A new generalized model for elliptical arc flexure hinges

Abstract

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 phi(m) ranges from 0 to pi/2) to distinguish from the existing elliptical flexure hinge (phi(m)=pi/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 (phi(m)=pi/2), circular (a=b), and right-circular (phi(m)=pi/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.

General design equations for the rotational stiffness, maximal angular deflection and rotational precision of various notch flexure hinges

“…Lobontiu, 2003;Meng et al, 2013) or the elliptical hinge (e.g. Smith et al, 1997;Chen et al, 2008) as a compromise. Furthermore, flexure hinges are designed with other elementary geometries to realize a special characteristic, like the parabolic or hyperbolic contour (e.g.…”

“…Furthermore, flexure hinges are designed with other elementary geometries to realize a special characteristic, like the parabolic or hyperbolic contour (e.g. Lobontiu, 2003;Chen et al, 2009), and cycloidal contour (Tian et al, 2010). Increasingly flexure hinges are designed with a combination of the mentioned basic geometries (e.g.…”

Design and analysis of a high-accuracy flexure hinge

“…The conformal mapping equations were much closer to finite element analysis (FEA) and experimental data when compared with other theoretical equations. Chen et al 11,12 proposed a generalized model for elliptical arc (circular, right-circular, and elliptical profiles) flexure hinges. The compliance of elliptical arc flexure hinges was deduced by introducing the eccentric angle of ellipse as the integral variable based on the theories of mechanics of materials.…”

A novel 5-DOF high-precision compliant parallel mechanism for large-aperture grating tiling

“…4. Compared with various flexure hinges, the right circular flexure hinge is considered a good candidate because of its excellent rotation capacity and lack of rotation errors (Lobontiu, 2002;Chen et al, 2008Chen et al, , 2009. Hence, the right circle flexure spherical joint as shown in Fig.…”