Performance Analysis of a Hyperbolic Flexure Hinge Based on its Closed-Form Equations

Abstract

In order to the effects of structural sizes of a hyperbolic on its performance, sensitivity and accuracy analysis are performed 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 are obtained using the Castigliano’s second theorem. According to the closed-form flexibility formulas, the effects of the four structural parameters, such as thickness, notch depth, length and width, on the flexibility of flexible hinge are analyzed, respectively. In order to study further the effects of the structural parameters on its flexibility, we derive the sensitivity equations, and the sensitivity analysis is carried out. Meanwhile, the accuracy analysis of the hyperbolic flexure hinge is performed. The analysis results have shown that the parameters have large influence on in-plane compliance, and have small effects on out-of-plane one. And the changes are larger within initial small range of parameters, while be small variation in larger size range. And the length has no effect of sensitivity.