Dynamics of Compliant Mechanisms Using Transfer Matrix Method

Abstract

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.