The 4SPS-2CCS Generalized Stewart-Gough Platform Mechanism and Its Direct Kinematics

This paper presents the 4SPS-2CCS generalized Stewart-Gough platform(GSP) Mechanism and its direct kinematics. We prove that the direct kinematics problem(DKP) of the 4SPS-2CCS GSP has at most 160 non-singular solutions by using Mourrain variety. We also obtain all 160 non-singular solutions of the direct kinematics problem in a numerical example by using quaternion and homotopy continuation method. The example shows that the upper bound of 160 solutions can be reached in the general case. The use of quaternion, in stead of using Euler angle rotation matrix, can reduce the Bezout number of the equations and the calculation time. The result is verified by a numerical example. Based on this result, the proposed algorithm is simple and can make the computer program easy to write. And the research builds the theory basis for dimensional design, trajectory planning and control of this type of manipulator.