detasFLEX – A computational design tool for the analysis of various notch flexure hinges based on non-linear modeling

Abstract. Notch flexure hinges are commonly used in compliant mechanisms for precision engineering applications and yet important rotational properties of a hinge like the bending stiffness, maximum angular deflection and rotational precision are difficult to predict accurately and simultaneously. There exist some closed-form equations and a few design tool approaches for calculating flexure hinges with particular geometries, but apart from that no comprehensive calculation program for the contour-specific analysis is known to the authors. Developed in MATLAB, this paper presents a novel computational design tool using a non-linear analytical approach for large deflections of rod-like structures to calculate the elasto-kinematic flexure hinge properties by numerically solving a system of differential equations. Building on previous investigations, four certain hinge contours are implemented, the circular, the corner-filleted, the elliptical, and the power function-based contour with different exponents. In addition to the theoretical approach and the implementation it is exemplarily shown, that finite elements method (FEM) results correlate well with the analytical design tool results. For a given deflection angle of 10° and a corner-filleted contour as an example, the deviations of the bending stiffness are between 0.1 % and 9.4 % for typical parameter values. The presented design tool can be beneficial for the accelerated and systematic synthesis of compliant mechanisms with optimized flexure hinges.