Avoiding the singularities of 3-RPR parallel mechanisms via dimensional synthesis and self-reconfigurability

• Singularity avoidance of the 3-RPR parallel robots is treated in this paper.
• Two methods are proposed, dimensional synthesis and self-reconfigurability.
• The proposed algorithms are based on convex programming and convex relaxations.
• A relaxation method based on the McCormick relaxation is presented.
• The running times of the proposed algorithms are remarkably low.

This paper deals with the avoidance of singularities of 3-RPR parallel mechanisms, for a given workspace. Two approaches are proposed: (1) the dimensional synthesis of such robots for a prescribed singularity-free workspace, and (2) their reconfiguration via actuation redundancy. The proposed approach for the dimensional synthesis of 3-RPR parallel mechanisms considers the constraints required for obtaining the optimal mechanism geometry in order to contain a desired workspace while avoiding singularities. A relaxation method based on the McCormick relaxation is presented to convexify the associated optimization problem. To prevent the relaxation from becoming too loose, a branch-and-prune algorithm is proposed, which converges to the globally optimal solution. Upon a different approach, a 3-RPR PM with self-reconfiguration capability is introduced. This redundant manipulator can change its geometry to obtain singularity-free paths between prescribed points inside its workspace. The proposed trajectory planning strategy works in 2 phases: the first where the mechanism acts as a 2-PRPR PM, and the second where it behaves as a 3-RPR PM. Finally, several case studies are presented to demonstrate the performance of the proposed algorithms. The running times of the proposed algorithms are remarkably low compared to those of other methods proposed in the literature.