Self-Motion of the 3-PPPS Parallel Robot with Delta-Shaped Base

This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equi-lateral mobile platform and an equilateral-shaped base. Like the other 3-PPPS robots studied in the literature, it is proved that the parallel singularities depend only on the orientation of the end-effector. The quaternion parameters are used to represent the singularity surfaces. The study of the direct kinematic model shows that this robot admits a self-motion of the Cardanic type. This explains why the direct kinematic model admits an infinite number of solutions in the center of the workspace at the "home" position but has never been studied until now.