Development of a midcurve for analyzing the deformation of transversely symmetric hinges

Abstract Transversely symmetric flexure hinges are a special type of hinges defined by their one-sided contour, which determines their moment of inertia. Although widely used, transversely symmetric flexure hinges remain analytically challenging due to their complex geometry. The theory of large-deflection of rod-like structures based on Euler–Bernoulli assumptions is difficult to apply, as identifying the beam axis is nontrivial for asymmetrical hinges. This paper introduces a novel, geometry-based approach for determining a midcurve from two distinct boundary curves, independent of any specific hinge configuration. Several methods for determining this midcurve are presented and evaluated. To demonstrate the utility of these methods, their results are applied to transversely symmetric hinges, providing a new means of identifying the effective beam axis. The midcurve is computed for a variety of hinge contours, facilitating accurate deformation analysis. Parameter studies and comparisons with FEM simulations reveal that the proposed model achieves agreement with less than five percent deviations. Finally, the method’s efficiency and effectiveness are highlighted through its application in the analysis of a mechanism incorporating these hinges, with computation times under one second. The approach offers a highly promising tool for rapid and precise mechanism design.