中文摘要：

为描述柔顺机构动力学特性,需要建立其动力学模型。基于有限元法,根据Lagrange方程建立柔顺机构的动力学方程。在此基础上,得到机构各阶固有频率和模态,并给出固有频率和模态对各项设计变量的灵敏度计算方法。推导出柔顺机构中柔性杆件上任意一点应变的算法,计入应变中的非线性项。求解柔性杆件上任意位置的动应力,并计算杆件在各个时刻的最大应力及出现的位置。以平面柔顺四杆机构为例进行分析,说明基于有限元法对柔顺机构的动力学特性分析的可行性和有效性,并且指出柔顺机构杆件的动应力和应变分析对柔顺机构的优化设计具有重要意义。

英文摘要：

In order to describe the dynamic characteristics of a compliant mechanism, the dynamic model thereof is built. Based on the finite element method, the dynamic equation of compliant mechanism is developed by using Lagrange equation. On this basis, the natural frequencies and modes of the mechanism are derived. A method for calculating the sensitivity of natural frequencies and modes to the design variables is then presented. An algorithm for calculating the strain at any point on a flexible link in the compliant mechanism is derived. Nonlinear terms in the strain are also reckoned in the algorithm. The dynamic stress at any position on the flexible link is solved, and the maximum stress and its position on the link at any time are also calculated. The numerical simulation of a compliant four-bar mechanism indicates that the dynamic characteristic analysis of compliant mechanism based on finite element is feasible and effective, and the analysis on strain and dynamic stress of the link of compliant mechanism has important significance to the optimization design of compliant mechanisms.