Generalized Kinematics Analysis of Hybrid Mechanisms Based on Screw Theory and Lie Groups Lie Algebras

Abstract The advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms, and the generalized analysis method and concise kinematics transfer matrix are obtained. First, according to the kinematics analysis of serial mechanisms, the basic principles of Lie groups Lie algebras in dealing with the spatial switching and differential operations of screw vectors are briefly explained. Then, based on the standard ideas of Lie operations, the method for kinematics analysis of parallel mechanisms is derived, and Jacobian matrix and Hessian matrix are formulated both recursively and in closed form. After that, according to the mapping relationship between the parallel joints and the corresponding equivalent series joints, a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are studied. A case study is performed to verify the calculated matrices, in which a humanoid hybrid robotic arm with the parallel-series-parallel configuration is taken as an example. Simulation experiment results show that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practicable.