Instantaneous Kinematics and Singularities of Two Types of Under-Actuated Parallel Wrists

S-(nS)PU-SPU and S-(nS)PU-2SPU are two out of three types of under-actuated wrists that are generated from the “ordinary” wrists of type S-3SPU (fully-parallel wrists), by replacing a spherical pair (S) with a nonholonomic spherical pair (nS) according to the rules stated in [1]. Position analysis, controllability, and path planning of these two wrist types have been addressed and solved in two previous papers [2, 3] of this author. Their kinetostatics and singularity analysis have not been addressed, yet; and they are studied in this paper.