Elasto-Kinematic Modeling of Planar Flexure Hinge-Based Compliant Mechanisms Incorporating Branched Links

Abstract

Compliant mechanisms with notch flexure hinges are widely used in industry and research, especially in precision engineering applications. The motion and deformation behavior of these systems is a result of bending of the compliant segments, mainly influenced by the notch geometry. The accurate analysis is a challenging task and the synthesis of compliant mechanisms is done non-intuitively and iteratively due to the materially coherent joints and the monolithic design. Apart from FEM simulations, analytical modeling methods are proposed which are mostly restricted to certain hinge contours or do not offer the possibility to calculate important elasto-kinematic properties. Therefore, this paper presents an analytical approach based on the theory for large deflections of rod-like structures to support the design process. The planar mechanisms are analyzed with respect to arbitrary oriented and shaped flexure hinges using power functions. The non-linear approach is extended by the modeling of a branched link to also consider guided coupler points. For this purpose, two example path-generating mechanisms are regarded. The four-bar mechanisms are modeled as curved rods of arbitrary geometry, and the properties are numerically calculated with the use of MATLAB. It is shown, that the results are in good correlation with FEM-based simulations. Thus, the approach allows for the contour-specific accelerated and accurate analysis of compliant guidance mechanisms with respect to optimized flexure hinge shapes.