Kinematic modeling of flexure hinges and compliant mechanisms

Abstract

In this paper, the kinematic performance of flexure hinges and compliant mechanisms calculated by conventional modeling techniques are compared. As these exhibit certain drawbacks with regard to control strategies, mainly large number of degrees of freedom or unacceptable errors, a novel modeling approach for flexure hinges is presented. Instead of the entire flexure hinge only its significant regions are modeled by 3-D structural solids. These master patterns are positioned appropriately and connected by rigid constraint conditions to build a compliant mechanism. The resulting model is characterized by considerably fewer degrees of freedom than a full solid model as well as a marginal deviation of the deflection compared to that of pseudorigid-body models, 3-D tapered finite beam elements and analytical Timoshenko beam theory.A new approach to enable feed units for small machine tools producing small workpieces is based on the application of compliant mechanisms (CM) being a monolithic structure composed of flexure hinges (FH) and their stiff connections, see [1] for details. A flexure hinges provides relative motion between two adjacent stiff members by locally decreased bending stiffness being achieved by a variable cross-section. Its elastic deformation and therewith its kinematical properties depend on the geometric parameters and the material, respectively. In this work, different modeling techniques for flexure hinges with application to control strategies of compliant mechanisms are investigated including pseudo-rigid body modeling (PRBM) [2], Timoshenko beam theory (TBT) [3] and finite element methodology (FEM). The main results are listed in Table 1.The application of structural solid elements in 3-D finite element analysis reveals that the kinematic characteristics and significantly deformed region strongly depend on the flexure hinges' geometric parameters and may not be confined to the flexure hinge itself but also on the adjacent structure, especially for thick hinges. Table 1: Summary of advantages and disadvantages of the different modeling approaches Model Advantages Disadvantages FEM + accurate results -multitude of DOF + easy to generate -inapplicable for control TBT + analytical model -imprecise results + easy to implement -inapplicable for CMs PRBM + few DOF -imprecise results + easy to implement -inapplicable for CMs 2 Significant regions of flexure hingesAs depicted in Figure 1(a) and being valid for almost all types of FHs, only minor parts of the structure contribute to the overall performance of the FH. Therewith, an essential reduction of DOF is achieved by taking into account only relevant structural regions for adapted meshing to obtain a master model of that specific FH having less DOF than complete solid modeling strategies. This motivates the selection of the significantly deformed zone (which needs to be independent of the absolute load value) by means of a tolerance value t SR and the occuring von Mises stress. The nodes and corresponding finite elements, for which t SR · σ vM is...

Nonlinear modeling of compliant mechanisms incorporating circular flexure hinges with finite beam elements

“…The implementation of a Timoshenko beam element is an alternative approach, especially for modeling short an compact beams. However, the main deformation of the flexure hinge occurs in the center of the flexure hinge as detailed 3D finite element analysis shows [21]. In the center of the flexure hinge the lengths to thickness ratio justifies an Euler-Bernoulli beam model.…”