Publications

A compliant mechanism gains its mobility fully or partially from the compliance of its elastically deformable parts rather than from conventional joints. Due to many advantages, in particular the smooth and repeatable motion, monolithic mechanisms with notch flexure hinges are state of the art in numerous precision engineering applications with required positioning accuracies in the low micrometer range. However, the deformation and especially motion behavior are complex and depend on the notch geometry. This complicates both the accurate modeling and purposeful design. Therefore, the chapter provides a survey of different methods for the general and simplified modeling of the elasto-kinematic properties of flexure hinges and compliant mechanisms for four hinge contours. Based on non-linear analytical calculations and FEM simulations, several guidelines like design graphs, design equations, design tools or a geometric scaling approach are presented. The obtained results are analytically and simulatively verified and show a good correlation. Using the example of a path-generating mechanism, it will be demonstrated that the suggested angle-based method for synthesizing a compliant mechanism with individually shaped hinges can be used to design high-precise and large-stroke compliant mechanisms. The approaches can be used for the accelerated synthesis of planar and spatial flexure hinge-based compliant mechanisms.

Compliant mechanisms based on flexure hinges are widely used in precision engineering applications. Among those are devices such as precision balances and mass comparators with achievable resolutions and uncertainties in the nano-newton range. The exact knowledge of the mechanical properties of notch hinges and their modeling is essential for the design and the goal-oriented adjustment of these devices. It is shown in this article that many analytical equations available in the literature for calculating the bending stiffness of thin semi-circular flexure hinges cause deviations of up to 12% compared to simulation results based on the three-dimensional finite element model for the considered parameter range. A close examination of the stress state within the loaded hinge reveals possible reasons for this deviation. The article explains this phenomenon in detail and shows the limitations of existing analytical models depending on specific geometric ratios. An accurate determination of the bending stiffness of semi-circular flexure hinges in a wide range of geometric parameters without the need for an elaborate finite element analysis is proposed in form of FEM-based correction factors for analytical equations referring to Euler-Bernoulli's beam theory.

A novel computational design tool to calculate the elasto-kinematic flexure hinge properties is presented. Four hinge contours are implemented. It is shown, that FEM results correlate well with the analytical design tool results. For a given deflection angle of 10˚ and a corner-filleted contour, the deviations of the bending stiffness are between 0.1 % and 9.4 %. The design tool can be beneficial for the accelerated and systematic synthesis of compliant mechanisms with optimized flexure hinges.