Stiffness characterization of corner-filleted flexure hinges

TLDR: In this paper, the authors derived closed-form stiffness equations for corner-filleted flexure hinges, which can be used to characterize the static, modal, and dynamic behavior of single-axis corner-face flexures.

Abstract: The paper formulates the closed-form stiffness equations that can be used to characterize the static, modal, and dynamic behavior of single-axis corner-filleted flexure hinges, which are incorporated into macro/microscale monolithic mechanisms. The derivation is based on Castiliagno’s first theorem and the resulting stiffness equations reflect sensitivity to direct- and cross-bending, axial loading, and torsion. Compared to previous analytical work, which assessed the stiffness of flexures by means of compliances, this paper directly gives the stiffness factors that completely define the elastic response of corner-filleted flexure hinges. The method is cost-effective as it requires considerably less calculation steps, compared to either finite element simulation or experimental characterization. Limit calculations demonstrate that the known engineering equations for a constant cross-section flexure are retrieved from those of a corner-filleted flexure hinge when the fillet radius becomes zero. The analytical model results are compared to experimental and finite element data and the errors are less than 8%. Further numerical simulation based on the analytical model highlights the influence of the geometric parameters on the stiffness properties of a corner-filleted flexure hinge.