of working seconds
in the year. It was defined in equation(5.2)in the simple
configuration modeling of Chapter 5.
NSPY = UT * DY * HD * 3600 (5.2)
where NSPY = the effective number of working seconds
per year.
Using equation(5.2)in equation (6.42) above results in a
simplified equation for the total annual operating time.
POPT = NSPY*PUEF (6.43)
UT
Following the example of th- labor analysis of the transfer
machine, the number of workers assigned will be modeled as
proportional to the number of parts in the product.
NWRKR = NWPP*NPART (6.44)
where NWRKR = number of workers assigned
NWPP = number of workers assigned per part.
This is reasonable since these workers would be performing
many of the same tasks that the workers who tend transfer
machine systems would do--restocking the feeding equipment
and clearing any jams of parts that may occur.
171
The total annual labor cost for the system is the
product of the number of workers, the total work time, and
the labor cost rate per second.
APLCST = NPART*NWPP*NSPY*LABCST*PUEF (6.45)
UT
where APLCST = the annual labor cost for a programmable
system
The labor cost attributed to each product unit is the
annual labor cost divided by the annual volume.
NPART*NWPP*NSPY*LABCST*PUEF (6.46)
PLCPU = UT*VOL
where PLCPU = the programmable system labor cost per
unit of product.
Finally, we may combine the labor cost per unit of
the programmable system, equation (6.46), with the pro-
grammable equipment cost per unit, equation (6.12), to ob-
tain an improved estimate of the unit assembly cost of the
programmable system.
STAP*PARTTIME*(R-T*DPPA) TOLPP*(R-T*DPTL)
PCPUI = NPART NSPY*CEF*PUEF + VOL(1-T)
NWPP*NAPY*PUEF'LABCST](6.47)
UT*VOL
where PCPUI = programmable cost of assembly per unit
product for the improved model.
Notice in this formulation that the unit assembly cost
is still proportional to the number of parts in the product.
An example illustrating this equation follows in the next
172
section.
6.3.4 A Comparative Example Using the Improved Models
An example plot of unit cost of assembly against
production volume for the three improved models of the
production methods is shown in Figure 6.9. The values
used for the variables in this example are illustrative
only. They are meant to be plausible values but not-
necrssarily accurate estimates of the true average values
of the variables.
The assumed values of the variables are
NPART = 10 parts
STAP = 30,000 $/station
PARTTIME = 3 sec/part unit/station
NSPY = 1.152 x 10 sec/year
PUEF = .95
CEF = .8
TOLPP = 7,500 S/part
NWPP = .1 worker/part
UT = .8
LABCST = .0020833 $/sec ( = 7.50 $/hour)
TMCPP = 30,000 $/part
MATP = 7 sec/part unit/worker
MECPP = 2000. $/part
TTIME = 2 sec/part unit
173 
Figure 6.9, Coapariaon of Unit Assembly Costa using 
I,aproved Model 
Assumes hypothetical product with 10 �arts 
Transfer Machine 
0.5 
...... 
� .... 
0.2 Manual 
r-1 ... 
0 
't:I ..... Progralftlllable .. 0.1 Programmable Savings Region 
II 
0 
0 
>, 
0.05 
II 
< 
� .... 
0.02 
Oo01'--�� ...... ��.__ ....... -L-L....&.....&...1L...L���-L-�....a....�.___,__..__L..L...J...J 
0.1 0.2 1.0 2.0 5.0 to.o 
Annual Production Volume (millions) 
174
DPTM = .1 per year
DPPA = .125 per year
DPME = .25 per year
DPTL = .25 per year
T = .48
R = .25 per year
The variables presented above are essentially the same
as the example variables discussed in section 6.1.4 with
the exception of certain new variables introduced in the
improved model.
The assignment offoneworker for every ten parts being
assembled both in the programmable and transfer systems
is a guess; the actual numbers may vary widely depending on
the work rules and the number of programmable systems in-
stalled in the factory. A transfer machine index time
TTIME of 2 seconds is typical, although many transfer
systems can operate at twice this speed. Finally, a
manual assembly equipment cost per part of $2000 represents
only a rough estimate of the cost of hand and power tools,
work area, convey segment, and installation costs.
Notice that the general shape of the curves in Figure
6.9 is the same as those in Figure 6.2 for the simple model,
except that the region in which programmable assembly is
most -economic is somewhat smaller. This comparison will
be made more quantitative below with volume boundary anal-
ysis using the improved model.
175
When the improved model is used, the expressions for
the volume boundaries and price-time product criterion are
more complex, harder to handle, and harder to grasp intui-
tively. Consequently, only a compact set of volume boundary
equations is presented here.
The improved model for the programmable, manual, and
transfer cost per unit may be expressed in the following
compact form:
PCPUI = NPART*[AP+ (6.48)KBM1
MCPUI = NPART* AM+OL(6.49)
TCPUI = NPART*[AT+ (6.50)
where the stants are defined as follows:
AP = STAP*PARTTIME*(R-T*DPPA) (6.51)NSPY*CEF*PUEF*(l-T)
BP =TOLPP*(R-T*DPTL),NWPP*NSPY*PUEF*LABCST(1-T) UT (6.52)
AM = MATP*LABCST (6.53)
BM= MECPP* (R-T*DPME) (6.54)(1-T)
AT= NWPP*TTIME*LABCST (6.55)
UT
BT = TMCPP*(R-T*DPTM) r (6.56)(1-T)
The volume boundaries that divide the ranges of economic
assembly as defined in section 6.1.5 for the simple model
can now be expressed in terms of these constants here in
the improved model.
176
VOLMTI = BT-BM (6.57)AM-AT
VOLPMI = BP-BM (6.58)AM-AP
= BT-BPVQLPTI \AP-AT (6.59)
where VOLMTI = v blume boundary between economic manual
and transfer machine assembly, improved
model
VOLPMI = volume boundary between economic program-
mable and manual assembly, improved model
VOLPTI = volume boundary between economic program-
mable and transfer machine assembly,
improved model.
Finally, the constraint on the price-time product for
an assembler can be determined in the case of the improved
model. If an assembler has a price-time product above this
value, then it cannot be used to create programmable systems
that are economic compared to manual or transfer machine as-
sembly, on the average. This was expressed in the simple
model in equation (6.16). Following the same reasoning with
the improved model, the constraint is
NSPY*CEF*PUEF*(1-T)
STAP*PARTTIME( (R-T*DPPA)
* (AT* (BP-BM) +AM* (BT-BP)) (6.60)
BT-BM
Using the example values for illustration, the system
volume boundaries and the price-time product constraint
177
have the following values in both the simple and improved
models:
Quantity Improved Model Simple Model
Manual-transfer .793x106 units/yr .799x106 units/yr
volume boundary
6 6
Programmable-manual .390x10 units/yr .173x10 units/yr
volume boundary
Programmable-transfer 2.14x106 units/yr 2.60x106 units/yr
volume boundary
Price-time product 2.23xl05 $-sec 2.93x105 $-sec
upper bound
At least for the example values, the effect of the improved
model is to tighten the constraint on programmable assembly
by slightly reducing the range in which programmable assem-
bly is on the average most economic, and to lower the upper
bound on the assembler price-time product. In general,
however, the results are very similar to those of the
simple model.
6.4 Summary
The economic modeling provides a framework which per-
mits a number of results based on a consistent set of assum-
ptions. Hence, not only does it model the three principal
methods of assembly, but also it allows a comparison among
them to understand how the applicability of programmable
assembly depends on the economics of the other two methods
178
as well as its own. The model also provides a means of
examining hybrid methods of assembly--combinations of the
principal methods. The model identifies distinct volume
ranges where the various alternate methods are each most
economic and provides a way of examining the sensitivity of
the economic production volume range of programmable
assembly to general economic parameters, such as wage
scales or the required rate of return.
The principal result of the economic modeling has
been to identify the assembler price-time product as an
important measure of assembler performance. The price-
time product directly affects the unit assembly cost of
programmable systems. The price-time product was also
shown to affect directly the range of production volume for
which programmable systems composed of a given assembler
would be applicable. The economic analysis also provided
a way of estimating bounds on the price-time product for
economic assembler designs--designs which could compete
with manual and transfer machine assembly. An example
showed how this might be calculated for a specific case;
other cases could be easily examined. The nature of the
price-time product as a measure of assembler design will
be examined more closely in the next chapter.
179
7. CONSEQUENCES OF THE ECONOMIC MODELS
Both the simple and improved models of the pre-
ceding chapter were developed to gain an understanding
of how the general characteristics of assemblers influ-
ence the economics and application of programmable assem-
bly systems.
The modeling framework provides a way of investigating
the sensitivity of the economic applicability of program-
mable assembly to various economic parameters as well as
the properties of an assembler. In the first section of
this chapter we will examine how alternate values for the
labor wage rate, the required rate of return, and the
assembler price-time product affect the applicability of
programmable assembly.
The chief measure of economic performance of an assem-
bler to emerge from these models is the assembler price-
time product. Having used the simple model to identify Lne
price-time product as a measure of assembler economic per-
formance under the severe simplifications of the simple
model, we now examine the price-time product as a measure
under less restrictive assumptions to see under what.con-
ditions it remains valid.
Finally, the relationship of the configuration effi-
ciency to assembly system design will be examined.
I-
180
7.1 Variation of Parameters of the Comparative Example
One use for the modeling framework developed in the
previous chapter is to examine how the relative economics
of the alternate assembly methods change with changes in
important parameters. We now take a brief look at how
changes caused by variations in the required annual rate of
return, the labor rate, and the price-time product will
appear in the context of the simple example developed in the
previous chapter.
All values for the variables used in this example are
the same as in the example developed in the previous chap-
ter. However, the required minimum annual rate of return is
allowed to have the values of .3 and .2 in addition to the
value of .25 used before; the labor rate is allowed to have
the value of $10 per hour in addition to the value of $7.50
per hour used before; and the price-time product is given
the values of 50,000 $-sec and 200,000 $-sec in addition to
the value of 90,000 S-sec used in the example.
The results of the comparison are shown in Figures
7.1, 7.2, and 7.3. In Figure 7.1 are shown results for dif-
ferent rates of return and wage rates for assemblers with
price-time product equal to $90,000 $-sec. As can be seen,
181
Figure 7.1. Comparison of Unit Assembly Costs with
Price-Time Product Equal to 90,000 $-sec
Assumes hypothetical product with 10 parts
LOV
STransfer Mae hine-
0.5 -
0.2 Manuai ,N$1 O/hr _
$7.50/Ar
0.05-
Programmable
0.01
0.1 0.2 o.5 1.0 2.0 5.0 10.0
Annual Production Volume (millions)
R - required annual rate of return
0.4C
N
U
H0
+2
U
CC,
>2
H
.0U
U
U
4
4'
"4C
182
Figure 7.2a Comparison of Unit Assembly Costs with
PriceeTime Product Equal to 200,000 $-sec
Assumes hypothetical product with 10 parts
- 4 0 Transfer Machine
0
Mam%
*j0
I I-I TI I]1-2
al
$10/hr
i $7.50/hr
Programmable
0.2 0.5 1.0 2.0
Annual Production Volume (millions)
R m required annual rate of return
1.0
0.5F
E
O.2
0.1
"4
C-0
"4 0.051-
0.02k-
00011
0.1 5.0 10.0
I - - --- IF- . Ev we - i -0
A a
183
Figure 7.3 Comparison of Unit Assembly Costs with
Price-Time Product Equal to 50,000 $-vec
Assumes hypothetical product with 10 parts
0.1 0.2 0.5 1.0 2.0 5.0
Annual Production Volume (millions)
10.0
R a required annual rate of return
1.0
0.5
.,
.4
C
Oo
0.02
0.01
- #
- Transfer Machine
Manual $1P/mr
$7 -50/hr
Prograamable
184
the required annual rate of return and the labor rate can
drastically affect the range of applicability of the program-
mable assembly systems. For a manual rate of $7.50 per hour
and a required annual return of .3, the range of applicabil-
ity of programmable assembly is only between production
volumes of 270,000 to 2.4 million per year. On the other
hand, if the labor rate were $10 per hour and the required
annual return were .2, then the applicable production vol-
umes range from about 75,000 to about 2.8 million. The
upper end of the volume range does not change much because
it is the boundary between to two automated methods subject
to the same required annual rate of return: labor rates
are not involved. The lower end of the volume range is
drastically affected because it is a boundary between a
labor method and a capital method; changes in labor rate or
required return will affect one and not the other.
The same type of results for assemblers with price-
time product equal to 200,000 $-sec, a slower and/or more
expensive assembler, are shown in Figure 7.2. Such assemb-
lers are only marginally competitive if the required annual
rate of return is .30 and the labor rate is $7.50 per hour.
Then the production volume is only from about 650,000 to
about 1.1 million. At the other extreme, if the labor rate
were $10 per hour and the required annual rate of return
were .20, then this assembler would have a production volume
range from about 90,000 to about 1.2 million.
185
Finally, these same results are shown in Figure 7.3
for assemblers with price-time product equal to 50,000 $-sec.
This corresponds to a cheap and/or fast assembler. Such an
assembler product produces competitive systems for volumes
from 210,000 to 4.4 million if the manual labor rate were
$7.50 per hour and the required minimum return were .30 . On
the other hand, if the labor rate were $10 per hour and the
required annual return were .20, then the competitive volume
range would be from about 70,000 to 4.9 million.
The results of these comparisons show that price-time
product, labor rate, and required annual return are signi-
ficant influences on the competitive relation between pro-
grammable assembly and manual or transfer machine assembly.
The labor rate and the required annual rate of return will
change over time, largely due to national economic condi-
tions, but the model provides a framework to take these
changes into account. The price-time product of the pro-
grammable assembler is a measure of the state of the techno-
logy. It is a variable whose value can be reduced by fur-
ther research and development. Reducing the price-time pro-
duct will improve the competitive range of programmable
assembly for any set of economic conditions represented by
labor rate and required annual return.,Accordingly, we now
examine the price-time product as a measure of assembler
design to see how it may be used.
186 
7.2 Significance of the Price-Time Product 
In the simple economic model, the equation for 
progranunable assembly cost per unit is a function of the 
product of the price and part assembly time of the pro­
grammable station, not price or time individually. This 
equation is 
where 
PCPU NPART*[STAP*PARTTIME*(R-T*DPPA)+TOLPP*(R-T
*DPTL)l
(1-T) NSPY*CEF*PUEF VOL j 
( 6 .12) 
PCPU = programmable assembly cost per unit 
STAP = price of the programmable station 
PARTTIME = part assembly time for one part, sec 
This functional dependence on the price-time product has the 
following implications: 
1. Assuming the other parameters, such as parts feeding
tooling costs, are held constant, design of assembly
stations for minimum assembly cost per unit is
achieved by minimizing the product of the station
price and the part assembly time, not price or
time individually.
2. Programmable assembler designs with different prices
and assembly times but the same price-time pro-
duct will result in systems having the same assem­
bly cost per unit, on the average.
3. The sensitivities of the cost of assembly to frac­
tional changes in price and part assembly time are
187 
equal �n the following sense: reducing the price 
of the programmable station by a certain fraction 
will result in the same cost savings as reducing 
the part assembly time by the same fraction. 
These implications make sense intuitively. By reducing 
the price of the programmable stations the unit assembly 
cost can be reduced. By reducing the assembly time per part, 
fewer programmable stations are needed to meet the required 
annual production volume of the product. (We are assuming 
that the amount of parts feeding tooling remains the same.) 
This means lower system price and consequently lower 
assembly cost per unit if the station price is constant. 
A station design that is twice as fast as another but has 
twice the price gains no advantage. It will replace two of 
the slower stations in performance but for exactly the same 
price. 
