General design equations for the rotational stiffness, maximal angular deflection and rotational precision of various notch flexure hinges

Notch flexure hinges are often used as revolute joints in high-precise compliant mechanisms, but their contour-dependent deformation and motion behaviour is currently difficult to predict. This paper presents general design equations for the calculation of the rotational stiffness, maximal angular elastic deflection and rotational precision of various notch flexure hinges in dependence of the geometric hinge parameters. The novel equations are obtained on the basis of a non-linear analytical model for a moment and a transverse force loaded beam with a variable contour height. Four flexure hinge contours are investigated, the semi-circular, the corner-filleted, the elliptical, and the recently introduced bi-quadratic polynomial contour. Depending on the contour, the error of the calculated results is in the range of less than 2% to less than 16% for the suggested parameter range compared with the analytical solution. Finite elements method (FEM) and experimental results correlate well with the predictions based on the comparatively simple and concise design equations.