Analysis and design of symmetric notch flexure hinges

This article presents the analytic models of four types of flexure hinges (elliptic, circular, parabolic, and hyperbolic flexure hinges). The analytic models are developed based on the theory of elasticity and infinitesimal method. The hinge index, denoted by the ratio of rotational precision and rotational stiffness, is proposed in this article to estimate the mechanical properties of diverse flexure hinges synthetically and quantitatively. The finite element analysis method and the experiments are performed to verify the accuracy of the analytic model. The relationships between the geometric parameters and the mechanical properties of the flexure hinges are analyzed using the analytic models established in this article. The comparisons of the mechanical performances among the four types of flexure hinges are performed.