New and efficient method for the direct kinematic solution of the general planar stewart platform

In this paper a new and efficient algorithm to solve a closed-form direct kinematics solution of the general 6-6 planar Stewart platform is presented. The main idea is to compute the reduced Groebner basis under degree lexicographic ordering for the closed-form equations by using computer algebra firstly. Secondly, select 10 Groebner bases from the obtained 41 ones and construct a 10times10 Sylvester´s matrix, which is relatively small in size. A 20th degree univariate equation is obtained from the determinate of the matrix and all 40 sets closed-form direct kinematics solutions are obtained. The proposed algorithm is simple and reduces greatly the computation burden than the existed methods. The process also shows that there exist many different resultants that will lead to the same univariate equation. The same results can be obtained by using the continuation method. Finally a numerical example is given to verify the algorithm and its results without extraneous roots agree with the original equations.