Kinematics of a Novel Single-Loop Under-Actuated Wrist

A novel type of parallel wrist (PW) is proposed which, differently from previously presented PWs, features a single-loop architecture and only one nonholonomic constraint. Due to the presence of a nonholonomic constraint, the proposed PW type is under-actuated, that is, it is able to control the platform orientation in a three-dimensional workspace by employing only two actuated pairs, one prismatic (P) and the other revolute (R); and it cannot perform tracking tasks. Position analysis and path planning of this novel PW are studied. In particular, all the relevant position analysis problems are solved in closed form, and, based on these closed-form solutions, a path-planning algorithm is built.