Base invariance of the manipulability index

The manipulability index suggested by Yoshikava is an important tool for the design of mechanisms and their control. It represents a quantitative measure of the functionality and the ability for realizing some tasks or groups of tasks. This index is some kind of performance measure and should be taken into consideration in the design phase of a mechanism and also in the design of control algorithms.In this paper two important properties of the manipulability index are investigated. The first part of the present work demonstrates that manipulability of a mechanism is independent of task space coordinates. In the second part, a proof of the independency of the manipulability index on the first DOF is given.This invariance is important for simplification of the mechanism's Jacobian matrix and gives excellent insight into the dependences of configuration space coordinates on this index. Moreover, it proves that the manipulability index is determined only by relative positions of the mechanism itself and by the mechanism's geometry.Finally, the properties of the manipulability index are illustrated by some examples for fundamental open kinematical chain structures.