Screw theory and higher order kinematic analysis of open serial and closed chains

Abstract

In a pair of recent contributions by the authors of this paper, it has been shown that screw theory can be successfully employed in the acceleration analysis of open and closed spatial chains. In this contribution, a novel method for the velocity, acceleration, and jerk analysis of spatial chains is introduced. The method is based in obtaining recursive expressions for the velocity, acceleration, and jerk of the end effector of a serial manipulator. This new method facilitates greatly the derivation of some well known results concerning the velocity and acceleration analyses of spatial chains. Furthermore, the method provides proofs of several new results for the jerk analysis which were not possible using methods developed previously. In addition, the contribution shows how the results of open serial chains can be applied to closed chains and parallel manipulators. Finally, the method can be easily generalized to higher order analyses.