The range of self-motion of redundant robots

One way to represent and analyze the amount of manipulator kinematic redundancy is by visualizing and evaluating the mechanism´s self-motion ability. The self-motion of a D-degree-of-redundancy manipulator can be represented as a D-parametric hyper-volume (area when D=2, or curve when D=1) in the n-dimensional configuration space of joint coordinates whose form and size depend on the mechanism´s parameters, mechanism´s configuration, and on the current values of the primary task coordinates. We propose a general computational procedure and display the self-motion curves of 1-degree-of-redundancy mechanisms corresponding to various combinations of primary task coordinates that regularly appear in today´s robotic practice. We observe that the self-motion curves are periodic functions of joint coordinates (in revolute-joint manipulators, the period in the direction of each joint coordinate is 2/spl pi/). We also observe that only in special cases of mechanism´s structure and values of primary task coordinates, the self-motion produces connected curves (such as circles, ellipses, fans, etc.) in joint space. This is related to the capacity of the mechanism to circulate through all possible (groups) of configurations.