A generalized analytical compliance model for transversely symmetric three-segment flexure hinges

Abstract

This paper presents a generalized compliance model for a three-segment notch flexure hinge with transverse symmetry. This flexure hinge configuration is most frequently employed in planar-motion, small-displacement compliant mechanisms. The axial and bending compliances are derived for this flexure hinge based on the compliances of two flexure components. The derivation is generalized such that it can be applied to various segment geometries. Using this open-ended model, a three-segment right elliptical corner-filleted flexure hinge design was analyzed. This geometric configuration introduces additional geometric parameters, which can be used to optimize the compliance of the flexure hinge without modifying its gross dimensions. The results of the analysis were validated in part by modifying the geometric parameters of the center segment and elliptical corner fillets to form limiting cases corresponding to several previously investigated configurations, namely right elliptical, three-segment right circular corner-filleted, and right circular geometries. Finite element analysis simulation and experimental testing were used to further validate the three-segment right elliptical corner-filleted analytical model. Additional simulations based on the analytical model were performed to highlight the influence of geometric parameters on compliances and to investigate shear effects for short flexure hinges.

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

“…Increasingly flexure hinges are designed with a combination of the mentioned basic geometries (e.g. Zelenika et al, 2009;Lobontiu et al, 2011;Chen et al, 2011). Rarely special mathematical functions are used that allow more precise shape variations of the partial or whole hinge contour due to a higher number of geometric parameters, like the spline contour (Christen and Pfefferkorn, 1998;De Bona and Munteanu, 2005), the powerfunction contour , the exponent-sine contour (Wang et al, 2013), the Lamé contour (Desrochers, 2008), and the Bézier contour (Vallance et al, 2008).…”

Note: Bending compliances of generalized symmetric notch flexure hinges

“…Through its address of transverse-and-axial symmetry, this note extends the work of Lobontiu et al, 10 which studied generalized flexure hinges with transverse symmetry. Generalized flexure profiles have previously been analyzed by Chen et al 11 (elliptical arc configurations) and Zelenika et al 5 (predefined or free-form designs).…”

“…This section is based on experimental data obtained for a right elliptical corner-filleted notch flexure hinge (a design with both transverse and axial symmetry) as discussed in Lobontiu et al 10 A similar flexure design was also studied by Zelenika et al 5 and Chen et al 4 The flexure hinge specimen was bending-loaded by point forces applied outside the flexure hinge in two separate tests and the resulting deflections were measured at two different locations (also outside the flexure span) in each test. …”

“…The reference frame can be displaced either outside the flexure's boundaries, at O 1 , or inside it, at O 2 . Based on the coordinate connections: x = x 1 − d and x = x 2 + d, the following in-plane bending compliance relationships are derived in Lobontiu et al:10 …”

Compliant linear-rotation motion transduction element based on novel spatial helical flexure hinge

“…Currently, many types of flexure hinges were developed to construct the CMs in micro-machining systems [4,5], micro/nano manipulators [6,7], and micro/nano positioning stages [8,9]. For satisfying the ever-increasing working requirements, flexure hinges with improved performances were recently introduced.…”