Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016, Article ID 5602142, 11 pages
Research Article

Empirical Compliance Equations for Constant Rectangular Cross Section Flexure Hinges and Their Applications

Manufacturing Engineering Institute, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

Received 7 November 2015; Accepted 13 March 2016

Academic Editor: Dane Quinn

Copyright © 2016 Tiemin Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents the derivation of empirical compliance equations of the constant rectangular cross section flexure hinge. The stress concentration caused by changes in cross section is analyzed based on finite element analysis results for the purpose of overcoming compliance calculation errors. It shows that the stress concentration has great influence on axial compliance calculation, while it has little influence on shear and bending compliance calculation. Then empirical compliance equations with a relative wide range of and are derived based on the exponential model in conjunction with consideration of all geometrical parameters of flexure hinges and the influence of the stress concentration on axial compliance calculation. Finally, in order to verify the validity of the empirical equations, the input/output compliance and displacement amplification ratios of bridge-type microdisplacement amplification mechanisms are analyzed. Meanwhile, an experimental platform of displacement amplification mechanisms is set up. The experimental results and finite element method (FEM) values are in good agreement with the theoretical arithmetic, which demonstrates the accuracy of the empirical compliance equations. It provides a reference point for further studies on the design and optimization of flexure hinges and compliant mechanisms.