Improved dialytic elimination algorithm for the forward kinematics of the general Stewart–Gough platform

This paper presents the forward kinematics of the general Stewart–Gough platform using dialytic elimination. The proposed algorithm, when implemented in a computer language, provides all the solutions in fairly less computation time compared to the existing ones, mainly due to the fact that it directly leads to a 40th-degree univariate equation from a constructed 15×15 Sylvester’s matrix which is relatively small in size. In addition, the ways to avoid ill-conditioned linear systems in the solution procedure are dealt with for the purpose of enhancing the accuracy of the computed poses. Numerical examples are given to demonstrate the developed algorithm.