中文摘要：

基于有限元法、Lagrange方程和运动协调条件，建立了3-RRS柔性并联机器人的弹性动力学模型。分析了含有Rayleigh阻尼的3-RRS柔性并联机器人的振动特性。通过算例，揭示了系统阻尼固有频率与模态衰减系数的变化规律。研究3-RRS柔性并联机器人系统的振动特性可为此类机器人的机构优化设计、控制和工程应用提供指导。

英文摘要：

A new model of spatial flexible beam element is presented. The dynamics model of a 3-RRS flexible parallel manipulator is derived based on the finite element method, Lagrange formulation and constraint conditions of the legs and the movable platform. Then, the vibration characteristics of the flexible parallel manipulator with Rayleigh damping are discussed. After that, the damped natural frequencies and modal damping coefficient of this mechanism are analyzed through an example. The results of the example show that, because of Rayleigh damping, the amplitude of the free vibration response of the system sharply decay with time. For the system with small damping, the approximate solution of the primarv natural frequency can be calculated by neglecting the influence of the damping.