Closed-form forward kinematics for a symmetrical 6-6 Stewart platform using algebraic elimination

This paper studies the forward kinematics of a symmetrical 6-6 Stewart platform, in which both the base and the mobile platform are hexagons and the joint centers satisfy some conditions. A concise algebraic elimination algorithm to solve the closed-form forward kinematics of the Stewart platform is presented. Based on the presented algebraic method, an interesting result that comes out of our study is that the forward kinematics problem is reduced to solve a univariate polynomial equation of degree at most 14. The 14th degree univariate polynomial is derived from the determinant of the 15 × 15 Sylvester’s matrix, which is relatively small in size, without factoring out or deriving the greatest common divisor. The algorithm is comparatively concise and requires fairly less computation time. The result is verified by a numerical example.