Forward kinematics of the general 6-6 Stewart platform using algebraic elimination

It is known that the number of solutions of the forward kinematics of the general 6-6 Stewart platform is up to 40 in the complex domain. Finding all the solutions is necessary when all the possible postures are of interest or a unique actual posture is to be determined by choosing the correct one out of the solutions. In such cases, algebraic elimination method can be a powerful tool. In this article, an elimination procedure for the forward kinematics of the general 6-6 Stewart platform is presented, which leads to a 40th-degree univariate equation without factoring out or deriving the greatest common divisor. In addition, the proposed method, when implemented in a computer language, requires less computation time than the existing algorithms do mainly because the size of the final Sylvester's matrix is relatively small. The algorithm is demonstrated by two numerical examples.