In this paper, a new closed-form dynamic model describing vibration characteristics of compliant mechanisms is proposed by using transfer matrix method. The advantage of the method is that it can simply and accurately describe the dynamic performance without the need for overall dynamic equation of the system, which is different from previous the dynamic modeling methods of compliant mechanisms. The vibration mechanical model of compliant mechanisms is established at first and the transfer matrices of the compliant mechanisms with serial and parallel configuration are derived. The transfer matrices of planar elliptic flexure hinges and vibration rigid bodies are deduced in detail according to the basic idea of the free vibration characteristics of elements. Finally, the dynamic performances of compliant mechanisms, such as the natural frequency, vibration model, and frequency response, are analyzed utilizing the established model. A comparison of the method with the finite element method for three typical compliant mechanisms discovers a maximum error of the natural frequency is less than 4.65%, which verifies the feasibility of the presented approach.

本文采用传递矩阵法，提出了一种新的描述柔顺机构振动特性的闭式动力学模型。该方法的优点是它可以简单，准确地描述动态性能，而无需系统的整体动力学方程，这与以前的顺应性机制的动态建模方法不同。首先建立柔顺机构的振动力学模型，并推导出具有串行和并行配置的柔顺机构的传递矩阵。根据单元自由振动特性的基本思想，详细推导了平面椭圆挠性铰链和振动刚体的传递矩阵。最后，顺应机制的动态性能，例如自然频率，利用建立的模型分析振动模型和频率响应。将该方法与有限元方法对三种典型的柔顺机构进行比较，发现固有频率的最大误差小于4.65％，这证明了该方法的可行性。