Definition, Determination and Characterization of Acceleration Sets for Spatial Manipulators

In this report the approach developed by the authors, for systematically studying the acceleration capabilities and acceleration properties of the end-effector of a planar 2 degree-of-freedom manipulator, is extended to the general spatial manipulator with three degrees-of-freedom. A central feature of this report is the determination of the properties of the quadratic mapping between the joint-velocity space and the acceleration space of P which then makes it possible to obtain analytical solutions for most acceleration properties of interest. We show that a fundamental way of studying these quadratic mappings is in terms of the mapping of input line congruences into output line congruences. KR