Dynamics of Manipulators with Less Than One Degree of Freedom
Acknowledgments. This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. My thanks to Marvin Minsky, Phil Agre, and David Chapman for pointing out relevant trends in current robotics research. A.I. Laboratory Working Papers are produced for internal circulation, and may contain information that is, for example, too preliminary or too detailed for formal publication. it is not intended that they should be considered papers to which reference can be made in the literature.
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.