Closed-form direct position analysis of the general Stewart-Gough manipulator robot

General Stewart-Gough manipulator robot is a six degree of freedom, parallel manipulator, which consists of a base platform, a mobile platform and six limbs connected at six distinct points on the base platform and the mobile platform respectively. The direct position analysis problem of General Stewart-Gough manipulator relates to the determination of the mobile platform pose for a given set of the lengths of the limbs. In this paper, we present a concise algebraic method for solving the direct position analysis problem for the fully parallel manipulator with general geometry, often referred to as General Stewart-Gough manipulator. Based on the presented algebraic method, we derive a 40th degree univariate polynomial from a determinant of 20 x 20 Sylvester´s matrix, which is relatively small in size. We also obtain a complete set of 40 solutions to the most general Stewart platform. The proposed method is comparatively concise and reduces the computational burden. Finally the method is demonstrated by a numerical example.