Some Considerations on the Self-Motion Curves of a Planar 3R Manipulator

In this article, we evaluate the self-motion curves of a 3R planar manipulator possessing one-degree-ofredundancy, different link lengths and joint limits. We demonstrate that one or two self-motion curves correspond to a given combination of values of primary task coordinates. Because of the manipulator’s mechanical restrictions, the self-motion can at one time be realized within one curve and the manipulator cannot switch to another curve without violating the constraints of the primary task. Partition of the self-motion domain into disconnected curves can disrupt the control process and thus decrease the ability of the manipulator to solve secondary tasks in the best possible way. We display and discuss the self-motion curves of this manipulator solving two different primary tasks.