Modeling of flexure-hinge type lever mechanisms

A general approach for the design of flexure-hinge type lever mechanisms that are commonly used in the design of translational micro-positioning stages is presented in this paper. The paper focuses on the development of design equations that can accurately predict the behavior of such stages especially the “lost motion” due to hinge stretching. The development of these equations is based on a static analysis of a general configuration of a single-axis, translational, flexure-hinge type, piezo-driven micro-positioning stage using a multi-lever structure. The displacement ratio between the input and output motions of one of the levers, plus the stiffness at either end of this lever are obtained based on the analysis. The overall displacement and stiffness of the micro-positioning stage are then obtained by cascading the individual results from every lever. The developed equations include the effects of the flexure hinge bending and stretching. The developed equations were applied to design of a vertical motion micro-positioning stage. The stiffness and displacement of this stage are predicated by these equations, which are compared to the stiffness and displacement directly obtained from the finite element modeling and actual testing of the same micro-positioning stage. The comparison shows that the analytical approach gave nearly similar results (within 10%), which implies that the developed equations can accurately predict the characteristics of flexure-hinge type lever mechanisms.