Abstract: The elastodynamics model of a spherical 2-DOF redundantly actuated parallel robot was established.Firstly，the six space curved rods of the robot system were divided into six substructures，considering the space curved rod bending， tensile and torsion deformations，the elastodynamics model of each substructure was derived based on finite element method.Then，according to the constraint characteristics of the joint rotations，elastodynamics models of every branches were established，and according to the deformation coordination constraints between each branch and the output shaft， the system's elastodynamic model was obtained by assembling the three branches.Finally，based on the comparison of the inherent frequencies which were gained by the theoretical calculation and finite element simulation when the robot was in the initial positions，the correctness of the natural frequencies was verified.By comparing the dynamic responses of spherical 2-DOF redundant and non-redundant actuated parallel robots，it is verified that the output maximum elastic displacement of the output may be significantly reduced by introducing redundant actuation.The research results provide a reliable basis for the structure optimization design and the vibration research of the parallel robots with spatial curved rods.

Key words: parallel robot, elastodynamics, natural frequency, redundant actuation

摘要： 建立了球面2-DOF冗余驱动并联机器人弹性动力学模型。将机器人系统的6个空间弯杆划分为6个子结构，考虑空间弯杆的弯曲、拉伸和扭转变形，基于有限元法求出了各子结构的弹性动力学模型；根据转动副的约束特点以及各分支与输出轴的变形协调约束关系，将子结构组装成3个分支并进行装配，得到系统的弹性动力学模型；将理论计算与有限元仿真得到的机构在初始位置时的固有频率进行对比，验证了系统弹性动力学模型的正确性。通过对比分析球面2-DOF非冗余与冗余驱动并联机器人输出端的动态响应，验证了冗余驱动的引入可以明显减小机器人输出端的最大弹性位移。研究结果为含有空间弯杆并联机器人的结构优化设计以及振动分析提供了理论依据。

关键词: 并联机器人, 弹性动力学, 固有频率, 冗余驱动