Accurate stiffness modeling method for flexure hinges with a complex contour curve

Background: Flexure hinges have certain advantages, such as a simple structure, smooth movement, no need for lubrication, frictionless movement and high precision. The flexure hinge’s transfer of force and displacement relies on its deformation. Thus, stiffness is an important index for evaluating hinge flexibility. Objective: Stiffness analysis of the flexure hinges is necessary to be performed. This paper aims to present a unified stiffness model solving method of the flexible hinges with complex contour curves. Method: The transfer matrix of a flexure hinge was derived based on balance equations and the virtual work principle with consideration of axial, shear, and bending deformations. The element stiffness matrix of a flexure hinge was obtained from the relationship between the transfer and stiffness matri-ces. In this manner, the unified formula of element stiffness of a general flexure hinge was established. By using this method, rigidity models of parabolic, corner-filled, and the right circular flexure hinge have been deduced. By taking the right circular flexure hinge as an example, the results obtained using this method were compared with those of methods provided in other studies and the finite element re-sults. Result: The comparison results revealed that the proposed method increases the rigidity accuracy be-cause the effect of the uneven distribution coefficient of shear stress was considered. The stiffness er-ror was within 7%, which demonstrates the validity of this method. In contrast to the other methods, the proposed method can be applied by determining the first integral element stiffness of a common flexible hinge. Moreover, the proposed method provides better commonality, flexibility, and ease of programming. In particular, it is much easier for the flexure hinges with a complex contour curve. Transitivity can be used to calculate the rigidity after the flexure hinge has been divided into subunits, thus making it unnecessary to convert to the global coordinate system.