Forward Kinematics of the 6-5 Planar Stewart Platform

This paper examines an efficient algebraic method to solve the forward kinematics problem of 6-5 planar Stewart platform is presented. Based on the algebraic method, we convert a non-linear equation system solving the problem into a 20th-degree univariate equation. We also find all solutions corresponding to the possible configurations of the platform for a given set of leg lengths. All computations are performed symbolically or using rational arithmetic. Therefore, no numerical error is incurred in the whole computation process. The result is verified by a numerical example, whose solutions agree with the original equations without extraneous roots.