Type synthesis of 2R1T parallel mechanism based on lie group theory

Based on Lie group theory, the type synthesis of 2R1T (2 rotations and 1 translation) parallel mechanism was systematically studied. By analyzing the Lie group algebraic structure of the moving platform to meet 2R1T degree-of-freedom nature, and based on the correspondence between Lie group algebraic structure and the rigid body motion, the Lie group structure of the three limbs and their equivalent kinematic chains were determined. Finally, 4394 configurations of 2R1T parallel mechanisms were obtained, and the schematics diagrams of the limbs and some configurations of 2R1T parallel mechanisms were listed. These results show that the method of type synthesis is simple, normative and effective, which can provide the foundation for the evaluation and optimization of configurations and can be applied for other kinds of parallel mechanisms type synthesis.