基于李群理论的2R1T并联机构构型综合

应用李群理论,对2R1T(两转动—移动)并联机构的型综合问题进行了系统地研究. 通过分析满足2R1T自由度性质的动平台的李群代数结构,并依据李群代数结构与刚体运动的对应关系,确定出各支链的李群代数结构和它们的等效运动链,最终综合出4394种2R1T并联机构新构型,并绘制了支链机构简图和部分机构简图. 研究结果表明,该方法简单、规范、有效,可作为构型评价及优化的基础,也适用于其他类型并联机构的型综合研究. 

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.