Comparison of circular flexure hinge design equations and the derivation of empirical stiffness formulations

Flexure hinges are commonly used in many applications which require precise and smooth motions in the nanometer scale. There were various formulations derived using different methods to calculate the stiffness of circular flexure hinges. This article compares these equations with FEA predictions. The limitation of these equations at different
t/R
(
R
is the radius and
t
is the neck thickness) ratios are revealed. Based on the limitations of these design equations, a guideline to select the most accurate equations for hinge design calculations is 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 simulations) for a wide range of
t/R
ratios (0.05 les
t/R
les 0.8).