Necessary and sufficient condition for a generic 3R serial manipulator to be cuspidal

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 cusp point in workspace 3R serial robots. proved be necessary and sufficient condition for orthogonal cuspidal, but it not possible extend this non-orthogonal goal paper is prove that stands any generic robot. This result would give designer more flexibility. In presented work, geometrical interpretation kinematics revisited important observations nonsingular change posture are noted. presents theorem regarding reduced aspects Based these theorem, we robot cuspidal.