Under-Actuated Nonholonomic Parallel Wrists

The introduction of nonholonomic constraints in parallel manipulators, in general, allows the reduction of the actuated-joint number without consistently affecting the reachable workspace. This principle is applied here to obtain new architectures of under-actuated parallel wrists. New hardware solutions are proposed for a nonholonomic spherical (nS) pair that was proposed in a previous paper. Then, this nonholonomic pair is used to generate ten novel architectures for under-actuated spherical wrists. Eventually, the controllability of the architectures with only one nS pair is demonstrated without resorting to the use of Lie brackets.