Kinematics of the 3-RSR wrist

Among the new architectures for parallel wrists, recently presented in the literature, one of the simplest is the architecture of the 3-revolute-spherical-revolute (RSR) wrist. The kinematics of the 3-RSR wrist has not been presented yet, in the literature. This paper presents the kinematic analysis of the 3-RSR wrist. In particular, the demonstration that the 3-RSR wrist makes the end-effector perform finite spherical motion is reconsidered from a different point of view. The new demonstration directly provides the constraint singularities of the 3-RSR wrist. Moreover, the position analysis of the 3-RSR wrist is reduced to the solution of problems already solved in the literature. Finally, the mobility analysis of the 3-RSR wrist is addressed, and all its singularity conditions are found in analytical form and geometrically interpreted.