The equivalent relative sensitivities of assembly cost 
to station price and part assembly time can be seen from 
equation (6.12). A reduction of ten percent in the price 
of a programmable assembler station will produce the same 
ultimate reduction in assembly cost per unit as a ten per­
cent reduction in average part assembly time. The reduction 
in assembly cost per unit will decline by less than ten per­
cent because the cost of parts feeding tooling has remained 
the same. 
188
7.3 Programmable Assembler Station Design
7.3.1 Choosing Between Alternate Assembler Designs
To develop the concept of the minimization of the
price-time product in the choice of an assembler for a
system or in the design of an assembler, it is helpful to
take the position of a designer of a particular programmable
system. Because of the nature of the product for which the
system is to be designed, the designer has certain con-
straints on his choice of programmable assemblers from which
to build his system. The size and weight of the parts
will place a lower bound on the size and force capabilities
of the assemblers that he can consider. The groupings of
the parts, the nature of the assembly directions and axes,
and the production volume will influence the choice of
number and kind of degrees of freedom needed. Given these
basic constraints, the designer can now collect price and
time data on all of the acceptable assemblers. In theory,
he could display this data on a price-time chart such as
Figure 7.4 where points for several hypothetical assemblers
are plotted.
In Figure 7.4 the curved line represents the price-
time frontier for all assemblers that meet the designer's
constraints for his particular application. The dotted line
is a line of constant price-time product for the assembler
189
Figure 7.4. Price-Time Product Data for Hypothetical
Set of Assemblers
Price
Proc
Fro:
Di
Stat
i-Time
luct
itier 
.A c
B
0
F. ,GH
ual I J
ion "KI
K ,
Minimum
Price-Time
Product
Constant Price-Time Product Decreasing
Price-Time
Product
Log Part Assembly Time
40
0
#4
I
190
with the minimum price-time product. The points plotted
in Figure 7.4 represent many different assembler technolo-
gies (electric, hydraulic, or pneumatic) and degrees of
freedom (so long as the right degrees of freedom are in-
cluded for the designer's needs). The price-time product
criterion enables the designer to choose among the assem-
blers of widely varying technologies, costs, and single
part assembly times. By choosing the assembler or assem-
blers with the lowest price-time product, he can then
proceed to design a minimum cost system for the pro-
duction constraints.
The price-time product criterion can also help to op-
timize a tradeoff in the design for a particular kind of
assembler. Suppose that for other reasons an assembler
design is almost fixed with respect to its size, force,
capacity, and number and arrangement of degrees of freedom.
Yet to be determined are the part assembly time for this
design and the corresponding actuator power requirements
necessary to move the assembler fast enough to meet this
part assembly time. Increasing the speed of the assembler
requires increased power in the actuators which leads to
an increased price for the assembler. Figure 7.5 illus-
trates the range of prices and speeds for this particular
assembler design as the actuator power is varied. The
price-time product minimization criterion can be used to
191
Figure 7.53
41
40
Example Assembler Design Problem to
Minimize Price-Time Product
High Power,
High Speed,
High Price
Dual Optimal \
Station Low Power,
Low Speed,
Low Price
Minimum
Price-Time
Product
Constant Price-Time Product2
Decreasing
Price-Time
Product
Log Part Assembly Time
\ /*t
192
pick the best choice of power and part assembly time to
give the most economic assembler performance.
7.3.2 Parallelism and the Price-Time Product
If assemblers that are optimal in the price-time
sense are too slow for a given application, then the price-
time advantages of the optimal design can be had at twice
the speed by using dual parallel station assemblers.
It can be shown that a given programmable station, when
used in a parallel manner, will result in a dual station
with exactly the same price-time product. If, for a given
application, the assembly rate of a station is too low, a
higher assembly rate can be obtained by operating two such
stations in parallel sharing the same parts feeding equipment.
The arrangement is illustrated in Figure 7.6. The pair of
stations can be regarded as a dual station with twice the
price but half the time. Hence, the price-time product for
the dual station is exactly the same as the individual sta-
tion. A system configured from these dual stations for a
given maximum production volume would have half as many
dual stations as individual ones in the conventional arrange-
ment. The cost of assembly per unit would remain the same
because the total cost of the system has not changed.
As was noted in section 5.2.2, there may be practical
upper limits to the number of assemblers that can share the
193
Figure 7.6s Parallelism of Programmable Assembly
Stations
Single Station
PARTTIME w x
Station Price s y
Price-Time
Product - xy
Dual Station
PARTTIME - x/2
Station Price -
PriceeTime
Product - xy
L . I_ . j
"art A Part B
Feeder Feeder
2y
Part A Part B
Feeder Feeder
Each Individual Station Handles Every Other Assembly
i i
I
194
same part feeder. However, to have several assemblers
sharing one feeder would likely correspond to a high
volume production--circumstances under which transfer
assembly tends to have an economic advantage. Hence,
there may be relatively few situations in which one would
want to have several assemblers share one part feeder.
When used to create a dual station, a slower assembler
station design can compete with a faster one if it is cheap
enough. It need not be restricted to lower production
volumes because of its longer part assembly time. Figures
7.4 and 7.5 show where the price-time point for a dual
optimal station is located relative to the other assembler
designs.
7.3.3 Minimization of the Price-Time Product with
Integral Station Number
The concept of minimizing the price-time product
was developed from the simple model for a restrictive
set of assumptions, but it now can be shown to be a valid
and useful criterion under a much less restrictive set of
assumptions.
To develop the general concept, it is helpful to take
again the point of view of a designer of individual program-
mable systems. This designer uses programmable assemblers
to create assembly systems for specific products or product
195
families. He is given a product with a certain production
volume requirement and a specific number of parts. Suppose
for the moment that there is a three axis assembler on the
market that he could use in the construction of his particu-
lar system.
To continue the example, suppose that his product has
two distinct directions of assembly and that one direction
has more parts to be assemnuled than the other. Our designer
considers the problem and decides that he wishes to use one
or more three axis assemblers aligned with one of the direc-
tions of assembly and also one or more three axis assemblers
aligned with the other direction of assembly. He now must
choose the number of assemblers needed for each direction
to meet the production volume requirements. He should consi-
der a chart such as Figure 7.7.
In Figure 7.7 is a plot of the price and capacity of
a given assembler design used by itself and in parallel.
The capacity is the number of parts that could be assembled
per year. Assume that the basic assembler unit has a given
price STAP and a given capacity CAP. Then CAP can be ex-
pressed as follows (as in equation (5.1))
CAP = NSPY
PARTTIME (7.1)
For any situation in which the number of parts that must be
assembled by a single station is less than CAP, one station
is required with a corresponding cost equal to STAP. When
196
Figure 7.71 Price-Capacity Chart
4r3TAP
*3*gflp
0
+31
4) Ac%a.S
- --
/00
STAP*PARTTIME
_____ insT NSPY
Number of Assemblers Needed
A2
CAP 2*CAP 3*CAP 4*CAP
Number of Parts Assembled per Year
STAP - programmable station price
CAP - capacity of station, parts per year
PARTTIMZ w part assembly time
NSPY w number of seconds per year
197
the number of parts that must be assembled per year is be-
tween CAP and 2 * CAP, then two stations are required with
a corresponding price of 2 * STAP. Because integral numbers
of stations are used, the chart has a stairstep appearance.
Next our designer must determine the annual capacity
that is required for each principal direction of assembly
of his product. The required capacity for each direction
is the number of parts assembled in that direction times
the required production volume of the product. This gives
the number of parts units per year that the assembler (or
assemblers) aligned in that direction must assemble per
year. By examining Figure 7.7, the designer can determine
how many assemblers will be needed for each direction and
how much they will cost.
Only rarely will any assembler on the market be used
to its maximum capacity. This full capacity utilization
will occur only when the required number of parts per year
in a particular application happens to be an exact multiple
of the capacity of one assembler and no extra capacity is
purchased. The busiest assembler-the one with the most
parts to assemble-will be the one which paces the entire
system, but even it may not be working at its maximum capa-
city.
If the number of parts that must be assembled by the
system in one direction is, say, only half of the capacity
of the available assembler on the market, our designer may
198
well wish that another assembler were available with less
capacity but at a cheaper price. This would allow him to
reduce the cost of the system that he is designing and
consequently reduce the unit assembly cost of the product.
In fact, our designer may wish that there were a range of
assemblers available so that he could buy just the capacity
that he needs and no more if future flexibility were not
important to him.
In this simple model, the optimal assembler design is
defined as the one which minimizes the price-time product.
It can be shown that the slope of the staircase in Figure
7.7 is proportional to the price-time product. The slope
is the ratio of the individual station price STAP to the
annual capacity of the individual station:
SLOPE = STAP (7.2)
CAP
where SLOPE = the slope of the staircase.
Substituting from equation (7.1), we obtain
SLOPE = STAP * PARTTIME (7.3)
NSPY
The assembler which minimizes the price-time product
also has the lowest slope. See Figure 7.8.
A non-minimum design in which both the capacity and
the price were less would create the second stairstep pattern
in Figure 7.8. Notice that the steps of the stairs are smaller
but the slope of the stairs is larger. (Another kind of non-
199
Figure 7.8a
ID
C
0
mu'
4J
U)
Price-Capacity Comparison for Optimal
versus Suboptimal Assembler Designs
Suboptimal t.-.
Savings.r:-.-a-.- :.a
Region :.-.-y-
::.Slope of As
-.. ..-.. a .-....'MW ith Mmi
.. ,,Price-Time Pi
Regions Where Suboptimal
Assembler Is More Expensive
I __ Ii
embler
mum
roduct
Number of Parts Assembled per Year
200
minimum design would have higher price and higher capacity
with larger stairsteps and also larger slope.) Regions where
the non-minimum design represents a savings in assembler
price compared to the minimum design are shown shaded.
It can be seen that the non-minimum design does lead to
a savings in price of over the minimum design in some ranges
of required capacity. However, it is more costly where its
reduced capacity means that more of them have to be used
than would be necessary of the optimal design.
Tf it is assumed that the distribution of the number of
potential applications for such an assembler in industry
over the range of required capacities is uniform, then the
industry wide savings for the non-minimum assembler is pro-
portional to the area of the shaded boxes in Figure 7.8.
This savings is more than offset by a much larger area
representing the additional expense of the non-minimum assem-
bler in this example. If only the non-minimum assembler
were on the market, then the average programmable cost of
assembly would be higher than it needs to be.
If only one design is to be built and marketed, it
should be a minimum price-time product design. But, whether
only one design should be built or more depends on other
factors not yet considered. One of the important factors
is the shape of the price-time function. If there is a
well-defined point at which the minimization of the price-
time product occurs, then only the minimum design would
201
probably be justified. This is because for a well-defined
minimum there must be a sharp bend in the price-capacity
curve, or, equivalently, the price-time curve. For capaci-
ties below the minimum point, relatively little additional
price reduction is possible; for capacities above the mini-
mum point, significantly greater prices are necessary.
If, on the other hand, the location of the minimum is
not well-defined, then significant reductions in capacity
will result in almost as great a fractional reduction in
the price. Greater prices will result in almost as great
an increase in capacity. In either case, the price-time
product is nearly the same over a wide range of designs,
which means that very little price penalty is paid for
the suboptimal assemblers. Figure 7.9 illustrates the
well-defined and the ill-defined cases. If the minimum
is ill-defined then a range of assembler capacities and
prices would make sense because it would allow significantly
lower average programmable system costs.
7.3.4 Ways of Reducing Price-Time Product
There are two primary ways of reducing the price-time
product: First, reducing the number of degrees of free-
dom; and, second, reducing the overall physical size. Both
have the effect of reducing the number and size of the parts
in the assembler equipment and the power required to move
202
Figure 7.9s Comparison of Assembler Price-Capacity
Curves for Individual Assembler Design
Problems
Well-Definsd Minimum Price-Time Products
"4
d
4P
Moe
0 de minimum
Annual Part Capacity
Minimum
Log Part Assembly Time
Ill-Defined Minimum Price-Time Products
Minimum Range /
Annual Part Capacity
C,
-4
A:
CC
-4
(/,
C
'4
Minimum Range
Log Part Assembly Time
Each curve represents a range of design alternatives
assuming certain parameters, such as size and number of
degrees of freedom, are held constant. Curves are
assumed monotonic, i.e., greater capacity costs more.
64
41
In
-4
4
V),
203
that equipment through its motions for any given part p
assembly time.
Reducing the number of degrees of freedom is particu-
larly effective. Each additional degree of freedom in an
assembler design requires an additional actuator, position
sensor, control circuit, and perhaps tachometer.' For
hydraulic systems, additional hydraulic capacity is required
as well as another control valve. For electric actuators
an additional driving amplifier is required. When another
degree of freedom is added, the control strategies for the
entire assembler must be expanded in capability to deal with
the extra dimension. For the same part assembly time, a
six axis assembler will certainly cost significantly more
than a three or four axis one.
When the number of degrees of freedom increases, not
only is more hardware needed for the extra degrees of free-
dom, but also some of the degrees of freedom will have to
increase in size, power, and expense. The reason is that
the degrees of freedom located relatively nearer the base
will have to be stronger and more powerful to carry the
additional degrees of freedom distributed out along the
assembler if the part assembly time is to remain the same
as that for the reduced degree of freedom device.
Of course, a six axis assembler is more versatile than
a three axis one. It may be argued that this versatility
combined with economies of scale would allow the six axis
U
204
assembler price to be reduced significantly. The six axis
assembler could certainly handle all the jobs the three
axis assembler could do and more. The argument is that this
versatility leads to a larger production volume of six axis
assemblers which by the economies of scale leads to a reduc-
tion in price and then more demand and so on.
However, the fact is that a significant fraction of
assembly can be done by a three or four axis device. As
has already been discussed in Section 5.1.2, Kondoleon (19)
has found for a small set of products that roughly two thirds
of the parts are assembled in one principal direction and
over 80 percent are assembled in only two principal direc-
tions. A three or four axis device aligned with a principal
direction could do almost all of these tasks. Kondoleon has
also found that many products have only one or two principal
directions of assembly so that three or four axis devices
generally aligned with these directions would be adequate.
Since the three axis assembler is cheaper than a six
axis one of equivalent speed, the three axis assembler should
be preferred when it can do the required tasks. If the num-
ber of assemblers required by production volume of the pro-
duct is equal to or greater than the number of principal
assembly directions anyway, then a system configuration
using three axis devices aligned with the principal assembly
directions would be more economic than using an equivalent
number of six axis assemblers of equivalent speed.
205
Since system configurations based on three axis assemb-
lers could handle a large fraction of all the programmable
assembly applications, and do it cheaper than the six axis
devices, the demand for three axis assemblers would be such
that at least the same economies of scale would apply to
them as apply to the six axis type. Consequently, the
three axis assembler will always be cheaper than the six
axis, and should be the economic choice whenever it can do
the required tasks.
The six axis assembler will find use where its extra
versatility is required -- jobs which assemblers with fewer
degrees of freedom cannot do. In particular, the six axis
assembler might be most useful where the following condi-
tions exist:
1. Complexity of assembly motions
2. Large number of parts assembled in different
directions at one station, perhaps associated
with products with low production volume where
relatively few stations are needed to satisfy
productions requirements.
3. Large uncertainty of future assembly tasks, perhaps
due to volatile product design or job shop operation.
The price of versatility is the premium paid for the
extra degrees of freedom.
7.4 Maximization of Configuration Efficiency
The configuration efficiency indicates how well
balanced the work is among the assemblers in the system.
206
If one assembler must wait idly for another assembler to
complete its work, or if an assembler is not performing
assembly tasks and instead is transferring parts or some-
thing else, the configuration efficiency is reduced.
