Forward Kinematics of the 6-6 Stewart Platform with Planar Base and Platform Using Algebraic Elimination

Abstract

This paper presents a new algorithm to solve the closed-form forward kinematics of the general 6-6 Stewart platform with planar base and moving platform. Based on the presented algebraic method, we derive the 20th degree univariate polynomial from the determinant of the 15x15 Sylvester's matrix, which is relatively small in size, without factoring out or deriving the greatest common divisor. We also find that the highest degree of the univariate polynomial is in accordance with the determinant of the univariate coefficient matrix, however, many prevenient methods are not so. The algorithm is comparatively concise and requires fairly less computation time enough to be used for real-time applications. The result is verified by a numerical example.