Kinematics of the 3(RPSP)-S Fully Spherical Parallel Manipulator by Means of Screw Theory

In this work, the kinematics of a spherical parallel manipulator composed of three peripheral limbs equipped with linear actuators and a passive center shaft is approached by means of the theory of screws. The displacement analysis is carried out solving closure equations, which are obtained upon simple linear combinations of the components of two unit vectors describing the orientation of the moving platform. After, the input-output equations of velocity and acceleration of the spherical parallel manipulator are systematically obtained by resorting to reciprocal-screw theory. This strategy avoids the computation of the passive joint velocity and acceleration rates of the robot manipulator. Numerical examples illustrate the efficiency of the proposed method.