The configuration efficiency enters in the first term
in the expression for the programmable unit assembly cost,
equation 6.12.
NPART*_TAP*PARTTIME*(R-T*DPPA)+ TOLPP* (R-T*DPTL)
U(-T) NSPY*CEF*PUEF VOL I
Since the configuration efficiency appears in the denomin-
ator of the term, reductions in configuration efficiency
lead to increases in unit assembly cost. The reason is that
reduced configuration efficiency means that more assemblers
will be required to build a system to achieve the required
production volume. Also, since the configuration efficiency
appears in the denominator of the term related to total
assembler investment in the system, the portion of the unit
assembly cost that comes from the cost of the assemblers is
inversely proportional to the configuration efficiency.
Configuration efficiency should be maximized to achieve
lower unit assembly costs. Maximization of configuration
efficiency in the design of an assembly system is accomp-
lished by two methods. First, the assembly work should be
balanced among the assemblers so that no station is slower
to complete its cycle of tasks than the others thereby forc-
ing the others to wait for it. Secondly, stations should
207
devote as much of their time as possible to assembly
operations, and pacing stations especially should avoid
doing non-assembly tasks (such as part transport, part
loading and unloading ). Such functions should be performed
by other devices, such as conveyors or the pallet indexing
system.
7.5 Summary
This chapter dealt with three consequences of the
simple economic model. First, the economic model can be
used to examine the sensitivity of the economic applica-
bility of programmable assembly to important parameters
such as labor wage rate, required annual return, and
assembler price-time product. Each of these factors can
have a significant influence on the economic applicability
of programmable assembly, but the assembler price-time
product is a variable representing the state of programmable
assembly technology, and may be improved by further research
and development.
The second, and primary, implication concerned indivi-
dual assemblers: minimization of the price-time product as
a means of selecting among competing assemblers and as a
means of resolving tradeoff issues in the design of assem-
blers. The third implication, concerned with assembly sys-
tems, was the maximization of the configuration efficiency
208
as a means of reducing the number of assemblers required
and thereby reducing the unit assembly cost.
As a means of choosing between competing assembler
designs, minimization of the price-time product is useful
to the user of programmable assemblers as well as the
designer of assemblers. The user of course must select
between competitive brands; the assembler designer must
resolve design tradeoff issues in a way that produces an
economic and competitive product.
In the design of an assembler, the tradeoff issues
will produce a range of design options that may have a
sharp, well-defined price-time product minimum or a shallow,
ill-defined minimum. In the case of the well-defined
minimum, one design is significantly more economic than the
others. In the case of the ill-defined minimum, a range
of designs are "nearly" best. Then, other considerations
will be necessary to resolve the assembler design tradeoff.
Alternatively, the builder of assemblers may decide to
offer a range of assembler designs of near-minimum price-
time product to the user so that he may choose the design
that best fits his system needs.
The price-time product criterion, having been ob-
tained from the simple economic model in which continuous
station numbers were permitted, can be shown to be valid for
integral station numbers when examined from the point of view
of the assembly system designer.
209
Configuration efficiency as a measure of assembly
system design was examined. Configuration efficiency should
be as high as possible because this leads to a requirement
for fewer assemblers in the assembly system, which will ul-
timately reduce system cost. Configuration efficiency may
be improved by balancing the assembly tasks so that there
is as little waiting time as possible for any assembly assem-
bler and by reducing the number of nonassembly tasks that
are performed by the assemblers.
210
8. EXAMPLE DESIGN PROCESS FOR A THREE AXIS
PROGRAMMABLE ASSEMBLER
8.1 Introduction
It has been shown in the previous chapter that the
minimization of the price-time product provides a means
to choose between assemblers of very different configuration
and technology with respect to application in specific
assembly systems. The minimization of the price-time
product is also helpful in the design of a specific type of
assembler. An example of such a design process will be
given in this chapter. It will be concerned with only one
important design tradeoff.
The designer of an assembly system has specific re-
quirements for the assemblers he uses in his system in
211
addition to the need for them to be economic. Because
of the product and its assembly sequence, the system
designer may require a certain payload capacity, a
certain number and arrangement of degrees of freedom,
and/or a minimum range of motion. Assemblers with less
payload capacity, fewer degrees of freedom, and/or smaller
size will almost certainly have lower price-time products,
but will just as certainly be inadequate for the system
designer's specific application.
This chapter concerns the design of a particular
three axis assembler in which the arrangement of the
axes is fixed. The problem is formulated so that the
size of the assembler can be fixed at any value within a
size range. Once the size of the assembler is fixed, the
torque capacity of the actuators remains to be chosen.
Suppose that we have selected a nominal choice of
actuator torque capacity. If actuators with greater torque
are chosen, then the assembler may have a shorter part
assembly time. However, these stronger actuators will
certainly cost more, and so the station price will increase.
The price-time product will probably change, but because
the factors move in opposite senses, it is not clear whether
their product will increase or decrease. Minimization of
the price-time product can be used as a way to choose the
actuators to achieve an economical design. In this chapter
it will be shown that, as actuator power is varied, there is
212
a region of actuator power where the price-time product is
a minimum.
The design process described in this chapter requires
the ability to model the actuator power needed for a cer-
tain single part assembly time and the assembler station
price as a function of the actuator power as well as the
other components. These two functions will allow us to
plot curves on the price-time chart showing how price and
time vary as actuator power is varied while assembler size
is held constant.
The remainder of the chapter includes a description
of the assembler and the design process for the actuators,
the development of the assembler station pricing model,-
sample results of the design process, and an analysis of
these sample results with respect to consequences for
research and development of programmable assembly.
8.2 Physical Description
The device is illustrated in Figure 8.1. It is a
three axis assembler with cylindrical symmetry. A part
gripper is carried at the end of a horizontally moving
degree of freedom. This horizontal degree of freedom is
rotated about a vertical axis by a rotary actuator.
Finally, both.the horizontal and rotary degrees of freedom
are raised and lowered by a vertical degree of freedom.
213
Figure Re Sketch of Example Three Axis Assembler
Rotary Axis
Motor'
Horizontal Axis Motor
Horizontal Axis Ball Screw
4$
Stiffening Shaft
Part
Gripper
Vertical Axis Ball Screw
Stiffening Shaft
vertic
Axi s
motor
214
This arrangement of actuators was chosen because of the
simplicity of construction it offers. Another arrangement
would have been to switch the positions of the rotary and
vertical axes, so that the rotary axis carries the other
two. The actuators for all three axes are electric. Motion
for the vertical and horizontal axes is accomplished by
means of ball screws. Certain limitations on ball screw
design, such as maximum critical speed, are not considered
here. it is assumed that the ball nut is preloaded to
eliminate backlash. The moving frame carrying the part
gripper is assumed to be made of aluminum, and its mass
is estimated from its size.
Resolvers are assumed for measuring the axes' positions.
One resolver converter will be multiplexed to read all three
resolvers. Each axis is also assumed to have a tachometer
to provide velocity informasion to the servo electronics
for that axis. A processor will be dedicated to each
assembler and will be responsible for issuing position and/or
velocity commands to each axis servo system. The processor
will also contain the programming necessary for the assembler
to execute its specific assembly task sequence.
The assembler is mounted on a segment of an index table
or conveying device. This device carries subassemblies
to and from the assembler itself. Together the assembler
and the segment of conveying device upon which it is mounted
form the assembly station.
8.3
8.3.1
215
Actuator Selection Process
Selection Process Outline
In the actuator selection process the single part
assembly time is regarded as a fixed value. Once this part
assembly time is given, the design procedure will choose a
consistent set of actuators for the three axes.
It will be assumed that the requirements of the
gross motion will largely determine the motor require-
ments and that the time the assembler spends in gross
motion will be a certain fraction of the total part
assembly time. With these assumptions a given part assembly
time implies a given gross motion time which will in turn
be used to estimate the actuator power requirements.
Specifically,-the power requirements are determined for a
certain nominal gross motion trajectory completed within
the given gross motion time.
The sequence for determining the actuator power is
as follows:
1. Estimate the power required for the horizontal
axis. This is the axis farthest from the base.
2. Estimate the corresponding mass for the horizon-
tal actuator.
h
L
216
3. Estimate the required actuator power for the
rotational axis including the mass of the horizon-
tal motor.
4. Estimate the mass of the rotary axis actuator.
5. Estimate the required actuator power for the
vertical axis including all of the moving hardware
mass including the horizontal and rotary actuators.
Hence, each actuator is automatically chosen to move its
axis and any attached load.
A procedure will be developed to estimate the power and
torque required to move a single axis if its load mass and
required gross motion time is known. This procedure will
then be used to estimate the power and torque requirements
for each of the three axes in the design sequence described
above.
8.3.2 Motion Cycle of the Single Part Assembly Time
The microeconomic analysis of the previour chapters
treated the single part assembly time as a basic parameter,
but actually it is made up of a series of individual opera-
tions. For the purpose of this analysis the following
sequence of operations will be assumed to occur during one
part assembly cycle:
1. Assembler moves to part presentation site (gross
motion).
217
2. Assembler grasps part from part presentation
device (fine motion).
3. Assembler carries part in gross motion to assembly
site (gross motion).
4. Assembler fits parts together (fine motion).
5. Assembler releases part (fine motion).
Notice that there are no tool changes involved. It is
assumed that one part gripper will be satisfactory for all
parts handled by any one assembler, which means that it is
not necessary to consider any time devoted to ch jing tools
or the part gripper. This is a favorable assumptuon since
it tends to increase the production rate of the assembler
station. This same analysis could also be done assuming that
the assembler must change tools or grippers for every part
and so would represent the other extreme.
The total part assembly time is composed of two gross
motions and three fine motions. Accordingly, we may model
the single part assembly time as follows.
PARTTIME = 2*TGM + FMT (8.1)
where PARTTIME = average single part assembly time
TGM = average time for one gross motion
FMT = total time for all fine motions during
the single part assembly cycle.
We now make the additional assumption that the total fine
motion time FMT is proportional to the time for one gross
218
motion TGM. We make this assumption by reasoning that an
assembler with fast gross motion capability will also be
able to execute the small fine motions quickly. This
assumed proportionality will be expressed by defining the
ratio of the total gross motion time in a part assembly
cycle to the total part assembly time as follows:
GRATIO = 2 * TGM (8.2)
PARTTIME
where GRATIO = fraction of part assembly time in gross
motion
8.3.3 Torque Requirements for a Single Degree of
Freedom
A gross motion is a large displacement of one or more
assembler axes, perhaps from one extreme of its travel range
to the other. This motion should be made in minimum time.
We will make the assumption that principal limitation of
the actuator that drives an axis is with respect to its
torque. To obtain minimum time, gross motion trajectories
will be generated by applying maximum torque in the forward
direction for the first half of the motion, then maximum re-
verse torque for the second half. A roughly triangular
velocity profile would result for a single gross motion, as
shown in Figure 8.2.
219
Figure 8.92s Modeling Gross Motion
>2 seeTriangular Area
sesameRepresents Distance
gos@Traveled (DIST)
seasns oom* ease 0*.* * . *a
eases*s* *so a 0 a am,
. . * :oes 0 ..
Ti a0me a0,1 0001
TGMTa TOM
Settling Time
220
Notice that two forms of the motion are shown in
Figure 8.2: First, a triangular shape with sharp corners
representing the ideal motion, and, second, a smoother
shape with rounded corners and longer duration representing
the way the axis will actually move under servo control.
The duration of the theoretical motion will be designated
TGMT, and the longer duration of the servo motion will be
designated TGM. Similarly, the duration of the theoretical
single part assembly time will be called PARTTIMET; the
actual single part assembly time, PARTTIME. The analysis
will proceed using the theoretical motions as the bases for
the modeling. Later, a correction factor will be applied
to estimate the lengthening effects of the settling time of
the motions.
It will be assumed that the actual motions are longer
than the theoretical ones by a fixed fraction.
SETLF = TGM-TGMT (8.3)TGMT
where SETLF = fractional duration of the actual gross
motion time beyond the theoretical time,
i.e., the settling time fraction
TGMT = theoretical gross motion time.
We will assume that the same correction factor applies
to fine motion time. Hence, by extension, the factor
applies to the entire single part assembly time.
221
SETLF = PARTTIME - PARTTIMET (8.4)
PARTTIMET
where PARTTIMET = theoretical single part assembly time
Finally, it can be shown that the gross motion ratio can
also be expressed in terms of the theoretical times defined
above.
GRATIO = 2 * TGMT(8.5)
PARTTIMIET
We now seek to derive a simple model for the torque
requirements for a single assembler axis assuming that a
desired gross motion time and a desired gross motion dis-
placement are given. Later this relation will be combined
with a model of electric motor thermal limitation and the
previously developed model relating single part assembly
time to gross motion 'time. The result will be a model
estimating the electric motor capacity needed for a given
assembler axis.
The physical model of one degree of freedom is shown in
Figure 8.3. A mass M, consisting of supporting beam,
part gripper, and part, moves along dimension x. This is
driven through ball screw or rack and pinion gearing by a
motor or rotary actuator. The rotary parts have combined
inertia J in the rotary displacement direction 6. The rela-
tionship between x andO is
Ax = CAG (8.6)
where Ax = small change in x
AO = small change in 6
222 
Pigure 8.J, Model of Single Aaeeabler Axis 
Rotary 
Inertia 
J 
Torque Tran .. ieaion 
Inefficiencies 
Motor + Tachometer + Resolver 
Linear Moving Mass M 
.. 
X 
Rotary-Linear ConYeraion Relation, 
�x • C �8
223
C = conversion constant
The ideal relationship between torque about axis 6 and
force F in direction x is
TORQ = C * F (8.7)
where TORQ = torque about axis 6
F = force in x direction
This relationship ignores torque transmission inefficiencies,
which will be dealt with later.
For a given gross motion, the maximum velocity is a
function of the length and the time of the gross motion.
VMAX =2*ST (8.8)
TGMT
where VMAX = peak velocity in x direction
DIST = distance of gross motion
TGMT = time of gross motion, theoretical
The magnitude of the equal and opposite initial and final
accelerations is a function of the motion time and maximum
velocity.
VMAX
ACC =TMT/(8.9)(TGMT/2)
where ACC = magnitude of required acceleration
The required acceleration as a function of distance and
motion is given by combining equations 8.8 and 8.9.
4*DIST
ACC = TGMT(8.10)
TGMTt
The iner tia tha t mus t be ac ce lera te d is a c ombina tion
224
of the linear moving mass (supporting beam, part, part
gripper, and other axes) and the rotary inertia (motor
rotor, gear, and shaft). This effective mass is modeled
here.
EM = M +(8.11)
C
where EM = effective mass to be moved in x direction
M = linear moving mass
J = rotary inertia
The mass M will vary in practice for two reasons.
First, the paylcad of the assembler will vary as different
parts are assembled. As parts change and the load varies,
the mass that must be moved by every axis will vary.
Secondly, certain axes may interact in such a way that the
position of one axis will affect the load or inertia on
another axis. For example, the extension of the horizontal
axis will affect the rotary inertia seen by the rotary
axis motor: If the horizontal axis is fully extended, the
rotary inertia on the rotary axis is large. If the hori-
zontal axis is retracted, the rotary inertia is less.
We now have both effective mass and required accelera-
tion in the x direction. Using Newton's law we may express
the required force as
FR M+J 4 * DISTFR -IST(8.12)
C TGMT
where FR = required force in x direction
225
The ccrresponding torque required from the motor is ob-
tained by combining equation 8.12 with equation 8.7.
