Inverse Kinematics of 2 (3RPS) and 2 (3SPR) Serial-Parallel Manipulators

Abstract Serial-parallel manipulators are of great interest to academic community in recent years, especially those composed of classical parallel mechanisms. There have been many studies around 2(3RPS) and 2(3SPR) S-PMs, but unfortunately their inverse kinematics have not yet been resolved. This paper discovers that the unknown kinematic parameters of middle platform are responsible for the unresolvable of inverse kinematics, meanwhile the unknown kinematic parameters of middle platform also have huge coupling relationships. Therefore, to break through this challenges, the huge coupling relationships are decoupled layer by layer, the kinematic parameters of middle platform are solved by combining Sylvester’s elimination method, and the inverse displacements of 2(3RPS) and 2(3SPR) S-PMs are obtained subsequently. This paper not only solves the inverse kinematics of classical 2(3RPS) and 2(3SPR) S-PMs, but also reveals the essence of the inverse kinematics of general (3-DOF)+(3-DOF) 6-DOF S-PMs and proposes a corresponding solution.