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 problem involving only two branches which are mathematically defined and related with the manipulatorʹs assembly configurations. For solving that problem, the analytical solution of two simple quadratic equations is found. A simple existence criterion is also obtained to detect the set of points forming the manipulatorʹs workspace. On the other hand, the singularity curves are composed of sets of singular points. In order to obtain the singular points, the properties of the Jacobian matrix are used. The complete method has been implemented and tested, as illustrated with examples for different geometrical properties of the manipulator. For each of these examples, the corresponding singularity curves are graphically generated to obtain the practical manipulatorʹs workspace. This feature is a very powerful design tool which is indispensable in visualizing and analyzing the kinematic working capability of the manipulator.