TR = C* M+ 4*DIST (8.13)
TGMT
where TR = torque required on load
The derivation so far has assumed that there are no
losses in the system. It is now assumed that there are
losses that result in a torque transmission efficiency less
than one. The torque at the motor must be greater than the
required torque to account for this.
TR = TEF * TORQ (8.14)
where TORQ = torque that motor must deliver
TEF = torque transmission efficiency (less than
one)
Here the torque transmission efficiency is used to
describe the losses that occur in the mechanism of the
axis. Frequently motion transmission and conversion de-
vices such as gearboxes and ball screws are described with
efficiencies defined in terms of power. For example, ball
screws are described as about 90 percent efficient, meaning
that 10 percent of the input power is lost. A constant tor-
que transmission efficiency corresponds to a constant power
efficiency and has the same value. The actual loss pro-
cesses are usually functions (often nonlinear) of the velo-
city of the device, and the true power efficiency varies
226
accordingly. However, in keeping with the level of modeling
established for this analysis, we will assume the torque
transmission efficiency to be a constant and will choose
a representative value.
Combining equations 8.14 and 8.13 we have
TORQ = 4*DIST*C * (M+- (8.15)22TEF*TGMT2C
Solving for time of gross motion gives
TGMT = 2 * DIST*C * M + - (8.15)
TEF*TORQ C2
8.3.4 Torque Limitation of Electric Actuators
We have developed models for the single part assembly
cycle and the torque requirements of a single gross motion.
A model must now be developed for the torque an electric
motor can deliver for the gross motions in a single part
assembly cycle.
The torque requirements of a single part assembly
cycle (assuming constant load mass) are illustrated in
Figure 8.4. During the gross motions the torque history
has a square wave character because tne axis is undergoing
maximum acceleration and deceleration. During the rest of
the .part assembly cycle it will be assumed that the torque
will be at comparatively low levels, or essentially zero
when compared to the maximum values. During these fine
227
Figure 8.4.
TMAX
0
-TMAX
Torque Requirements for Single Part
Assembly Cycle
Time
Gross
-Motion-
TGMT
Gross
Motion
TGNT
Cycle Period
PARTTIMET-I[4
I
I
I
228
motion times only very small movements are taking place.
(The effect of a constant gravitational loading will be
discussed later).
The common limitation on electric motors is electrical
resistance heating of the windings. At any moment the
power dissipated as heat is proportional to the square of
the current through the device. Since the torque of a DC
motor is proportional to the current through the winding,
then the instantaneous power lost as heat is proportional
to the square of the instantaneous torque. This proportion-
ality also applies to the time averages; that is, the
average power lost as heat is proportional to the average
of the square of the torque.
For mechanical systems such as this one where the
periodic motions are much faster than the thermal time
constant of the motor (about half an hour), temperature
deviations about the mean values due to the part assembly
cycling are small. Therefore, the following analysis will
be concerned only with average thermal effects.
One of the parameters with which electric motors are
rated is their maximum continuous torque. This essentially
represents the thermal limit of the motor. The square of the
maximum continuous torque is priportional to the maximum aver-
age power that the riotor can safely dissipate as heat.
We now model the average of the square of the torque
for the single part assembly cycle illustrated in Figure 8.5.
229
Figure 8.5, Gross Motion in Part Assembly Cycle
____ L ______________ I.Li
I
I
I
I
I
I
--K
- - - +TORQ
-- -TORQ
40
4-)
W.4
go
Gross
Motion
to Part
Site
TGMT
P.
a e
842if.
Gross
Motion to
Assembly
Site
TGNT
Fine Motion at
Assembly Site
Single Part Assembly Time (Theoretical
PARTTINET
I
I i
1
I I
S
0 t
) b
-u-- - - m -- I I
Ml
I w
-
230 
This is easy to do because of the square = ve character of 
the torque history. 
AVTSQ = (��!;;iMET) * TORQ
2 
(8.17)
where AVTSQ = average value of square of torque 
TORQ = 11Bgnitude of torque during gross motion 
If we wish to operate the electric motor at its 11Bxi-
mum capacity, then the average value of the square of the 
torque AVTSQ should equal the square of the continuous torque 
�ating of the motor. 
where 
AVTSQ = CONTRQ
2 
(8 . 18)
CONTRQ = IIBximum continuous torque rating of the 
the motor 
Equation 8.17 and equation 8.18 may be combined to 
produce an expression far the gross motion maximum torque. 
-!,; 
TORQ = ( 
PARTTIMET
)2*TGMT * CONTRQ (8.19) 
Finally, the definition of the gross motion ratio GRATIO, 
equation 8.5, can be used to simplify this last expression. 
TORQ = GRATIO-J,, * CONTRQ ( 8. 20)
The case when there is a constant gravitational load 
on the electric motor is illustrated in Figure 8.6. In 
this case there are two components of the torque history 
the inertial component as before and a constant gravitation­
al component. The average square of the torque can be 
231
Figure 8.6. Torque History with Gravitational Component
fl .-
Time
Single Part Assembly Time (Theoretical) J
PARTTIMET ri
TG = gravitational torque component
S
vS
- - 1 -1 I 
232
expressed as
r PARTTIMET 2
AVTSQ = PARTTIMET] (TG+TI) dt
where TG = constant gravitational torque
TI = "square wave" inertial torque
t = time
This integral may be expressed as follows:
2 (PARTTIMET
AVTSQ =PARTTIMET dt
(8.21)
fPARTTIMET
2+TG TI dt
PARTTIMETATj
+ PARTTIMET TI 2 dt (8.22)
The first integral in the sum above reduces to TG2. The
second integral is equal to zero because the average value
of the ,inertial torque is zero. The third integral corres-
ponds to the average va lue of the square of the torque
without gravity, equation 8.17. This results in the following
expression for the average squared torque:
AVTSQ = TG2- + GRATIO * TORQ2  (8.23)
Here TORQ still represents the amplitude of the square
wave of the inertial torque without the gravitational torque.
In order to operate the motor at its maximum capacity,
we specify that the average squared torque should equal the
square of the maximum oontinuous torque rating of the motor.
CONTRQ 2 = TG2 + GRATIO * TORQ (8.24)
233
The amplitude of the inertial torque becomes
2 _ 2 (.5TORQ = (CONTRQ - TG ) * GRATIO2 (8.25)
8.3.5 Model for Single Part Assembly Time
Now the models developed in the previous sections can
be combined to develop a model for the motor requirements
for a single assembler axis. The single part assembly
time can be expressed as a function of the theoretical
gross motion time from equation 8.5.
PARTTIME = (l+SETLF) 2*TGMT (8.26)GRATIO
This expression may be combined with equation 8.20, an
expression for the time for a single gross motion.
PARTTIME = 4*(1+SETLF)(/DIST*C * M+-2 (8.27)
GRATIO \EF*TORQ( C,2 (2
Finally, the expression for the torque that the electric
motor can deliver, equation 8.25, can be substituted above.
PARTTIME=4*(l+SETLF)* ,/DIST * C M+- *GRATIO-3/4
TEF*(CONTRQ2
-TG2 I2 C2
(8.28)
There are still some functional relationships to be
determined. For example, the distance of the gross motion
DIST an the mass M of the assembler axis may be related to
the size of the unit. The motor rotational inertia will be
related to the motor power. The torque transmission effi-
ciency TEF will be related to the type of gearing used.
234
These relationships are dependent upon the specifics of
the design and upon empirical relationships, such as those
relating power to rotor inertia. The empirical and design
relations have been kept separate in this analysis so that
in future work different relations could be substituted
and examined.
The equation for the single part assembly time (8.28)
is used three times in the design process for the three
axis assembler--once for each axis--according to the out-
line given in section 8.3.1. The values for moving mass
M and effective gravitational torque TG will vary depending
upon which axis is being considered. For example, in the
configuration of the example, there is no gravitational
torque on the horizonL L or rotary axis actuator,. but there
is such a torque on the vertical axis actuator. This ver-
tical axis torque will depend on the weight of the other
axes including their actuators. In order to estimate the
inertial load of the rotary axis, the horizontal axis was
considered to be extended to one half of its length.
The linear/rotary conversion constant C for each axis
will depend on the lead length of the ball screws used.
(For the rotary axis no conversion is necessary.) In this
analysis the ball screw lead length is chosen as a fixed
fraction of the ball screw diameter. The ball screw diameter
is chosen to provide a certain deflection of the horizontal
axis endpoint under the assembler payload. The deflection
235
is computed by assuming that the structural members of the
horizontal and vertical axes consist of the ball screw and
a stiffening shaft of the same diameter (sce Figure 8.1),
and that the direction of the applied force is perpendicu-
lar to the plane formed by the ball screw and the stiffen-
ing shaft. Therefore, the axis is twice as stiff as the
ball screw alone. Finally, the required payload is estimat-
ed from a power law based on the size of the assembler.
The design sequence is shown in Table 8.1.
Table 8.1
236
Three Axis Assembler Design Sequence
1. Choose assembler size and desired single part assembly
time.
2. Specify payload corresponding to assembler size.
3. Choose ball screw diameter for acceptable deflection of
horizontal axis.
4. Estimate horizontal axis moving mass and ball screw lea
5. Estimate necessary horizontal actuator torque rating.
6. Estimate horizontal actuator mass, power, and size.
7. Estimate rotary inertial load for rotary axis actuator.
8. Estimate necessary rotary axis actuator torque rating.
9. Estimate rotary axis actuator mass, power, and size.
10. Estimate mass load of vertical axis.
11. Estimate necessary vertical actuator torque rating.
12. Estimate vertical actuator power.
d.
237
It is important to the economic analysis to estimate
an average single part assembly time. To do this a test
motion for each axis was chosen to be two thirds of the
range of motion of that actuatcr. This will result in a
single part assembly time that is average under the assump-
tion that a grcss motion of any given length is just as
likely as any other length. The factor two thirds is a
result of the fact that gross motion time is a functicn of
the square root of the motion distance.
8.3.6 Empirical and Assumed Relationships
Several empirical relationships are needed to complete
the modeling of the dynamics of the example three axis
assembler design. Among them are relationships between
motor power and motor mass, rotor inertia, continuous torque
capacity, and motor length. (Motor length of the horizontal
axis motor was used to compute a rotational inertia seen by
the rotary axis motor.) Data for the empirical relationships
for the motors was obtained from catalogs for DC torque
motors. Additional assumed relationships were developed re-
lating ball screw lead length to ball screw diameter, bali
screw diameter to axis deflection, and payload to assembler
size. These relationships will be treated briefly below:
1) Continuous torque vs. actuator motor power. This
relationship is shown in Figure 8.7. The manually
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239
fitted curve. used to represent the relationship is
CONTRQ = 6.372*10~4 * P.357 (8.29)
where CONTRQ = continuous torque rating, newton-
meters
P = motor power rating, watts
2) Motor mass vs. motor power. This relationship is
shown in Figure 8.8. Here, the manually fitted curve
is
MM = 6.76*10 -2 875 (8.30)
where MM = motor mass, kg
P = motor power rating, w
3) Motor length vs. motor power. The data and the
following manually fitted relationship are shown in
Figure 8.9.
ML = 2.34 * 10 *2,P-4(8.31)
where ML = motor length, m
P = motor power rating, watts
4) Motor rotor inertia vs, motor power. The following
relationship was fitted to the data shown in Figure
8.10.
JM = 3.2 * 10-6 *P (8.32)
where JM = motor rotor inertia, nt-m-sec 2
P = motor power rating, watts.
5) Ball screw lead length vs. diameter. Ball screw lead
length (that is, the distance the ball nut travels down
240
Figure 8.8. Motor Mass versus Motor Power
100.0
0W
01
10 100 1000 10,000
Notor Power Rating (watts)
241
?igure 8.9. Motor Length versus Motor Power
.1-
01
t I I I 111111 1 1 I I trl I I I iii
0L
10 100
Motor Power
1000
Rating (watts)
109000
I
o
4
A
0
64
0*0
242
Figure 8.10u Motor Rotor Inertia versus Motor Power
10-41L
10
1111 I I li I '
10,000100 1000
Mtsr Power Rating (watts)
10 l
40a:
Ito
0
I I I I 1 1111
e0
i i i i10
MMMIS&
-
I I I I I 1 1
A-L
243
the long axis of the screw during one screw rotation)
may be modeled as proportional to the diameter of the
ball screw. However, the proportionality constant way
vary through a range from .1 to 1.0 -
6) Ball screw diameter and axis stiffness. The diameter
of the ball screw was specified so that the vertical
deflection of the horizontal axis (ball screw and
stiffener) was less than a certain maximum amount when
carrying the payload. This deflection was set at
5 * 10- inch. The diameter of the vertical axis ball
screw was specified so that the vertical axis (ball
screw and stiffener) would meet the same deflection
criterion if the assembler were rotated so that the
vertical axis was horizontal.
7) Payload scaling law. A power law was used to specify
payloads for the different sizes of assemblers. Thi:
power law was
PL = 10 * DH1.301
where PL = payload, kg
DH = length of horizontal axis, i
The effect of this law is to specify a 10 kg payload
for an assembler with a reach of 1 m, and a 0.5 kg
payload for an assembler with a reach of .1 m. This
scaling law was used as a sp'ecification rule, and was
not meant to describe current industrial manipulator
244
design. Furthermore this scaling law is not meant
to describe absolute maximum payloads, but rather pay-
loads for the purpose of computing power requirements
for gross motions.
8) Gross motion ratio. A gross motion ratio GRATIO of
.4 has been assumed. This is really an estimate based
on several different estimates of the time breakdown
in a part assembly cycle. One such breakdown is given
below. It was generated by examining performance data
for an industrial robot currently under development.
a) Gross motion to pick up part -- 1.0. sec
b) Grasp part -- .5 sec
c) Gross motion to assembly site -- 1.0 sec
d) Assembly fine motion -- 2.0 sec
e) Release part -- .5 sec
Total -- 5.0 sec
The total average assembly cycle time is about 5 sec
for this device, and, since a single gross motion
time is roughly 1 sec, the gross motion ratio for the
cycle is about .4.
9) Settling time fraction. A settling time fraction
SETLF of .2 was assumed. This number was cbtained
from observations of the motion of certain currently
available industrial robots.
245
8.4 Modeling Station Price
Until now we have concentrated on describing the per-
forrance of a degree of freedom in terms of the physical
parameters of the hardware and the characteristics of the
motor. We now turn to estimating the costs associated
with the assembly station.
8.4.1 The Basic Model
A basic assumption of the microeconomic modeling
work was that the station price should include all costs
associated with the station. Therefore, the station price
must include
1) The cost of the assembler itself.
2) The cost of all system equipment directly related
to the assembler, such as the cost of the portion
of the conveying or indexing device on which the
assembler is mounted.
3) Cost of engineering, building, and debugging
the station.
These costs must all be measured from the point of view
of the user of the programmable assembly system.
For the purpose of modeling station price, all station
costs can be divided into variable and constant costs.
246
Variable costs are functions cf the parameters that are
allowed to vary in a particular design study; constant costs
are rot. In the present analysis of the three axis assem-
bler, motor power and the size of the assembler are the
principal parameters that are allowed to vary and are de-
termined by the part assembly time specification. Costs
that are not a function of motor power or assembler size
will be assumed constant. In this station price model the
variable costs will be developed as functions of motor
power and assembler size.
The assumed model for the station price is as follows:
STAP = ASMPRC + IDXCST + INTCST (8.33)
where STAP = total station price
ASMPRC = purchase price of assembler
IDXCST = cost of portion of index or conveying
device dedicated to the assembler (assumed
constant)
INTCST = cost of engineering, building, and
debugging station (assumed constant)
Of the terms composing the station price, only the assembler
price will be assumed variable.
