Unified infinitesimal kinematics of a 3-RRR/PRR six-degree-of-freedom parallel-serial manipulator

In this work, the kinematics of a parallel-serial manipulator is approached by means of geometric algebra and the theory of screws. The proposed hybrid robot manipulator is composed of a 3-RRR planar parallel manipulator and a spatial PRR serial manipulator attached to the center of the moving platform of the lower 3-RRR parallel manipulator. The combination of the 1R2T motion of the lower parallel manipulator with the 2R1T motion of the upper serial chain allows to perform general motions with the combined parallel-serial manipulator. The inverse-forward position analysis of the robot yields closed-form solutions that allow to determine all the possible configurations of the robot. Thereafter, the velocity and acceleration analyses are approached by resorting to reciprocal screw theory. Numerical examples are included in order to confirm the reliability of the method of kinematic analysis employed in the contribution.