Algebraic elimination-based real-time forward kinematics of the 6-6 Stewart platform with planar base and platform

This paper presents the closed-form forward kinematics of the 6-6 Stewart platform with planar base and moving platform. Based on algebraic elimination method, it first derives a 20th-degree univariate equation from the determinant of the final Sylvester's matrix of which size is only 4x4. Then, it finds all solutions corresponding to the possible configurations of the platform for a given set of leg lengths. The proposed algorithm requires fairly less computation time enough to be used for real-time applications than the existing ones. Unlike numerical iterative schemes, this algorithm demands no initial estimate and is free from the problem that it fails to converge to the actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and the accuracy of the developed algorithm.