The assembler purchase price ASMPRC is not the same as
the manufacturing cost cf the assembler. The firm that makes
the assembler must charge a price higher than its direct
costs to cover the indirect costs of doing business and to
make a profit. Therefore, we assume
247
ASMPPC = PFCTR * ASMCST (8.34)
where PFCTR = price factor
ASMCST = direct manufacturing costs of the assembler
In the industrial robot and manipulator industry, the most
common value of the price factor is two, and this is the
value we will use in this example.
We now turn to the modeling of the direct manufacturing
cost of the assembler, ASMCST. Some component costs will be
considered constant and some will be considered as functions
of motor power or assembler size; that is,
ASMCST = EVARIABLE COSTS + ECONSTANT COSTS (8.35)
The items which will contribute to the variable costs are
listed in Table 8.2.
Power laws were used to model the parameters of the
physical model of assembler performance, but linear models
will be used to model the cost relationships. The reason is
that the cost data is fitted better by linear relationships,
at least in the area of interest. In particular, the cost
function of an assembler component is often the sum of a
constant, fixed cost and a variable cost that is linear with
respect to the cost function. When plotted on log-log
scales, the constant cost component produces a horizontal
asymptote at the low end of the curve resulting in a
curved plot.
248
TLble 8.2 Variable Component Costs for Example
Three Axis Assembler Design
Horizontal Axis Motor
Horizontal Axis Amplifier
Horizontal Axis Hardware (inchudes ball screw)
Rotary Axis Motor
Rotary Axis Amplifier
Vertical Axis Motor
Vertical Axis Amplifier
Vertical Axis Hardeare (includes ball screw)
I
249 
Table 8.3 lists the components whose cos�s will be 
considered constant for this analysis. Notice that a 
direct labor cost for assembling the components is 
included. 
250
Table 8.3: Components with Assumed Constant Cost
Horizontal Axis Tachometer
Horizontal Axis Resolver
Rotary Axis Tachometer
Rotary Axis Resolver
Rotary Axis Hardware
Vertical Axis Tachometer
Vertical Axis Resolver
Assembler Base
Gripper
Resolver Converter
Processor
Miscellaneous Components
Direct Labor
Index Device Segment
System Integration Cost
251
8.4.2 Empirical Price Relationships
Empiral price relationships have been developed for
DC motors and their driving amplifiers as a function of
the motor power. Also, an approximate price relationship
has been assumed for the ball screw axes as a function of
their length. Nominal values have been assumed for the
remaining constant costs and will be presented here.
1) Motor price vs. motor power. The data and the fitted
empirical relationship are shown in Figure 8.11.
The relationship is
MOTCST = 580. + .446 * (P-1118.55) (8.36)
where MOTCST = motor cost, dollars
P = motor power rating, watts
This relationship gives a reasonable estimate
for motors up to about 2000 watts.
2) Amplifier cost vs. motor power. The data and the
manually fitted relationship are shown in Figure 8.12.
The relationship is
APCST = 180. + .2667 * (P-500) (8.37)
where APCST = driving amplifier cost, dollars
P = motor power, watts
The amplifier power capacity is usually higher than
that of the motor with which it is matched. The pricing
function for the driving amplifiers must take this into
account.
252
Figure 8.11 Motor Cost versus Motor Power
0 500 1000 1500
Motor Power Rating (watts)
2000
800,
60
.4
*C 0
4.
253
Figure 8.12. Amplifier Cost versus Motor Power
800
6001
4001
2001
0
- -
0 500 1060 1500
Motor Power Rating (watts)
I
2000
U
'4
C
'0
'a,
43
U
C
C,
'4
S
wE
'4
wE
254
3) Ball screw Cost vs. ball screw length. The data
and empirical relationship for the cost of the ball
screws is shown in Figure 8.13. This relationship is
approxinntely
BSCST = 24 * D (8.38)
where BSCST = ball screw cost, dollars
D = length of ball screw, m
Given the variation among ball screw prices, this
relation can only be a rough approximation at
best. Fortunately, the cost of the ball screw is
not a large fraction of the total assembler cost.
4) Constant costs. A list of constant costs is given
in Table 8.4. These costs do not vary as the actua-
tor power or size is varied.
The assumptions leading to one of the constant costs--
the system integration cost--are important and should be
discussed. The system integration cost is the engineering,
debugging, and machine shop labor that is devoted to the
integration of the programmable assembler into a station
of the programmable system. It does not include similar
labor devoted to the implementation of parts feeding equip-
ment surrounding the station. It is assumed that both the
assembler and the conveying or indexing chassis are pur-
chased complete from suppliers. The assembly station in-
tegration task consists of mounting the assembler on the
255
Figure 8.13a Ball Screw Price versus Length
50
0
40
410-
01
0
0 005 160 105 2.0
Ball Screw Length (motors)
R
256
Table 8.4: Values for Constant Prices for Example
Three Axis Assembler Design
Tachometer $150
Resolver $50
Rotary Axis Hardware $50
Assembler Base $100
Gripper $200
Resolver Converter $600
Processor $4000
Miscellaneous Components $1000
Direct Labor $500
Index Device Segment $2000
System Integration Cost $4000
257
conveying device in a location so that it is positioned
properly with respect to the product and the part presen-
tation devices. The programmability of the assembler
means that its location need not be specified particularly
accurately although angular alignment accuracy for a three
axis device way be important.
After the assembler and the parts feeding tooling are
mounted on the chassis, the assembler must be programmed
(using stock routines) to execute its assembly task sequence.
This programming process may go through a few cycles be-
fore a satisfactory program is developed. The system in-
tegration cost estimate of $4000 per station is roughly
one man-month of an engineer's time plus supporting
technician labor.
Both the variable and constant costs presented in
this section should be considered as examples only. They
should be viewed as merely estimates of unit costs for
quantity purchases of the components. They are certainly
not meant to represent the best available prices.
8.5 Sample Results
8.5.1 Sample Price-Time Curves
The design process described in the previous sections
has been used to develop a set of price-time curves shown
258
in Figure 8.14. Each curve represents a different assembler
size.
The assembler size is defined by the length of the
horizontal axis. The vertical axis is assumed to have the
same length as the horizontal one. The rotary axis is
assumed to have nearly 360 degrees of motion range, but
most of the motions made by the rotary axis are assumed
to be less than 90 degrees.
The curves in Figure 8.14 show how the station price
for an assembler increases with requirements for shorter
single part assembly time. The curves are plotted using
dashed lines where an individual actuator power was spec-
ified in excess of 3000 watts to show how power requirements
increase with assembler size. The actuators become very
heavy and bulky for large power, and so then the practi-
cality of the design becomes questionable. In cases for
the larger assemblers, the price-time product minimum
occurs in the region where an individual actuator power
exceeds 3000 watts.
The constant cost components begin to dominate for
the longer part assembly times where the price-time curves
become very flat. Station assembler designs in this
region have nearly the same price but widely varying speeds
and, therefore, widely varying price-time products.
The spacing of the price-time curves shows that, for
this three axis configuration, the effect of assembler
259
Figure 8.14t Price-Time Curves for Example
Three Axis Design
10001
20,
10,
000 - I t I I I
0.7m
000 -~
~\
0.1
000-
Priee-Time e+++
ProductV+ 0*ire 00
($-sec)o
000
1 2 3 4 5 6 78910
Single Part Assembly Time (seconds)
Price-time curves for example three axis designs
in which horizontal and vertical axes are both
.1 *, .4 m, .7 a. and 1.0 m respectively. Dashed
lines indicate that at least one actuator is over
3000 watts.
r-4
0
40
V)4
50.1
260
size on price-time product is less for the smaller assem-
blers (less than .4 m). Considering the set of minimum
price-time product designs, the increase in price-time
product from the .1 m assembler to the .4 m assembler is
relatively small compared to the increase from the .4 m
to the .7 m assembler, or from the .7 m to the 1.0 m assem-
bler. Hence, for the assembler design represented by this
model, the size of the assembler is a more important in-
fluence on the price-time product if the assembler is
large than if it is small.
The design of an assembler is a complicated process
involving rany kinds of constraints. The price-time
curves of Figure 8.14 represent the results of a very
simple model of assembler cost and performance for one
type of assembler. Their use in this thesis is to
examine general trends and to obtain some estimate of
what price and performance may be possible for a three
axis assembler of this particular type. In the following
section, the "sensitivity" of this design to various
important parameters will be defined and discussed as an
aid to identifying areas of further research work in
assembler design.
However, if the price-time curves of Figure 8.14
are used as part of a design process for a specific
assembler, then it is important that the curves be re-
fined at sUcceeding stages of the design process. These
261
initial curves should be used only to narrow the range of
possible designs under consideration rather than to pin-
point an exact one. Once such a range is defined, then the
various design relations and assumptions should be reeval-
uated to be more accurate in the narrower range. The
designs should be more thoroughly checked to see if there
are constraints not accounted for in the simple formulation
that would affect the design in the local range.
For example, the physical size of a 3000 watt motor
would make it impractical to use with a small assembler
(say .1 m assembler as defined above). The size of the
motor was not considered for all the axes in the simple
formulation. This is not a problem for the larger assemb-
lers but it is a problem for the smaller ones. Hence, for
small assemblers of this type, one of the new design con-
straints that shoulc be added for specific designs is motor
size.
Similar reformulation may have to be repeated several
times as the design becomes more specific.
8.5.2 Sensitivities of Price-Time Product to
Component Variation
We now examine a particular design point selected from
the price-time curves of the previous section corresponding
to horizontal and vertical axis length of .4 m and part
262
assembly time of 1.8 sec. The important physical design
statistics are given in Table 8.5. The price breakdown of
the assembler station is given in Table 8.6. This is
nearly a minimum-price-time product design.
By examining the price breakdown we can see that there
are certain large components of the station cost; such as
the system integration cost, the processor cost,, and the
cost of the index device. The average hardware cost of
each axis is about $1000, but, because of the price factor
of two, the cost per axis to the system user is about $2000.
These large price components are primary targets for further
work to develop economic programmable assembly stations.
In order to develop a procedure for assessing the
importance of further work in economic assembler design, we
define a price-time product sensitivity as follows:
A(STAP * PARTTIME)
PTS. (STAP * PARTTIME) (8.39)
J AP.
P.
J
where PTS. = price-time product sensitivity of parameter j
)
STAP*PARTTIME = price-time product
P. = parameter j
J
A(STAP*PARTTIME) = snall change in price-time
product
AP. = small change in parameter j
)
Essentially, the price-time product sensitivity is
Table 8.5 Example Design State for Three Axis
Assembler Design -- Physical Data
DESIGN STATE
AXES
HORIZONTAL:
MOTOR-
SHAFT-
HARDWARE-
ROTATE:
MOTOR-
ROTATION-
HARDWARE-
VERTICAL:
MOTOR-
SHAFT-
HARDWARE-
MASS LENGTH DIAM PITCH POWER
KG
22.2
3.3
1.0
M,RAD M
0.336
0.400
M/RAD WATT
750.0
0.026 .0041
41.8 0.449
0.0 1.571
38.7
12.5
3.0
0.434
0.400 0.050 .0079
1550.0
1417.7
CONTINUOUS ROTOR
TORQUE INERTIA
NT-M KGM**2
5.08 0.002400
13.60 0.004960
9.61 0.003840
264
Table 8.6: Example Design State for Three Axis
Assembler Design -- Price Breakdown
AXES
HORIZONTAL:
MOTOR-
AMPLIFIER -
TACH-
RESOLVER-
HARDWARE-
TOTAL-
ROTATE:
MOTOR-
AMPLIFIER-
TACH-
RESOLVER-
HARDWARE-
TOTAL-
VERTICAL:
MOTOR-
AMPLIFIER-
TACH-
RESOLVER-
HARDWARE--
TOTAL-
415.63
246.67
150.00
50.00
59.60
772.43
460.03
150.00
50.00
50.00
713.41
424.75
150.00
50.00
59.60
BASE-
GRIPPER-
RESOLVER CONVERTER-
PROCESSOR-
OTHER COMPONENTS-
DIRECT LABOR-
TOTAL ASSEMBLER DIRECT COST
INDIRECT BUSINESS COSTS-
ASSEMBLER PRICE-
INDEX DEVICE SEGMENT-
SYSTEM INTEGRATION COST-
100.00
200.00
600.00
4000.00
1000000
___50000
10202.12
10202.12
20404.24
2000.00
__4000.0s
TOTAL STATION PRICE-
921.90
1482.46
1397.76
26404.24
265
the fractional change of the product divided by the cor-
responding fractional change of the parameter that caused
the product change. All other parameters are held constant.
For example, in this analysis, the price-time product sensi-
tivity to processor hardware cost is about one third. There-
fore, fractional changes in the processor costs will result
in the price-time product of one third the size. This
definition allows us to rank the relative effectiveness
of similar fractional improvements or modifications in any
input parameters.
The major sensitivities, for this example, are listed
in Table 8.7. When examining these sensitivities it should
be remembered that the single part assembly time is a
design parameter, and so sensitivities for the other para-
meters are estimated under the condition that part assembly
time is held constant. Major ones are discussed below:
Gross motion ratio. The gross motion ratio is the frac-
tion of the assembly cycle that the assembler spends in
gross motion. Increasing the gross motion ratio increases
the time allowed for grossmotion, keeping the total assembly
time constant. The corresponding reduced acceleration re-
quirements mean that smaller, lighter cheaper actuators may
be chosen. The practical constraints from fine motion re-
quirements on assembler design are not now sufficiently well
understood to model this tradeoff.
MaNjor Price-Time Product Sensitivities
for Example Three Axis Assembler Design
Design Parameter
Gross Motion Ratio
Torque Transmission Efficiency for
Horizontal Axis
Processor Cost
Range of Motion for Rotary Axis
*
Single Part Assembly Time
System Integration Cost
Horizontal Axis Length
Torque Transmission Efficiency for
Vertical Axis
Vertical Axis Length
Horizontal Axis Deflection Specification
Other Fixed Costs
Index Device Segment Cost
Resolver Converter Costs
Price-Time Product
Sensitivity
-. 376
-. 372
.301
.243
.161
.149
.128
-.111
.106
.104
.0752
.0746
.0451
*Sensitivity to Single Part Assembly Time is nonzero
because this design point is not at the minimum price-time
product.
Table 8.7
266
267
Tornue transmission efficiencies for the horizontal
and vertical axes. These efficiencies directly affect
how much torque is delivered to the load on the axes. How-
ever, there is not much room for improvement since ball
screws are very efficient. The model assumes a torque
transmission efficiency of 0.9 (1.0 is the maximum possible).
Processor Cost. In this example the processor hard-
ware cost, estimated at $4000, represents a dedicated pro-
cessor with 20K words of memory. The processor hardware
requirement is a rough estimate based on current experimen-
tal work. The price estimate correspcnds to currently
available equipment, and, since computing hardware costs are
dropping, corresponding decreases in the price-time product
can be anticipated.
Horizontal axis length. Increasing the length of the
horizontal axis increases its inertia. This occurs not
only because inertia depends directly on the axis length,
but also because the axis ball screw must increase in dia-
meter to maintain the deflection criterion, and because
larger paylcads are specified for larger horizontal axes
in this model. The increased inertia and motion distance
require a more powerful, and therefore heavier, actuator.
The sensitivity of the horizontal axis length also
includes the effects of increases in the other two axes
which are necessitated by the increase in the horizontal
axis length. The increased inertia from the horizontal
268
axis and the larger horizontal actuator require a larger
and more powerful rotary actuator. The accumulated inertias
of the horizontal and rotary axes require a larger and
more expensive vertical actuator. The larger rotary and
vertical actuators and the larger driving amplifiers that
they require add to the sensitivity of the horizontal axis
length.
