中文摘要：

基于李群分析了2T1R并联机构动平台运动的几何条件,得到满足动平台运动要求的李群结构。通过线性组合得到多种满足光滑位移子流形的支链构型。建立了并联解耦机构的设计准则。以此为据,得到了2T1R并联解耦机构的KP（kinematic pair）旋量系。从满足三维及四维光滑位移子流形的支链构型中确定出满足解耦条件的支链集。综合出9种基于基本副的2T1R并联解耦机构,绘制了构型简图。应用旋量理论对机构的输出特性进行了验证。研究表明：以李群作为型综合的基础,采用旋量理论进行解耦优化,对于并联解耦机构的型综合具有普适性。

英文摘要：

2T1R parallel mechanisms are analyzed based on Liegroup. Lie group structures are obtained to meet the character of the moving platform. Chain structures are got through the linear combination of Lie groups. The design criteria are established for the decoupling mechanism. According to the design criteria, the kinematic pair screw system of 2T1R decoupling parallel mechanisms are attained. The chain set of satisfied the decoupied condition are established from the chain type meet smooth displacement submanifolds. Nine mechanisms are synthesized based on three and four dimensional submanifoldsl dimensional chains and the figure of configuration are shown. The output characters of the mechanism are verified based on screw theory. The research shown： the Lie group can be the foundation of the type synthesis and the screw theory are adopt to optimization decoupling parallel mechanism has great universality.