Kinematics of the Gough-Stewart Platform by Means of the Newton-homotopy Method

Abstract

In this work the forward kinematic problem of the general Gough-Stewart platform is easily formulated and solved combining the homotopy continuation method and the Newton-Raphson method. Unlike most contributions approaching the topic, in this work the Gough-Stewart platform is considered as a parallel manipulator of general geometry, e.g., it is composed of two three-dimensional platforms. The closure kinematic constraints required to approach the forward displacement analysis are formulated based on linear combinations of three unit vectors attached to the moving platform and one vector relating the position of the moving platform as observed from the base. For the robot manipulator of general geometry a non-linear system of twelve non-linear equations are generated and solved by means of the Newton-homotopy continuation method. Numerical examples are provided with the purpose to illustrate the proposed method.