The Maximal Singularity-Free Workspace of Planar 3-RPR Parallel Mechanisms

To avoid kinematic singularities inside the workspace of parallel mechanisms is a basic requirement in robot design. This paper addresses the case of planar 3-RPR parallel mechanisms. By investigating the singularity equation, it is discovered that the singularity locus of any point on the platform is a circle, if the base and the platform are similar triangles. Furthermore, the centres of three circles for workspace have been proved to lie exactly on the singularity circle. With these useful information, the leg length ranges can be determined by analyzing the workspace. For a base of unit area, it is found that robots with equilateral triangle base and platform can obtain the maximal singularity-free workspace. Three case studies demonstrate this result. Finally, a geometric design procedure for this type of robot is proposed and an example is provided