Kinematics of a new spherical parallel manipulator with three equal legs: The 3‐URC wrist

Parallel manipulators are constituted of two rigid bodies, one movable (platform) and the other fixed (base), connected by a number of kinematic chains (legs). Manipulators with all equal legs that have the actuators adjacent to the base allow the use of simplified design procedures and manufacturing processes. Moreover, they are able to reach high performances. Further manufacturing simplifications can be obtained if only revolute pairs and passive cylindrical pairs are used. This article presents a new spherical parallel manipulator, named the 3‐URC wrist. The 3‐URC wrist is not overconstrained. It has three equal legs having only passive cylindrical pairs and revolute pairs with the actuators adjacent to the base. The 3‐URC wrist mounting and manufacturing conditions making spherical motions of the platform possible are defined. Then the position analysis and the mobility analysis of the 3‐URC wrist are solved. Finally, the singularity conditions are written in explicit form and geometrically interpreted.