Forward Kinematics of 3-RPS Parallel Mechanisms Using Conformal Geometric Algebra

In this paper, we propose a novel solution process for the forward kinematics of general 3-RPS parallel mechanisms based on conformal geometric algebra (CGA). First of all, the position of one of the three spherical joints is expressed in the rotational angle about the axis of one kinematic chain RPS. Secondly, the other two spherical joints can be determined by this angle via CGA operation. Thirdly, an explicit 16th-degree univariate polynomial equation is reduced from two geometric constraint equations. At last, one numerical example is employed to verify the solution procedure. The novelties of this paper lie in that (1) the modeling formulation and the elimination procedure have intrinsic geometric intuition due to the use of CGA and (2) the 16th-degree polynomial equation without extraneous roots is explicitly formulated and suitable for implementing the mathematics mechanization of this problem.