中文摘要：

用李群李代数理论方法研究具有三维空间柔性变形杆件的机器人的动力学分析问题。首先用李群李代数法描述空间二柔性杆件机器人的运动学，然后给出空间柔性杆件微小段的质量密度和刚性密度，通过积分得到空间二柔性杆件的动能和势能。用Rayleigh-Ritz方法进一步研究柔性杆件动力学，并用MATHEMATICA软件仿真分析机器人末端点的空间变形和空间位置，与ANSYS／ADAMS联合仿真的结果进行对比，证明了建模方法的有效性。

英文摘要：

The dynamics of a robot with spatial compliant links is studied by using Lie groups and Lie algebra. Kinematics of the robot with two spatial compliant links is investigated based on the concept of deflect screw, then mass density and spatial stiffness density of a infinitesimal element are discussed, kinetic energy and potential energy of the whole link can be obtained further by integral. The dynamic property of the robot is analyzed by using Rayleigh-Ritz method, deflection and the spatial position of the robotic tip are simulated by MATHEMATICA. Illustrative cases using Lie Group ＆ Lie Algebra method and ANSYS/ADAMS show the time response of the positions at the end of the second link in the same plots, which convinces the effectiveness of the study by using Lie groups and Lie algebra to solve the problems of robot with distributed compliant links.