A new generalized model for elliptical arc flexure hinges

Flexure hinges have been used in many engineering areas where high precision and sensitivity are required. Many kinds of flexure profiles were proposed during the past decade. Therefore, a general closed-form solution for flexure hinges of different profiles that incorporates the profile selection and parameter design will be of great benefit to the hinge design. The present work brings circular, right-circular, and elliptical profiles together by proposing a generalized flexure hinge model, which we call elliptical arc flexure hinges (whose maximum eccentric angle φm ranges from 0 to π /2) to distinguish from the existing elliptical flexure hinge (φm =π /2). Based on the theories of mechanics of materials, all the elements in the compliance matrix for elliptical arc flexure hinges are deduced by introducing the eccentric angle of ellipse as the integral variable. These compliance equations simply boil down to four integrals, thus simplifying the compliance calculation. These equations also apply to elliptical (φm =π /2), circular (a=b), and right-circular (φm =π /2 and a=b) hinges. These compliance equations were checked by comparing them with the results of finite element analysis, the existing equations, and experiment results. The comparison results show that these generalized equations are concise and adequate for most design purposes.