Design procedure for cuspidal parallel manipulators

In the design of parallel manipulators, a major problem is their reduced operational workspace. This is mainly due to the existence of a complex singularity locus within the workspace. The singularity-free workspace therefore corresponds to only a fraction of the potential workspace, and dimensioning the manipulator is intended to optimize such singularity-free workspace. The singularity locus often divides the workspace into isolated volumes according to assembly modes and working modes. As a result, it is common to restrict the operational space to a simple geometric shape inside a singularity-free workspace. However, it is well known that appropriate motion planning can make the most of a more complex workspace by means of transitions between working mode and/or assembly mode. In this paper, the authors obtain the locus of cusp points in the joint space entity, which will permit non-singular assembly mode changing in cuspidal manipulators. Making use of such entity, the optimum dimensional parameters are obtained which increase the possibility of non-singular transitions while obtaining a maximal, regular-shaped workspace.