Contour-independent design equations for the calculation of the rotational properties of commonly used and polynomial flexure hinges

Flexure hinges are often used as revolute joints in high-precision compliant mechanism, but without simulations the accurate prediction of their contour-dependent deformation and especially planar motion behavior is a challenging task. This paper presents contour-independent general design equations for the explicit calculation of the rotational stiffness, maximum angular deflection and rotational precision of various notch hinges in dependence of the geometric parameters. The non-linear analytical model describes a clamped beam with included flexure hinge which is loaded with a moment or a transverse force at its free end. In addition to the common semi-circular, corner-filleted, and elliptical flexure hinge, the high-performance polynomial hinge with five different orders is investigated. The deviation of the calculated results compared with the analytical solution depends on the contour and it is mostly relative low for the suggested parameter range. Furthermore, finite elements method (FEM) results correlate well with the predictions based on the analytical solution as well as the solution with the simple, concise and uniform design equations.