Inverse kinematics of the 2-RRS-1-RRRR cable actuated mechanism

This work presents an inverse kinematics (IK) formulation of a spatial, cable actuated 2-degree-of-freedom mechanism. The 2-RRS-1-RRRR mechanism studied in this work is derived from the well-known quaternion joint. The system of 13 constraint equations have mixed variables in joint and task spaces, and is solved using polynomial homotopy continuation. Further on, the extraneous solutions are eliminated using the filtering conditions.