On the workspace, assembly configurations and singularity curves of the RRRRR-type planar manipulator

In this paper, a broadly applicable approach for numerically obtaining the workspace and the singularity curves of a planar RRRRR-type manipulator is presented. The workspace generation is formulated as a direct kinematic pro blem involving only two branches which are mathematically defined and relat ed with the manipulator's assembly configurations. For solving that problem , the analytical solution of two simple quadratic equations is found. A sim ple existence criterion is also obtained to detect the set of points formin g the manipulator's workspace. On the other hand, the singularity curves ar e composed of sets of singular points. In order to obtain the singular poin ts, the properties of the Jacobian matrix are used. The complete method has been implemented and tested, as illustrated with examples for different ge ometrical properties of the manipulator. For each of these examples, the co rresponding singularity curves are graphically generated to obtain the prac tical manipulator's workspace. This feature is a very powerful design tool which is indispensable in visualizing and analyzing the kinematic working c apability of the manipulator. (C) 2000 Elsevier Science Ltd. All rights res erved.