Generalized model for conic-V-shaped flexure hinges

This paper presents a new class of flexure hinges, namely, conic-V-shaped flexure hinges (CFHs), which can be used as a generalized model for flexure hinges with profiles such as parabolic-V-shape, elliptical-V-shape, and hyperbolic-V-shape. Compliance and precision equations for the CFHs were derived as a set of nonlinear equations using Castigliano’s second theorem. The parameters of the nonlinear equations inputted to the compliance and precision matrices were based on the generalized equations used for conic curves in polar coordinates. Furthermore, the compliance equations were verified by means of finite element analysis and experiments. The errors in the finite element and experimental results were within 10% and 8% compared to the analytical results, respectively. Finally, the effects of dimensional parameters on the analytical model could be effectively analyzed by numerical simulations and comparisons.