DETERMINATION OF NATURAL FREQUENCIES OF A PLANAR SERIAL FLEXURE-HINGE MECHANISM USING A NEW PSEUDO-RIGID-BODY MODEL (PRBM) METHOD

Abstract

This paper presents an approach to the free vibration analysis of planar serial flexure-hinge compliant mechanisms basing on a pseudo-rigid-body method with 3-DOF (degrees of freedom) joints. The considered type of compliant mechanisms contains rigid links interconnected by flexure hinges. It is assumed that the flexure hinges undergo small in-plane deformations. Also, the masses of flexure hinges are ignored with respect to the masses of rigid links. Two lateral and one rotational springs with corresponding stiffnesses are placed in each joint in the pseudo-rigidbody model of the considered type of compliant mechanisms. The circular hinge type of flexure hinges is considered. Theoretical considerations are accompanied by a numerical example. In the numerical example a RRR compliant micro-motion stage is analyzed. The influence of the spring stiffnesses determined based on various flexure hinge compliance equations available in the literature on the vibration frequencies of the compliant mechanism is studied. Also, the comparison of accuracy in the determination of vibration frequencies of the compliant mechanism between the proposed pseudo-rigid-body method and the classical pseudo-rigid-body method (with one-DOF revolute joints) is given.