Abstract

A formulation for solving the direct kinematics of the general Stewart platform consisting of six moving and six grounded spheric joints is presented. The homotopy method is used for solving the direct kinematics of the platform, and it is shown that there exist a maximum of 40 possible solutions to the direct kinematics problem. These 40 solutions can be obtained by tracking only 64 homotopy paths. It is also shown that there are a maximum of 24 solutions for the Stewart platform with four spheric joints, and there exist a maximum of 16 solutions to the direct kinematics of the Stewart platform with three moving and three grounded spheric joints thus confirming the correctness of 24th and 16th degree direct kinematics polynomials obtained by other researchers.

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