Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges

Abstract

The flexure hinges are the most vulnerable parts in a flexurebased mechanism due to their smaller dimensions and stress concentration characteristics, therefore evaluating the maximum stresses generated in them is crucial for assessing the workspace and the fatigue life of the mechanism. Stress concentration factors characterize the stress concentrations in flexure hinges, providing an analytical and efficient way to evaluate the maximum stress. In this work, by using the ratio of the radius of curvature of the stressconcentrating feature to the minimum thickness as the only fitting variable, generalized equations for both the bending and tension stress concentration factors were obtained for two generalized models, the conic model and the ellipticarcfillet model, through fitting the finite element results. The equations are applicable to commonly used flexure hinges including circular, elliptic, parabolic, hyperbolic, and various cornerfillet flexure hinges, with acceptable errors. The empirical equations are tractable and easy to be employed in the design and optimization of flexurebased mechanisms. The case studies of the bridgetype displacement amplifiers demonstrated the effectiveness of the generalized equations for predicting the maximum stresses in flexurebased mechanisms.