Range of motion for rotary axis. The most powerful,
and expensive, motor in the design is the rotary axis motor.
Accordingly, among the three axes the range of the rotary
axis has the greatest sensitivity. In addition, if the
range of motion of the rotary axis is increased, it neces-
sitates an increase in the size of the vertical axis actua-
tor, similar to that described for the sensitivity of the
horizontal axis length.
Vertical axis length. An increase in the vertical
axis length does not affect either the horizontal or the
rotary axis. Therefore, the sensitivity of the vertical
axis length depends only on changes in the vertical axis
and actuator.
Single part assembly time. At the true minimum price-
time product design this sensitivity is zero. However, tlre
value here is nonzero because this design is close to, but
not exactly on, the true minimum.
System integration cost. The system integration cost
is a large fraction of the total station price. It will be
269
reduced if the ease of integrating the station is improved,
perhaps by creating standard mounting schemes using stan-
dard assembler base frames and standard indexing chassis
frames.
All of the remaining sensitivities listed in Table 8.7
should be used as an approximate guide to design refinement
work. They indicate only the degree of "leverage" of a
parameter or component. However, components may differ in
their present state of refinement; it may be "easier" to
develop a certain fractional, improvement in one component
than another. A combination of engineering judgment con-
cerning the state of development of a component and an
estimate of the component sensitivity should be used to
guide design refinement work.
8.6 Summary: Consequences for Research and Development
of Assembler Stations and Components
An example design process has been presented to illus-
trate the use of the price-time product in the design of a
programmable assembler. Minimization of the price-time pro-
duct is a means of resolving tradeoff analyses in favor of
the most economic designs. Sensitivity analysis using the
price-time product may be used to assess the potential im-
provement in assembler performance resulting from improved
cost/performance of an assembler component.
270
The example presented in this chapter is only one
possible formulation of a design tradeoff issue. Many dif-
ferent formulations could be made for different axis con-
figurations, different numbers of axes, different types of
actuators, and so on. As models become available for other
aspects of assembler performance, they may be incorporated
into similar price-time product analyses.
More research in the area of fine motion is required.
The gross motion ratio sensitivity indicates that reduced
fine motion time would be significant. Current estimates of
fine motion time are based only on limited experience.
Research should be directed toward identifying fine motion
options and modeling their cost and performance. Then these
models could be used in price-time product studies.
The sensitivity of the integration cost indicates more
research work is needed here. This is another case in which
better models are needed. In particular, how is the integra-
tion cost for a programmable assembler affected by:
1) Standardization of assemblers and indexing chassis?
2) Availability of a range of stock assembly task pro-
grams from which to choose?
3) Ease with which different programs may be tried in
the debugging process?
One way to obtain this modeling information would be to
execute a series of experiments in which an assembler
271
station is set up for a range of products or subassemblies,
keeping track of time spent in the various phases of the
integration.
The processor sensitivity is large, and, even though
processor costs are declining, it is still important to
strive for minimum cost processor designs. Delegation of
certain cumputing chores to microprocessors is one way of
reducing overall computing costs, and so identification of
candidqte functions for microprocessors becomes an import-
ant research goal.
Finally, both the size of the assembler and the number
of axes it contains have a strong influence on the price-
time product. Experimental work using real products would
provide data relating the lower limits of the practical size
of an assembler in relation to the subassembly and would
provide practical information about the number and arrange-
ment of degrees of freedom that are required.
272
9. ECONOMIC IMPACT ANALYSIS: BACKGROUND AND
APPLICATION TO PROGRAMMABLE ASSEMBLY
9.1 Introduction
We live in a complex and interrelated society. Techno-
logical innovations impact the society in a process that
develops over time and spreads throughout the society as the
new technology eventually becomes a part of it. The
societal changes which can be brought about by the new
technology include many which are economic.
This chapter will first discuss these changes, or
impacts, and then will develop the concept of an economic
impact analysis. Next, this general economic impact analysis
will be discussed with respect to programmable assembly
technology. Adequate data bases in a suitable form do not
exist yet for a thorough impact analysis of programmable
assembly systems, but a procedure for making such a study
will be presented.
I
273
9.2 Types of Economic Impact
Several different types of economic impact are listed
below:
Cost savings
Conservation of scarce resources
Job displacement
Changes in the balance of payments
Changes in business patterns
Although these results of technological change can be
identified individually, they are all interrelated. These
impacts and their interrelations are discussed in this
section.
274
The most obvious impact is the direct cost savings
that occurs when new technology is substituted for old
methods. Fewer inputs such as capital, labor, material,
or energy are required to produce the same goods. The
cost savings in these inputs that occur when a new tech-
nology is applied result in an increase in the national
wealth, or, alternatively, in conservation of scarce re-
sources.
If a new technology reduces labor requirements, then
job displacement can be a problem even though the per
capita national wealth has increased. The distribution
of the wealth has changed. Certain jobs have been elimin-
ated and others created by new technology; for example,
frequently, the new technology reduces unskilled labor
requirements and produces fewer jobs requiring greater
skill. This can bring industries back to the United
States that have moved overseas in search of cheaper un-
skilled labor. If new technology can produce the goods
cheaper than they can be made overseas, then skilled jobs
are created in this country, the per capita rational wealth
is increased, and the balance of payments is improved.
However, although the net effect of certain technologies
may be the creation of employment in the long run, those
workers-who are displaced will be adversely affected unless
compensatory measures are taken.
New technology can affect business patterns, particu-
275
larly if it affects the ease with which manufacturing lines
can be set up and modified. Inflexibility of present manu-
facturing processes has often blocked product improvements,
so that if the new technology increases manufacturing flex-
ibility, modifications can be made more easily in the
process and the product. Products can then be improved
without substantial modifications to the production equip-
ment, and product improvement will become more routine.
9.3 Economic Impact Analysis
9.3.1 General Description
Economic impact analysis is a study of the economic
impact of a new technology upon society. One method for
such an analysis is illustratec in Figure 9.1. First,
the method will be described in general, and then an
example will illustrate the use of the method.
The impact study of a specific new technology must
begin with a thorough understanding of the basic techno-
logical processes (Level 1 in Figure 9.1). The next step is
a microeconomic analysis in which the technical performance
is related to its costs (Level 2). Then the microeconomics
of the new technology is compared to the microeconomics
of the present methods to determine under what conditions
the new technology is economically superior and, if so,
I
276
Figure 9.ls Economic Impact Analysis Method
Level
Engineering Model
Old Process
Microeconomic Model Microeconom!fodal
Old Process I I New Proc .
_ I .v
Economic Criterion
Impact Function
[ Macroeconomic Impact
Analysis Techniques I
Net Assessment Estimate
I I Engineering ModelNew Process
2
3
4
5
Product and Process
Distribution Data
(Distribution Function)
FInltial Impact Estimaterfor Affected Industries6
7
8
jL-I I-
277
how superior it is (Levels 3 and 4). These conditions may
be espressed as an "applicability rule" or impact function
for the new technology. This impact function expresses
impact variables as a function of product and/or process
variables. An example of an impact variable is manufac-
turing cost per unit, and examples of product or process
variables are size of product and number of product units
made per year. Next, the impact function should be applied
to industrial or national data concerning the important
product or process variables (in the form of a distribution
function) to determine the extent of application of the
new technology and its direct economic impacts throughout
the entire economy (Level 8).
9.3.2 Example of Economic Impact Analysis
A simple example show in Figure 9.2 will serve to
illustrate this process. Suppose that a new type of
automobile engine is developed. First, the performance of
the new engine design must be well understood, especially
the relationships between weight, power, fuel consumption,
types of exhaust gases, serviceability, type of fuel
required, and so on (Level 1). The microeconomic analysis
would include relating the technological design parameters
such as operating cost, manufacturing cost, servicing cost,
and ultimate user cost (Level 2). If we assume that ultim-
278
Figure 9.2. Example of Economic Impact Analysis Using
a Hypothetical Automobile Engine
Level
Engineeri Model Engineeririf Model
Old Engn I New Eng no
Nicroeconomic Model
if Old Engine Usage
Microeconomic Model
of New Engine Usage
Lowest User Cost Criterion
Impact Functions
Savings*3 M~d~~~~~M M
rMOt on 1
2000 3000
Automobile Weight (lbs)
Distribution Functions
Utiate
User Cost
(dollars)
I I
Weight (lbs)
2000
Automobile
istimate of Savings in User Cost
Assessment of User Cost Savings on Entire Economy
I
2
3
4
5
6
7
8
bL-
M
acroeconcoic Invact Amalysio Techniques
MM "-
-
- i
EL
279
ate user cost is the important cost parameter that governs
the acceptance of the new engine design, then the ultimate
user cost of the new engine design should be compared to
the ultimate user cost of conventional engines in similar
automcbiles. Minimum ultimate user cost is the selection
criterion. The comparison between the new technology and
the old will then yield the impact function. The form of
the impact function will depend on the important variables
in the comparison. For example, a conceivable result of
the comparison might be that the new engine results in a
30 percent savings in ultimate user cost in automobiles
weighing between 2000 and 3000 pounds and no savings for
other weight ranges (Level 4). The impact function then
relates percentage savings of ultimate user cost to automo-
bile weight. The function is equal to zero for all
engine weights except those between 2000 and 3000 pounds,
where it is equal to .3 . The direct economic impact esti-
mate is obtained by applying this function to distribution
data for the total national user cost (Levels 5 and 6).
This data would be in the form of a distribution function
representing the total national user cost for all automo-
biles in different weight ranges. Finally, macroeconomic
techniques (Level 7) are used to estimate the way this
savings in cost stimulates the rest of the economy (Level 8).
280
9.3.3 Inclusion of Dynamic Factors
The example presented above is a static analysis be-
cause it does not directly take into account the dimension
of time. A static analysis shows the impact that would
occur if a new technology were instantly applied to all
the processes in the economy. However, conversion from an
old technology to a new technology is not, in general, in-
stantaneous. Alternatively, the analysis can be perceived
as an approximation of the current state of the economy
if the new technology had been available for a sufficient
length of time so that it had been fully integrated into
the society.
Another problem of a static analysis is that it
does not take into account trends which may affect the
impact of the new technology. For example, in the case
of the hypothetical automobile engine analysis presented
in section 9.3.2, a better impact analysis would result
if the impact function were compared to the predicted
future distributions of automobile weight. If cars are
growing smaller, then the fraction of new cars in the
relevant weight range will become smaller so that the
actual resulting impact is less. The impact analysis
should not be just a static estimate but shoul& incorpor-
ate any dynamic factors. Some examples and a discussion
of each are given below:
281
1) Changes in Product Demand
Impacts estimated using recent industry data must
be adjusted in light of the overall trends of product
demand leading to a growth or decline of the industry,
especially if the growth or decline is fast. Growing
industries may realize the benefits of the new technology
as a means of production growth and cost savings with
fewer of the job displacement problems than a more stable
or declining industry would experience. Declining indus-
tries contemplating a conversion to new technology face a
potentially greater risk of job displacement problems be-
cause they would be losing jobs even without the introduc-
tion of the new technology. Therefore, the reasons for
the decline have to be examined in order to perform an
accurate impact analysis. If the product of an industry
has simply become obsolete for many uses, as vacuum tubes
did when transistors were introduced, then reduced costs
of production would not materially affect the decline.
But, if the industry has declined because of cheaper foreign
competition, then reduced production costs in the United
States may well revive the industry and create new jobs here.
2) Changes in Manufacturing Technology
Technologies are continually emerging which profoundly
affect existing industries. Therefore, an important
initial part of an impact study is a technological forecast
both within the industry and outside of it. The purpose
282
would be to identify dominating trends which would affect
the fate of the industry beyond the influence of the new
technology considered for assessment. For example, it is
possible that changes occurring now will eventually elimin-
ate the process for which the new technology was intended.
If a product that was assembled from a few pieces is being
replaced by a similar product that is molded in one piece,
then not only will the assembly jobs be eliminated, but the
entire assembly process will be eliminated as well.
The process being considered for improvement by
the introduction of one new technology may be changed
indirectly by another new technology in such a way that
the planned improvement is no longer applicable. For
example, a change in the material of a product from metal
to plastic may require a change in the final inspection
procedure for plastic parts.
3) Changes in Product Technology
Most new technologies do not last forever-they are
eventually replaced by improved technologies. Realistic
impact analysis should take into account a reasonable life
cycle for the new technology. The history and traditions
of the industry could be used to help make this estimate
as well as any knowledge of advanced work in research lab-
oratories.
283
9.4 Economic Impact Analysis of Programmable Assembly
The discussion up to this point has been about impact
analysis of technological production innovation in general
terms. We now turn to impact analysis of programmable
assembly systems. A thorough study cannot be done at this
time because of the lack of adequate date on the industrial
or national level that is suitable for use in the impact
analysis described in this chapter. However, a simplified
impact analysis is presented in section 9.4.1, and the
remaining sections of the chapter discuss the important
issues of programmable assembly impact analysis.
9.4.1 The Impact Analysis Process
We now examine how an impact analysis appropriate for
the level of modeling presented in previous chapters could
be performed for programmable assembly automation.
The engineering modeling of the alternate assembly
technologies (Level 1) and the microeconomic modeling
(Level 2), the first steps of the impact analysis, have
already been performed in previous chapters. The compari-
son of the alternate assembly methods using an economic
criterion (Level 3) has also been discussed. The economic
criterion used was to choose the assembly method that
yields the lowest assembly cost per unit. (It was from
... 
................................. �� ....................................................................... ll!Sllllllll� ...... .,.:l!l:l!leil�oii;l'i;; 
284 
this comparison criterion that the design criterion of 
minimizing the price-time product was chosen.) 
The next step in the impact analysis is to develop 
an impact function. This function should represent the 
savings that occur witlc programmable assembly as a func­
tion of product and process variables. In the analysis 
of the preceding chapters, there are several variables 
that affect the application 'Jf programmable assembly as a 
function of product and process variables. Ir, the analysis 
of the preceding chapters, there are several variables 
that affect the application of programmable assembly, 
but the two most important variables are the required pre­
duct production volume and the physical size of the product. 
The production volume is used explicitly in the examples 
and the equations, but the influence of the size of the 
product is implicit in the values of the parameters of 
the equations. For example, the price of a programmable 
assembler must increase as its size increases to handle 
larger products. The average cost of the parts feeding 
tooling will also increase with an increase in product 
size. As was shown in Chapter 3, the transfer machine 
cost per part increases with product size. Finally, the 
average manual assembly time, and therefore cost, will 
also increase with product size. 
We will assume that all products will be divided into 
a set of product size classes. The smallest size class 
285
will be perhaps a maximum of four inches in dimension
and would correspond to the limits of the smallest trans-
fer assembly machine-the small rotary table. The largest
size class would perhaps be for products up to 30 inches
in length and would correspond to the size limits for the
non-synchronous transfer assembly machines. A few inter-
mediate size classes could correspond to the limits of
intermediate transfer assembly machine methods.
The impact analysis process will be repeated for each
product size class and the results will be summed for the
total impact. By choosing the set of product size classes
to correspond to the set of the major different types
of transfer machines or programmable methods, the results
can then have specific meaning for these major different
types, as well as contribute to the overall impact analysis.
Within the impact analysis for a particular size class,
the remaining important variable is production volume.
Figure 9.3 illustrates the derivation of the impact func-
tional relationship with product volume. The set of curves
at the top represents the unit assembly costs for the major
alternate methods of assembly as developed in Chapter 6.
