A Novel Semi-analytical Algorithm for Forward Kinematics of 6-DOF Parallel Mechanisms

This paper aims to provide a novel semi-analytical algorithm to forward kinematics for six degrees of freedom (6-DOF) parallel mechanisms based on the idea of topological reconfiguration. First, the concept of virtual limbs is introduced. Four source configurations are reconfigured into low-coupling 12-6 configuration, and topology coupling-reducing of parallel mechanisms is realized. Then, six low degree compatibility equations of 12-6 configuration are derived, and the correctness is verified. The explicit expressions of compatibility equations about the limb lengths are derived, and a 24th-degree univariate equation can be obtained by using the Grӧbner basis. Subsequently, the succinct and unique symbolic forward solution of 12-6 configuration are derived. Finally, the algorithm is demonstrated by the numerical example.