Dynamics of Manipulators with Less Than One Degree of Freedom

Abstract

We have developed an efficient Lagrangian formulation of manipulators with small numbers of degrees of freedom. The efficiency derives from the lack of velocities, accelerations, and generalized forces. The number of additions and multiplications remains constant, independent of the number of joints, as long as the number of joints remains less than one. While this is a restricted class of manipulators, we believe that it is important to understand it fully before studying of more complex systems. Manipulators with less that one degree of freedom are by far the most common manipulators used by industry. We have also noticed that many of the multiple-degree-of-freedom manipulators in our laboratory tend to be used in a zero-degree-of-freedom mode. With this formulation of the dynamics it should be possible in principle to compute the Lagrangian dynamics of manipulators with less than one degree of freedom in real time.