Dynamics of Compliant Mechanisms Using Transfer Matrix Method
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Online ISSN 2005-4602 Print ISSN 2234-7593
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Dynamics of Compliant Mechanisms Using Transfer Matrix Method Junfeng Hu1 · Tao Wen1 · Jiankang He1 Received: 23 August 2019 / Revised: 4 July 2020 / Accepted: 22 July 2020 © Korean Society for Precision Engineering 2020
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. Keywords Compliant mechanism · Transfer matrix method · Mechanical model · Dynamic performances
1 Introduction The compliant mechanism is a new type of mechanism that transfers or transforms motion, force, or energy through elastic deformations of constructional elements [1, 2]. With the merits of higher accuracy, smaller space, and no friction compared to conventional transmission mechanisms, compliant mechanisms are frequently used in the actuator of micro-operation platform [3–12]. However, the precision micromanipulation platform is vulnerable to the external environment [13, 14]. To eliminate external interference, it is necessary to establish a vibration mechanics model and analyze its dynamic performance. So far, many studies have been done on the dynamic analysis of compliant mechanisms, such as the pseudo-rigid-body * Junfeng Hu [email protected] Tao Wen [email protected] Jiankang He [email protected] 1
School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
method (PRBM) and finite element method (FEM) [15]. The PRBM regards flexible hinges as a traditional kinematic pair and then analyzes its mechanical properties using traditional methods [16]. This method is suitable to describe the static mechanical properties of compliant mechanisms. Meanwhile, the method regards the hinge as an ideal hinge, so its calculation accuracy is low [17]. The FEM divides the flexible hinges and other members of compliant mechanisms into several interconnected sub-elements in a certain way, which have several degrees of freedom [
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