Influence of geometric scaling on the elasto-kinematic properties of flexure hinges and compliant mechanisms

Flexure hinges with notches are typical elements in high-precision compliant mechanisms with a wide variety of sizes from macro to micro or nano applications. This paper investigates the elasto-kinematic hinge and mechanism properties in dependence of scaling the geometric parameters regarding the impact of using optimized flexure hinge contours within a unified synthesis method without the need of rerunning simulations. The three performance criteria stiffness, maximum strain, and precision are analyzed among others for a single symmetric flexure hinge and a parallel four-bar linkage. The analytical investigations and FEM simulations include semi-circular, corner-filleted, and special 6th-order polynomial hinge contours. Accordingly, the chosen rigid-body model is transferred into a compliant mechanism through replacing all revolute joints by notch hinges. Geometric scaling is investigated with a parametric non-linear FEM model for factors from 0.1 to 2. To obtain results for comparable relative hinge angles, the defined input displacement is scaled too. Three prototypes are tested to verify the simulations and to validate the influence of scaling by measurement. In addition to general scale dependencies of the properties it is shown, that optimized flexure hinge contours are promising for miniaturized compliant mechanisms with high precision and large stroke at once.