Design and Modeling of a Catapulting Magnetic Transmission for Tuning Energy Storage and Release

Abstract

The purpose of this work is to generate design rules and models for a catapulting magnetic leadscrew transmission. These rules and models empower scientists and engineers with the ability to tune energy storage and release, and thereby increase the peak specific power (power/mass) of an actuator. This enables rapid design and development of lightweight (< 0.5 kg), high peak power (>200 W) actuators. This has the potential to impact powered exoskeletons and force-controlled robotics for rehabilitation and strength augmentation of explosive movements such as locomotion, jumping, and throwing. This thesis provided the following scientific contributions: (i) the concept of a catapulting magnetic screw actuator, (ii) experimentally validated models that are useful for the design and optimization of the magnetic leadscrew, considering both magnetic and structural aspects, (iii) experimentally validated models of the catapulting event in a magnetic leadscrew, and (iv) use of these models in the context of a practical application, namely powered exoskeletons that may reduce the metabolic cost of walking. First, the catapulting magnetic screw is introduced. An equation of motion is derived and experimentally validated. The equation of motion demonstrates that the potential wells in the magnetic screw create a ripple in the power as a function of time. Then, despite the equation of motion being a nonlinear differential equation with no closed-form solution, bounds on the ripple magnitude and frequency are derived. This gives the slip force and the lead needed to meet a specified tolerance on power as a function of time. Then, a model is developed that enables rapid design of a magnetic screw that achieves a desired slip force. This model agrees with finite element analysis to within 10% error across varying each design parameter by multiple orders of magnitude. Then, given a magnetic screw, a structure is needed to be sufficiently stiff to keep the magnets from sticking together. Models of the magnetic stiffness matrix and structural stiffness matrix and simplifications thereof are given to ensure sufficient structural stiffness. Finally, the catapulting event may be too fast for a desired application, so it is shown how nonlinear springs may be used to meet requirements for powered exoskeletons that assist in walking.