In a previous work, this author showed that ten topologies for under-actuated parallel wrists can be generated from the fully-parallel wrist. Three of them are obtained by simply replacing a spherical pair (S) with a nonholonomic spherical pair (nS). The S-(nS)PU-SPU, and S-(nS)PU-2SPU wrists are two of these three. The position analysis of these two wrists is studied in this paper. In particular, all the four position-analysis problems, which are necessary for implementing their path planning, are addressed and solved in closed-form. Despite their different topology, the position-analysis of these two wrists can be practically solved by using the same formulas and algorithms. Based on the deduced formulas, a path-planning algorithm is proposed. The obtained results make the studied wrist topologies able to replace “ordinary” wrists in the manipulation tasks which do not require tracking.

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