Abstract: 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.

Key words: Compliant mechanisms, Dynamics, Lie algebra, Lie groups, Robot