Stiffness analysis of corrugated flexure beam using stiffness matrix method

Abstract

Precision positioning techniques present a significant opportunity to support the instrumentation development for state-of-the-art micro-positioning research. The requirement of large stroke and high resolution of the mechanism without a need for amplifier mechanisms is universally recognized. Corrugated flexure beam can have some potential if designed right because of its large flexibility obtained from longer overall length on the same span. This paper presents stiffness analysis of corrugated flexure beam using stiffness or compliance matrix method. Based on Euler–Bernoulli beam theory and Mohr’s integral method, the deformation analyses of straight segment and semi-circle segment are presented. And the stiffness matrix of corrugated flexure unit is then obtained via transformation matrix. By combining the stiffness matrix of every single corrugated flexure unit, the stiffness matrix of corrugated flexure beam is delivered, which reflects the relationship between the load and displacement. The analytical models are verified by taking advantage of the finite element method, which shows that all the results can be of considerable use in the design of corrugated flexure beam.