On the quantification of robot redundancy

We evaluate the measure of kinematic flexibility as an index that quantifies the manipulator's redundancy. Initially, we propose a general algorithm for its calculation, then present two illustrative numerical examples of redundant mechanisms and discuss the obtained results. We show that the distribution of the kinematic flexibility throughout the workspace can be a discontinuous function. There exist different sub-domains of joint angles corresponding to the same primary task. In some poses, the manipulator is able to pass from one sub-domain to another continuously, while in other cases the manipulator cannot change the current sub-domain without violating the primary task constraints. This fact may have important implications in robot control.