If we assume that assembly methods are chosen to obtain
the lowest assembly cost per unit, then the savings attri-
butable to programmable assembly over manual and transfer
machine assembly are represented by the impact function in
the lower part of Figure 9.3. The impact function can be
286
Figure 9.3a Graphical Derivation of Impact Function
Unit assembly costs as a function of annual
production volumesi
Transfer
\\)nual
--- Best Alternate
Assembly Cost
Programable
II
Annual Production
Volume (log scale)
Impact Function'
M4
000
41
o hC 1.0-
'In
w o 4
en
Impact Function
Annual Production
Volume (log scale)
r4 .
em'
U
ONE-MMEMM-1 \S
287
expressed as follows:
BACPU.(VOL) - PCPU.(VOL)
FCS.(VOL) BACPU.=(VOL)J BACPU. OLJ
if BACPU.(VOL) -PCPU.(VOL) > 0) J
FCS.(VOL) = 0 if BACPU.(VOL)-PCPU.(VOL)< 0J ] J
(9.1)
where FCS.(VOL) = fractional cost savings as a functionJ
of volume for product size class j
BACPU. (VOL) = unit assembly cost for the best
J
alternate method as a function of volume
for product size class j
PCPU. (VOL) = unit assembly cost for a programmable
system as a function of volume for product
size class j
Here, FCS .(VOL) is the impact function. The best alternate)
assembly cost per unit is either manual assembly or transfer
machine assembly, whichever is cheaper at a given production
volume. We are making the assumption that the best alter-
nate assembly function describes the present day, average
unit assembly costs. The savings that programmable assem-
bly bring must be calculated in relation to the unit assembly
costs of the best alternate assembly'function.
Next, the impact function may be used in combination
with a distribution function of the assembly costs incurred
at different production volumes to estimate the total cost
288
savings 'in an industry due to the introduction of program-
mable assembly. For the purpose of this analysis an indus-
try is defined as a collection of establishments or firms
which manufacture a similar type of product. Examples
of industries would include all manufacturers of motor
vehicles, "the motor vehicle industry," and all manufactur-
ers of farm machinery, "the farm machinery industry."
Different industries will be denoted by a subscript i, and
different product size classes by a subscript j. A sample
distribution is illustrated in Figure 9.4. A point on the
horizontal axis represents products of a specific produc-
tion volume. The total area under the curve represents the
total assembly cost for industry i for all eligible pro-
ducts in product size class j. (The concept of the eligible
products will be discussed later.)
The area under the curve between two vertical lines
representing two different production volumes VOL1 and VOL2
represents the total assembly cost for products which are
made in that range of production volumes. For any specific
product the production volume is measured with respect to
the firms making the product, not the total number of similar
products made throughout the industry. For example, assume
there are two firms making motorcycles -- Firm A and Firm B.
The annual motorcycle production for Firm A is 20,000 while
that for Firm B is 30,000. The assembly cost of motorcycles
289
Figure 9.41 CostaVolume Distribution Function
Applies to industry i and product size class J
%of %e %iW W W %%.,
%#,%%%r%,R%
%d dfW
WWWW t~
W x% dfe%
m-V-
VOL1 VOL2
V Anuiaj Produotion Volume (linear scale)
Area represents total assembly cost throughout
industry i for products in site class j
S*"Avg
'ho -p40
~0 boMo
e4 .
'.n.
V
290
would then be represented in the cost-volume distribution
function for two separate production volumes, 20,000 and
30,000, rather than combined under the industry total of
50, 000.
The only products that should be counted in these
distribution functions are the eligible products -- those
that can physically be assembled by programmable assembly
methods. In this way products that cannot be assembled
programirably are eliminated from the impact analysis. The
rules that determine eligibility should be broad for ease
of data manipulation; for example, rigid machined parts
should be considered ineligible. It is not necessary for
these broad rules to be absolutely correct in all cases;
there may be exceptions to them, and, as research progres-
ses in this area the concept of eligibility can be more
accurately and precisely defined.
The impact function and the distribution function can
be multiplied to obtpin a cost savings distribution function
for industry i and product size class j. (See Figure 9.5).
Then, the cost savings distribution function is integrated
over its volume range to obtain the total assembly savings
for industry i in product size class j.
SAV1 . =fFCS.(VOL)ACDi.(VOL)dVOL (9.2)
.th th
where SAV.. = savings in the i industry for the j
product size class
thACD. .(VOL) = assembly cost function for i
1)
291
Figure 9.5# Application of Impact Punction to
Distribution Data
Applies to industry I and product size class S
r.O
0O4
as
UP
C3
M
Annual Production 
Volume (log scale)
*
Area represents total savings for
industry I and product size classj
P
0 nulPouto Vlm lgsae
292
industry in product size class j
Then, this procedure may be repeated for all industries
with assembly processes and the results summed for a total
industrial sector impact for the prcgrammable assembly
automation for that particular product size class.
SAV. = E SAV. (9.3)
J i IJ
where SAV. = total industry impact for the jth
. J
size class
The entire foregoing procedure may be repeated for pro-
ducts of different size classes and these results summed
to obtain an estimate of the total impact of programmable
assembly systems for all product size classes.
SAV = E SAV. (9.4)
where SAV = total direct cost savings
Now the techniques of macroeconomic analysis, parti-
cularly input/output analysis, can be used to study how
the effects of these costs savings on certain industries
spread throughout the economy. These techniques have been
developed quite well by others and can be used in their
present form 4n connection with the impact analysis of
programmable assembly systems. This completes the major
steps of the impact analysis. Two comments concerning
the preceding analysis should be made at this point. First,
this impact analysis is concerned only with the use of pro-
grammable assembly in the manufacture of uniform products;
293
that is, this is not an assessment of the impact of pro-
grammable assembly on the manufacture of product families.
Second, even though this was a restricted, simple assessment
process, the amount of data required is large. Distribution
data of the assembly cost by product size and industry is
required for the entire economy. To obtain this distribu-
tion data would require large amounts of data obtained
originally at the level of the firm and then aggregated by
industry over many industries and then repeated for a few
different product size classes.
9.4.2 Extension ot Impact Analysis to Product Families
To assess the impact of programmable assembly on the
manufacture of product families would require detailed in-
formation obtained at the level of the firm and aggregated
to the industry level. Distribution data would be needed
relating the total assembly cost in an industry to the
annual volume of product families for a given product size.
It may be necessary to define a set of product family classes
in which the members of each class have roughly the same
degree of variation. At one extreme would be a product
family class in which only a small fraction of the parts
of a product varied between family members. At the other
extreme a large fraction of parts may vary between family
members. A microeconomic and engineering analysis of
294
programmable and hybrid systems applied to product families
such as described in Chapter 6 could be used to develop
a set of impact functions for products of different sizes
which belong to product families with different degrees of
differentiation.
9.4.3 Identification of Impact Costs
A thorough impact analysis of programmable assembly
systems should include as many affected costs as possible.
However, a simplified analysis such as that just presented
which looks at only the major costs is much easier to work
with and points out the major trends. The analysis of
earlier chapters has been based on only the major costs of
capital equipment and labor, but in specific circumstances
other costs nay determine whether or not the system is
economically justifiable. These other affected costs include
the following:
1. Production material costs. If the programmable system
results in lower material wastage, production materials
costs may be reduced.
2. Inventory costs. A programmable system can allow very
fast changeover of assembly from one product to another, and,
therefore the assembly system can respond very quickly to
variations in orders for a product. This means that less
product need be maintained in stock to meet the orders
se
295
(lower inventory), and this means there are lower inventory
costs because less company captial is tied up in nonproduc-
tive form. This savings can be particularly important if
the product unit is expensive.
3. Individual part costs. Programmable systems with adapt-
ability will sometimes be able to assemble lower quality
parts than transfer machine methods because the transfer
machine requires tighter tolerances on the part dimensions
than is necessary for proper functioning of the product.
The tighter tolerance parts are more expensive either be-
cause they are made more carefully or because they are
inspected to weed out the out-of-tolerance parts, and thus
individual part costs are lower for the programmable system.
4. Part design costs. Programmable assembly may lead to in-
creased part design costs because of necessary modifications
in the des.ign and manufacture of the incoming parts. How-
ever, the required modifications are often either simplifi-
cations of the parts or redesicn of the product to reduce
the number of parts. Consequently, the part redesign for
the assembly system may also reduce the manufacturing cost
of the parts. Whether or not the part redesign is ultimate-
ly an additional expense or savings depends on the circum-
stances.
5. Energy costs. Programmable systems will almost certainly
use more energy than manual assembly support equipment, but
whether they will use more energy than transfer machine
296
assembly is unknown at this time.
These non-capital and non-labor costs should be
examined in the justification of any particular program-
mable installation to see if they represent any significant
effect. However, because they are less important than the
principal capital and labor costs, they have been omitted
in the simple economic impact analysis of section 10.3.2
and from the preceding discussion of a method for program-
mable assembly impact analysis.
9.5 Summary
As our modern society becomes increasingly complex and
interrelated, it becomes more important for the economic
effects of a new technology to be assessed prior to its
introduction into the economy. One possible method for
such an assessment has been presented here. The outline of
this economic impact analysis is as follows:
1) A technical and microeconomic analysis of the new
technology is made.
2) From this technical and microeconomic analysis an
impact function is derived.
3) The impact function is used with industrial statistical
-data to estimate the direct impact of the new technology.
4) Traditional macroeconomic methods of assessment are used
to estimate the effect of the direct impact on the economy
297
as a whole.
The application of economic impact analysis to assess
the effect of the introduction of programmable assembly
systems has been demonstrated by use of a simplified analysis
because at the present time an adequate data base does not
exist for a thorough analysis. The type of data required
includes data showing the distribution of industry assem-
bly costs as a function of parameters such as production
volume and product size.
Although the simplified analysis considered only the
major impact costs of capital equipment and labor, other
important impact costs should also be considered in a thor-
ough analysis. These are listed below:
1) Production material costs
2) Inventory costs
3) Individual part costs
4) Part design costs
5) Energy costs
These costs should all be considered in the justification of
any individual programmable installation.
10. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH
Programmable assembly offers an alternative to manual
and transfer machine assembly. Modeling both the perform-
ance and the costs of a programmable assembly system can
298
help define design and research goals for programmable
assembly systems and to identify the circumstances under
which programmable assembly offers an economic alterna-
tive to manual and transfer machine assembly methods.
This research used microeconomic analysis to provide
a framework for comparison of programmable assembly to
manual and transfer machine assembly methods, three widely
varying assembly technologies. A common base of assump-
tions was used so that the assembly alternatives could be
compared consistently. The economic model that was devel-
oped for programmable assembly is simple and general, so
that many different technical approaches to programmable
assembly can be compared on the same grounds. An important
measure of programmable assembly performance -- the price-
time product -- was identified, and the minimization of the
price-time product was presented as a criterion to achieve
reduced assembly cost.
The type of microeconomic analysis used here can also
provide a means to estimate critical values of price-time
product that form boundaries between competitive designs
and non-competitive ones. The microeconomic analysis pro-
vides a framework in which the sensitivity of the competi-
tive advantage of programnable assembly to various economic
factors--such as labor cost, required annual rate of return,
and price-time product-,-can be examined.
The formulation of the economic analysis identified
299
certain noneconomic, sometimes difficult to quantify,
factors which influence the economics. For example, the
configuration efficiency, a measure of the "line balance"
of the programmable assembly system and the utilization
efficiency, a measure of the extra production capability
of the system, both play important roles in the economics.
Their presence in the model raises questions about how they
may be related to other properties of programmable assembly
systems and so identifies certain natural areas for further
resea rch.
The price-time product is a useful means of evaluating
alternative assembler designs. It is not dependent upon the
way that the assemblers are organized into an assembly sys-
tem. It can be used to compare assemblers with widely
varying numbers and configurations of axes and widely vary-
ing component technologies. The price-time product is use-
ful to the designer of an assembly system because it helps
him to choose cost effective assemblers. It is useful to
the designer of an assembler because it can help to resolve
design tradeoffs in favor of an economic design. Finally,
sensitivities defined in terms of the price-time product can
be used to assess directions for further research and devel-
opment for classes of assembler configurations.
The research of this thesis has been primarily involved
with the development of the price-time product as an assem-
bler criterion and the ways in which it and the supporting
4300
analysis can be used to study programmable assemblers.
Two classes of further research work are apparent: First,
work directed toward developing improved models of assembler
cost and performance; and, second, areas of research that
will be identified by the price-time product sensitivities.
More work is necessary to model the cost and performance
of the fine motions of assembly. The modeling of gross
motion for a given assembler configuration can be quite
straightforward, as was illustrated in the example design
process that was presented earlier; but the fine motion
process is not yet sufficiently well understood to lead to
a useful price-time product model. Research in assembly
fine motion should be directed at understanding not only
the basic processes but also the cost and performance of
the hardware implementation. Better models of assenIbler
fine motion requirements and performanme are necessary to
analyze the trade-off between the cost and performance of
special jigs to aid in fine motion as opposed to the cost
and performance of more sophisticated strategies to be im-
plemented by the assembler. Accurate models for both gross
and fine motions can lead to better price-time models for
assembler configurations.
Research should also be directed toward producing better
models for system integration costs and processor costs
and requirements. Just how programmability will influence
301
the system integration process is only speculation now,
although it certainly should be an improvement over transfer
machine integration.
Similarly, the functions necessary to the processor
dedicated to an assembler are not sufficiently well under-
stood to permit an accurate model. The existence of such
processor models is necessary to price-time tradeoff analysis
between processor capacity and special tooling.
Further research can also be done in developing a more
complete model of the economics of programmable assemblers.
This analysis was limited to assemblers in system configura-
tions that were dedicated to a particular product or product
family. The costs of tearing down a system and reusing the
assemblers in a new system was not analyzed explicitly, al-
though different useful lives for assemblers and assembly
feeding tooling were modeled.
The price-time product would survive such an analysis
as one measure of assembler performance, but new measures
may emerge that describe the cost effectiveness of the
assembler with respect to the system reconfiguration process.
More work can be done to verify or modify the assump-
tions used in the economic modeling. Is the tooling price
per part really independent of production volume? Is con-
figuration efficiency related to the number of parts per
station and thereby to the production volume? Is station
price related to the number of parts per station (because
302
of the number of degrees of freedom required) and, conse-
quently, to the production volume?
A logical next step in the development of the economic
model would be to reformulate the model without constraining
the assumptions to allow for easy symbolic maniphlation.
Such a model would be largely limited to numerical analysil4
by computer. It could be more complete by including many
more cost factors than were practical here. It could use
the actual return on investment instead of the annual rate
of return as an approximation to it, and could allow the
results obtained in earlier chapters to be obtained more
accurately.
However, most of the results of such a model would
have to be expressed only graphically rather than symboli-
cally and so would be somewhat more difficult to study.
This more complete model could be used to identify circum-
stances in which other economic factors besides the basic
equipment or labor costs would be important considerations
in the application of programmable assembly. The simple
model presented here was sufficient to identify the price-
time product as a useful measure of assembler performance;
the more complex model can be used to obtain better estim-
ates for the critical values for it.
As an assembler price-time model is developed, price-
time prcduct sensitivity analysis ca.. be used to identify
assembler components that have the greatest potential
303
influence on the price-time product. Research applied in
these areas can have the greatest impact on improving pro-
grammable assembly technology.
The assembler design process of Chapter 8 provides an
example of identification of research areas by sensitivity
analysis. The processor and system integration components
were identified as important areas of research. Also, it
was shown that the assembler size and number of degrees of
freedom are important factors in the price-time product.
This means that it is important to understand, for real
products, how the minimum assembler size is related to the
product size as well as the required number and arrangement
of the degrees of freedom.
As programmable assembly actually comes into use, it
will also be important to verify the modeling concepts pre-
sented here empirically. These results can then be used as
a basis for further study.
