Forward Kinematics Analysis of the Gough-Stewart Platform Using Orthogonal Complement Method

摘要

This paper presents a new method to derive the closed-form solution of the forward kinematics of the symmetrical Gough-Stewart platform, in which both the fixed base and the moving platform are symmetrical hexagons circumscribed in a circle, respectively. Firstly, analyzing the coupling relationships between the position and orientation variables of the moving platform, and their geometry meanings, eleven compatible algebra equations are obtained. Then, based those compatible equations obtained earlier, the orthogonal complement method is used to eliminate the redundant variables. In the end, the problem of the forward kinematics analysis of the symmetrical Gough-Stewart platform parallel mechanism is expressed as a 14th-degree univariate polynomial equation; and an example is presented to verify the correctness of the new method.