| An algorithm for generating the workspace for manipulator geometries involving orthogonal and parallel joint axes was developed. In addition, Gaussian Divergence Theorem has been introduced for computation of workspace volume, centroid, and moments of inertia about the three principal axes. This technique permits a closed form, high accuracy, quantitative measurement of geometric properties of a robot. The workspace generation algorithm traces singular surfaces and D-surfaces. Those are operating barriers within the workspace. Suggestions about the arrangement of joint parameters to minimize the occurrence of the re-entrant surfaces are presented. A penalty function is proposed to be combined with manipulability index. The manipulability can detect how close the robot is to a singular configuration as well as the nearness to a joint limit. |
