Abstract:

A 4SPS-2CCS generalized Stewart platform is put forward and its forward displacement is analyzed. Based on quaternion, the model of the forward displacement solutions is built up. In order to obtain the number of solutions of this kind mechanism, Mourrain variety is used. The results show that the number of the forward displacement solutions of the parallel mechanism has at most 160. In addition, all the 160 solutions have been obtained by using homotopy continuation method. The example shows that the upper bound of 160 solutions can be reached in the general case. In stead of using Euler angle rotation matrix, the use of quaternion can reduce the Bezout number of the equations and the calculation time to increase the efficiency, and make the computer program easy to write. The result is verified by a numerical example.

Key words: forward displacement analysis, parallel mechanism, homotopy continuation method, quaternion