This paper presents a closed-form expression of the mass matrix of the right circular hinges which are widely used in compliant mechanism systems. The flexure hinge is treated as a two nodes element, in which there are three degrees of freedom at each node. The cosine functions with high-order terms are introduced, and the closed-form expression for each element of the mass matrix of the single-axis right circular flexure hinge is obtained. Based on the closed-form expression, the dynamic equations of motion of a piezodriven 3-DOF compliant precision micro-positioning stage are developed. The lower order modal frequencies are experimentally identified and the dynamic analysis model is proved to be feasible. Dynamic and static output comparisons show that the dynamic analysis is highly necessary for a precision micro-positioning stage. The closed-form expression of the mass matrix of the right circular hinge made it more convenient for dynamic analysis of the compliant mechanisms by using finite element approach.

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