Necessary and sufficient condition for a generic 3R serial manipulator to be cuspidal. (May 2022) - Salunkhe, Durgesh Haribhau; Spartalis, Christoforos; Capco, Jose; Chablat, Damien; Wenger, Philippe
Abstract: Cuspidal robots can travel from one inverse kinematic solution to another without meeting a singularity. The name cuspidal was coined based on the existence of a cusp point in the workspace of 3R serial robots. The existence of a cusp point was proved to be a necessary and sufficient condition for orthogonal robots to be cuspidal, but it was not possible to extend this condition to non-orthogonal robots. The goal of this paper is to prove that this condition stands for any generic 3R serial robot. This result would give the designer more flexibility. In the presented work, the geometrical interpretation of the inverse kinematics of 3R robots is revisited and important observations on the nonsingular change of posture are noted. The paper presents a theorem regarding the existence of reduced aspects in any generic 3R serial robot. Based on these observations and on this theorem, we prove that the existence of a cusp point is a necessary and sufficient condition for any 3R generic robot to be cuspidal. Highlights: Geometric observations on the inverse kinematic model of generic 3R serial robot. Geometric interpretation of nonsingular posture change in a generic 3R serial robot. Proof of existence of reduced aspects in generic 3R serial robots. Proof of a necessary and sufficient condition for a generic 3R serial robot to be cuspidal.