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We present singularity-free workspace optimization of a class of two-degree-of-freedom (2-DoF) parallel wrists with large rotation range capability. The wrists in consideration are kinematically equivalent to two families of 2-DoF homokinetic couplings. The first family comprises fully parallel wrists with N (N ≥ 3) double-universal (
) legs. The second family comprises spherical N-
parallel wrists with interconnecting revolute (
) joints. Both families belong to the more general class of zero-torsion parallel manipulators, and are, therefore, collectively referred to as zero-torsion wrists (ZTWs). We carry out a unified singularity-free workspace optimization by utilizing geometric properties of zero-torsion motion manifolds. Our work may serve as a conceptual guide to the design of ZTWs for large tilt-angle applications.
D. Zhang and F. Zhang addressed the issue of designing and analyzing totally decoupled 3-DOF spherical parallel manipulators (SPMs) and concluded that the SPMs in Figs. 5(a) and 5(b) of ref.  are completely decoupled and fully isotropic (see Abstract, Section 5, and Conclusions in ref. ). This topic is of great interest to researchers working in the general area of parallel mechanisms. However, we disagree with the authors of ref.  on their conclusion.
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