304
REFERENCES
1 Samuelson, P.A., Economics: An Introductory Analysis,
tGraw-Hill Book Company, New York, 1964, p. 735.
2 Karger, D. W., and Bayha, F. H., Engineered Work
Measurement, Industrial Press Inc., New York, 1966.
3 Boothroyd, G., and Redford, A.H., Mechanized Assembly,
McGraw-Hill Book Company, London, 1968.
4 Production, Production's Manufacturing Planbook: 1976,
p.25.
5 Prenting, T.O., "Automatic Assembly -- The Economic
Considerations," ASME Paper No. 65-WA/PROD 5, 1965.
6 Nevins, J. L., et al., "Exploratory Research in
Industrial Modular Assembly," Report No. R-800, The Charles
Stark Draper Laboratory, Cambridge, Mass., March 1974.
7 Nevins, J. L., et al., "Exploratory Research in
Industrial Modular Assembly," Report No. R-850, The Charles
Stark Draper Laboratory, Cambridge, Mass., November 1974.
8 Nevins, J. L., et al., "Exploratory Research in
Industrial Modular Assembly, " Report No. R-921, The Charles
Stark Draper Laboratory, Cambridge, Mass., August 1975.
9 Whitney, D. E., "The Mathematics of Coordinated
Control of Prosthetic Arms and Manipulators," ASME Paper
No. 72- WA/Aut-4, 1972.
10 Tipping, W. V., An Introduction to Mechanical
Assembly, Business Books Limited, London, 1969.
305
11 Prenting, T. 0., and Kilbridge, M. D. , "Assembly --
The Last Frontier of Automation, " Management Review,
February, 1965, pp. 16-18.
12 Rosen, C., et al., "Exploratory Research in
Advanced Automation, First Semi-Annual Report," SRI
Project 2591, Stanford Research Institute, Menlo Park,
California, December 1973.
13 Rosen, C., et al., "Exploratory Research in Ad-
vanced Automation, Second Report," SRI project 2591,
Stanford Research Institute, Menlo Park, California, August
1974.
14 Rosen, C., et al., "Exploratory Research in
Advanced Automation, Third Report," SRI Project 2591,
Stanford Research Institute, Menlo Park, California,
December 1974.
15 Finkel, R., Taylor, R., Bolles, R., Paul, R., and
Feldman, J., "AL. A Programming System for Automation, "
Memo AIM 243, STAN-CS-74-456, Stanford Artificial Intelli-(
gence Laboratory, Stanford University, Stanford,
California, 1974.
16 Heginbotham, W. B., "Factors Affecting the Success-
ful Application of IR Technology," The Industrial Robot,
Vol. 1, Sept. 1973, p.6.
17 The Industrial Robot, published by International
Fluidics Services, LTD., Carlton, Bedford MK43 7JS, England.
306
18 Abraham, R., Yaroshuk, N., and Beres, J., "Requirements,
Analysis, and Justification of Intelligent Robots,"
Proceedings of the 5th International Symposium on Industrial
Robots, IIT Research Institute, Chicago, Illinois,, Sept. 22-24,
1975, p. 89.
19 Kondoleon, A. S., "Application of a Technological-
Economic Model of Assembly Techniques to Programmable
Assembly Machine Configuration," SM Thesis, Dept. of
Mechanical Engineering, M.I.T., Cambridge, Mass., June 1976.
20 Swalm, R., "Which Justification Method Gives the
Right Answer?", Metalworking,September 1962, pp. A14-A25.
21 Van Horne, J. C., Financial Management and Policy,
Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1971.
Appendix 1.
ACC
ACDijVOL)
APCST
APLCST
ASMCST
ASMPRC
ATLCST
ATU
AVTSQ
BACPU. (VOL)
BSCST
C
.4
307
List of Variable Definitions
Mgnitude of required acceleration
Assembly cost function for ith industry in
product size class j
Driving amplifier cost, dollars
Annual labor cost for a programmable system
Direct manufacturing costs of the assembler
Purchase price of assembler
Annual labor cost for transfer machine
operation
Assembly time per unit, sec.
Average value of square of torque
Unit assembly cost for the best alternate
method as a function of volume for product
size class j
Ball screw cost, dollars
Conversion constant from rotary to linear
motion
308
CAP. Number of parts that can be assembled
annually by the i th station
CAT Net annual cash flow after taxes
CEF Configuration efficiency
CONTRQ Maximum continuous torque rating of the
motor, newton-meters
D Length of ball screw, meters
DH Length of horizontal axis, meters
DIST Distance of gross motions
DPME Annual straight line depreciation rate for
manual equipment
DPPA Annual straight line depreciation rate for
the programmable assembler stations
DPTL Annual straight line depreciation rate for
the parts feeding tooling
DPTM Annual straight line depreciation rate for
the transfer machine
DY Number of days worked per year
EM Effective mass to be moved in x direction
309
F Force in x direction
FCS. (VOL)
FMT
FR
GRATIO
HATU
HCPU
HCST
HD
HPCPU
HTCPU
HTMCPU
HTPCPU
Fractional cost savings as a function of
volume for product size class j
Total time for all fine motions during the
single part assembly cycle
Required force in x direction
Fraction of part assembly time in gross motion
Hybrid transfer-programmable assembly time
per unit, sec.
Hybrid system assembly cost per unit
Hybrid system cost
Number of hours worked per day
Unit assembly cost component due to program-
mable assembler stations and associated
feeding equipment
Unit assembly cost component due to transfer
machine stations
Unit assembly cost for the hybrid transfer-
manual system
Hybrid transfer-programmable cost per unit
IIDXCST
INDEXTIME
INTCST
J
JM
LABCST
M
MATP
MAXVOL
MCPU
MCPUI
MECPP
MECST
MOTCST
ML
310
Initial investment
Cost of portion of index or conveying
device dedicated to the assembler (assumed
consta nt)
Average time between completed product units
Cost of engineering, building, and debugging
station (assumed constant)
Rotary inertia
Motor rotor inertia, newton-meter-second2
Cost rate of labor, dollars/second
Linear moving mass
Manual assembly time per part, seconds
Potential production volume of the product
Manual assembly cost per unit, dollars/unit
Manual unit assembly cost, improved model
Manual equipment cost per part
Total manual equipemnt cost
Motor cost, dollars
Motor length, meters
n
MM
MSCPU
n
NPART
NPPRT
NPT
NSEF
NSPY
NSTA
NWPP
NWRKR
P
-P.
PARTTIME
311
Motor mass, kilograms
Unit assembly cost for the parts assembled
manually
Number of years of investment project
Number of parts in the product
Number of parts assembled by programmable
stations
Number of parts assembled by transfer
stations
Net station efficiency of the system
Effective number of working seconds in the
years, including the effects of-downtime,
number of shifts, and so forth
Number of programmable stations in the system
Number of workers assigned per part
Number of workers assigned
Motor power rating, watts
Parameter j
Single part assembly time for one assembler
PARTTIMET
PCPU
PCPU. (VOL)
J
PcPUI
PECPU
PFCTR
PL
PLCPU
POPT
PRATIO
PSCST
PTS.
)
PUEF
312
Theoretical single part assembly time
Programmable assembly cost per unit
Unit assembly cost for a programmable
system as a function of volume for product
size class j
Programmable cost of assembly per unit
product for the improved model
Programmable equipment cost per unit
Price factor
Payload, kilograms
Programmable system labor cost per unit of
product
Total yearly operational time for the
programmable system
NPPRT/NPART, Programmability ratio
Programmable system cost
Price-time product sensitivity of parameter
Utilization efficiency of the programmable
system
RROI
SAV
SAV.
SAV.
1)
SETLF
SF
SLOPE
STAP
STAP*PARTTIME
T
TAX
TCPU
TCPUI
313
After tax rate of return
Return on investment
Total direct cost savings
.thTotal industry savings impact for the j size
class
th .thSavings in the i industry for the j pro-
duct size class
Fractional duration of the actual gross mo-
tion time beyond the theoretical time; i.e.,
the settling time fraction
Salvage fraction
The slope of the. staircase of the price-
capacity chart
Single station price
Price-time product
Tax rate
Taxes on income allocated to the transfer
machine
Transfer machine assembly cost per unit
Improved estimate of the unit assembly
cost of the transfer machine
314
TEF Torque transmission efficiency (less than one)
TG Constant gravitational torque
TGM Average time for one gross motion
TGMT Theoretical gross motion time
TI "Square wave" inertial torque
TLCPU Transfer machine labor cost per unit
TMCPP Transfer machine cost per part
TOLPP Price of parts feeding tooling per part
TOPT Total annual transfer machine operational
time, seconds
TORQ Torque about axis 0
TR Torque required on load
TRATIO Transfer ratio
TSCPU The unit assembly cost for the parts assem-
bled by the transfer stations
TSCST System cost for transfer machine
TSTCST- Total cost of the transfer stations
TTIME Average time between the production of
single product units, seconds
315
UT Uptime fraction
VMAX Peak velocity in x direction
VOL Actual production volume of the product
VOLMT Volume boundary between economic manual and
transfer machine systems
VOLMTI Volume boundary between economic manual and
transfer machine assembly improved
model
VOLPM Volume boundary between economic manual and
programmable systems
VOLPMI Volume boundary between economic programmable
and manual assembly, improved model
VOLPT Volume boundary between economic program-
mable and transfer machine systems
VOLPTI Volume boundary between economic program-
mable and transfer machine assembly, im-
proved model
316
Appendix 2. Annual Rate of Return as an Approximation
to the Return on Investment
In the economic modeling work of this thesis the
annual rate of return, defined using the annual cash flow
after taxes by equation 6.3, was used as part of the method
of computing unit assembly costs for programmable and trans-
fer machine assembly methods. This rate of return is an
approximation to the return on investment, ROI, that is
most commonly used in capital allocation analysis. Unfor-
tunately, the return on investment is often difficult to
work with and is more complex to calculate. The annual rate
of return is simple to work with and calculate, but is
only an approximation. In exploratory work such as this, the
ease of manipulation was more important, and so the annual
rate of return was used. In future work in this area, true
ROI should be used in all capital allocation analyses.
In this appendix an example is provided to indicate
the accuracy of the annual rate of return as an approxima-
tion to the ROI. In general, the annual rate of return is
a better approximation when the rate of return is lower and
the life of the project is longer. The annual rate of return
is not affected by the salvage value of a project (except
insofar as the annual depreciation rate affects taxes) nor is
it affected by the life of the project. In fact, the annual
rate of return is simply the inverse of the "payback
period," the time required for a
317
project to earn an amount of money equal to its original
investment.
To formulate an example, we consider a project in which
the original investment, at time equal to zero, is I. This
project earns an annual cash flow after taxes of CAT at the
end of each year, extends for n years, and recovers a sal-
vage fraction SF of the original investment at the end of
the nth year. The ROI of the project is that discount rate
for which the present value of all cash flows over time is
zero (21).
n CAT SF*I
o = -I + E +SI(A2.1)
i=1 (1+ROI) (l+RQI)n
where ROI = return on investment
In general, this expression mu3t be solved -_numerically, to
find the value of the ROI. However, this expression can be
used to relate annual rate of return as defined by equation
6.3 to the ROI. Equation A2.1 can be rewritten
SF
CAT 1 - (1+ROI)(A2.2)
I n 1
il (1+ROI)'
using equation 6.3 and simplifying the summation gives
R = ROI*(1+ROI)n -SF (A2.3)(l+ROI) -l
where R = annual rate of return
Examination of equation A2.3 reveals that the annual rate
318
of return R will equal the return on investment if the
salvage fraction is one; i.e., no loss of value on the
original equipment, an unrealistic situation.
As an example calculation, consider the programmable
assembly example of Section 6.1.5. Assume a production
life of 4 years over which the parts feeding tooling is
fully depreciated but the programmable assemblers are de-
preciated to half of their original value. All other
variable values remain- the same is in Section 6.1.5. We
consider two different 'systems; one designed to operate at
100,000 units per year (with few assemblers) and one de-
signed to operate at 1 million units per year (with more
assemblers). We assign an ROI of .25 and then compute the
corresponding annual rate of return required to give that
ROI for these two systems.
System Production Salvage Fraction R
Volume after 4 Years
0.1 x 106 .06 .41
1.0 x 106 .289 .37
As can be seen, there can be a 50 percent difference between
the ROI and the annual rate of return. If the tooling lasted
for eight years, as long as the assemblers are assumed to
last, then the entire system will fully depreciate after 8
years (SF = 0). In this case a 25 percent ROI would require
an annual return of only 30 percent.
319
Appendix 3. The I.C. Insertion Machine: A
Currently Available Programmable Assembler
The I.C. insertion machine is a currently available, but
highly specialized, programmable assembler that inserts elec-
trical components into printed circuit boards very quickly
(2300 to 19000 per hour). There are actually two types of
machines--those for assembling axial lead components and
those for I.C.'s (DIP's).
The systems that insert axial lead components have the
following parts:
1. Insertion machine (about $49000). The insertion speed
is about 8000 per hour with one work head, but 16000
with two workheads working on two identical boards.
2. Controller (about $14,000, but one controller can
handle up to 5 insertion machines).
3. Sequencer (about $31,000). The sequencer prepares a
tape containing the components in the proper sequence
at about 16000 per hour. Thus, the sequencer is bal-
anced with a dual workhead insertion machine.
The systems that insert DIP's have the following parts:
1. Insertion machine (about $48,000). The insertion
speed is about 2800 to 3600 per hour.
2. Controller (about $14,000, but one controller can
handle up to 5 insertion machines of either type.)
These machines do their own sequencing.
I
320 
In these assembly systems, the feeding hardware is 
really incorporated into the assembly station; this can be 
done because the nature of components assembled is highly 
restricted. In order to interpret these machines in terms 
of the model developed in this thesis, the sequencer should 
be considered part of the assembler. For example, counting 
a single dual head axial insertion machine, one fifth of a 
controller, and a sequencer, the price time product of the 
axial lead system is 18,630$-sec. The price time product 
of the DIP system ranges from 50,800$ -sec to 65,500$-sec 
depending on the speed. Using the price-time bound of 
equation 6.16, with some information about manual insertion 
rates (i.e., labor cost $8500 per year, 1.67 people opera­
ting collectively at 200 to 800 insertions per hour) and 
some other assumptions (R=.25 , T=�48, DPPA=.125, CEF=.8, 
PUEF=l.O� the upper bound on the price-time product becomes 
2.2xl0 5 to 8.9xlo
5 
$-sec depending on the manual rate. Hence, 
the component insertion �achines have price-time products 
well below the upper bound. 
-
-
321
BIOGRAPHY
Paul Michael Lynch was born in Laramie, Wyoming, on
April 15, 1948. Most of his public school education was
in Richardson, Texas. He entered MIT in the fall of 1966,
receiving a Bachelor's Degree in 1970, a Master's Degree
in 1972, and an Engineer's Degree in 1975, all in Mechanical
Engineering. In his senior year he won a Wunsch Foundation
Design prize for outstanding student design, and during his
undergraduate years was active in the student section of the
ASME and the MIT Concert Band. As a graduate student he was
a National Science Foundation Graduate Fellow (1970-1973)
and a research assistant (1973-1976) working at the
C. S. Draper Laboratory. He is a member of Pi Tau Sigma
and Tau Beta Pi. His publications include:
P. M. Lynch and D. E. Whitney, "Active Force Feedback
Rate Control of Manipulators," Proceedings of the Eighth
Annual Conference on Manual Control, Ann Arbor, Michigan,
May 17-19, 1972, pp. 221-226.
D. E. Whitney, W. J. Book, and P. M. Lynch, "Design
and Control Considerations for Industrial and Space
manipulators," Joint Automatic Control Conference, June
18-21, 1974.