On the 5R spherical, symmetric manipulator: workspace and singularity characterization

This article presents an integrated methodology for the determination of the workspace and the singularity distribution for the 5R spherical, symmetric manipulator. In the first instance, the branching problem of the manipulator was considered and its solution was used to locate positions on a sphere that can be attained by the end effector. Moreover, it was found that the bounds on the workspace depend on the relative position existing between two major circles and two minor circles, which were geometrically determined in terms of the manipulator’s link lengths. Second, singular configurations were defined and singularity curves were generated. Thus, it was possible to obtain an integrated characterization scheme for the workspace and singularity distribution, by analyzing the relative position of the major and minor circles. As a result, 14 different characteristic shapes of the manipulator’s workspace and their related singularity curves were obtained. This should be a key issue in the context of manipulator’s design and trajectory design.