Optimization design of a hyperbolic flexure hinge based on its closed-form equations

An optimization design method of a hyperbolic flexible hinge is presented in this paper. According to the structure feature and force exerted on the flexible hinge, the closed-form equations are formulated for compliances to characterize both the active rotation and all other in- and out-of-plane parasitic motions by using the Castigliano's second theorem. Meanwhile, the accuracy equations of the hyperbolic flexure hinge are obtained using the Castigliano's second theorem. The in-plane rotation angle of flexure hinge is optimization objective, and the constraints of optimization model are out-of-plane displacements and one described the accuracy of hinge, such that the optimization model can be established to meet performance requirements of flexure hinge. Based on the optimization model, the optimization designs of hyperbolic flexure hinge are performed to acquire its optimized structural parameters. And the optimization results have showed the optimization process can meet the design requirement.