Forward kinematics of the general Stewart-Gough platform using Gröbner basis

This paper studies the forward kinematics of the general Stewart-Gough platform, 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. A new concise closed-form solution to the forward kinematics of the general Stewart-Gough platform is obtained by using Grobner basis theory. The forward kinematics problem of the general Stewart-Gough platform is reduced to a 40th degree polynomial in a single unknown from a constructed 18 × 18 Sylvester´s matrix which is relatively small in size. A complete set of 40 solutions to the most general Stewart-Gough platform are also obtained. The proposed method is exemplified by a way of one particular example of a Stewart-Gough platform for which we obtain 40 postures.