中文摘要：

研究一种球坐标型并联机构的精确弹性动力学建模方法．以该机构为主进给模块的Tricept机器人已成功应用于汽车及飞机制造业．应用运动弹性动力学理论，分别建立其无约束主动支链、恰约束从动支链与动平台的运动微分方程，进而借助弹性变形协调条件组集系统的运动微分方程．为提高建模精度，各支链均离散为Euler-Bemoulli空间梁单元，其主动副（移动副）及连架副（虎克铰链）的处理则分别应用了节点自由度耦合技术与斜交支座原理．结合典型算例，进一步分析了工作空间中系统一阶固有频率的分布情况，明确了影响系统动态特性的关键设计参数，为具有自主知识产权的类Tricept机器人的动态优化设计及物理样机开发奠定了基础．

英文摘要：

An analytical approach to the accurate elasto-dynamic modeling of a spherical coordinate parallel mechanism （SCPM） is presented, which has been employed as the positioning module of the Tricept robot and found successful applications in the automobile and aircraft manufacturing industry. Firstly, the elasto-dynamic equations of the unconstrained active limbs and the constrained passive limb were formulated by utilizing the kineto-elastodynamics theory. To model the elastic deformations more precisely, all the limbs were discretized into several Euler-Bernoulli spatial beam elements, the elastic deformation coupling technique was utilized to simulate the actuated prismatic pairs, and the Hooke＇s joints attached to the stationary platform were treated as the skewed bearings. Then, the elastodynamic equations of the SCPM were assembled with the aid of the motion equations of the moving platform and the elastic deformations compatibility conditions. Finally, the distribution of the first order natural frequency of the SCPM throughout the entire workspace was analyzed, and the structural parameters having significant impact on the dynamic performance of the system were proposed. These investigations may provide designers with informative guidelines for the dynamic design and prototype development of novel Tricept-like robots.