A Unified Algorithm for the Forward Displacement Analysis of In-parallel Stewart-Gough Platforms

This paper presents a unified algorithm for solving the forward displacement problem of in-parallel Stewart-Gough platforms (SGPs), i.e., the connection joints are not restricted to lie in a plane. The novelty of this paper lies in that the new algorithm is versatile and robust for in-parallel SGPs. In this paper, we classify all in-parallel SGPs into five cases in terms of the number of solutions, i.e., I, 40; II, 32; III, 24; IV, 16 and V, 8. Firstly, the eight basic constraint equations are formulated based on the dual quaternion. Then, using Gröbner basis theory, 19 Gröbner bases are obtained for constructing the 19×19 Sylvester resultant matrix for the first four cases while 7 Gröbner bases are obtained for constructing the 7 × 7 matrix for the last one, and the constructed matrix directly leads to a corresponding high-degree univariate polynomial equation for the different case of in-parallel SGPs. At last, several numerical examples are given to validate the efficiency of the new algorithm.