Review of circular flexure hinge design equations and derivation of empirical formulations

This article presents the comparison of various compliance/stiffness equations of circular flexure hinges with FEA results. The limitation of these equations at different t/Rt/R (R is the radius and t is the neck thickness) ratios are revealed. Based on the limitations of these design equations, a guideline for selecting the most accurate equations for hinge design calculations are presented. In addition to the review and comparisons, general empirical stiffness equations in the x- and y  -direction were formulated in this study (with errors less than 3% when compared to FEA results) for a wide range of t/Rt/R ratios (0.05≤t/R≤0.80.05≤t/R≤0.8).