Design criteria and constructive schemes are presented for a nonholonomic spherical (nS) pair proposed previously, along with a reconfigurable version of the same pair, named nS pair. Type synthesis of the underactuated parallel wrists derived from the fully parallel wrist (FPW) topology is addressed by replacing passive spherical (S) pairs with nS or nS pairs. Ten novel topologies of underactuated spherical wrists with practically the same workspace as the original FPW are identified. Wrist architectures based on these novel underactuated-wrist topologies are proved to be globally controllable, and a general path planning algorithm is proposed for these wrists. Here, the substitution of holonomic constraints with nonholonomic ones reduces the number of actuators and, sometimes, the number of links, too.

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