Insights into Bending Stiffness Modeling of Elementary Flexure Hinges

Flexure hinges are widely used in mechanical devices, especially for micro- or even nano-scale applications, where conventional joints based on conjugate surfaces prove unsuitable. However, to achieve accurate motion of devices whose joints are flexure hinges, knowledge of stiffness models that correlate applied forces or bending moments with the resulting displacements is required. Nonlinear bending models are typically too complex and difficult to implement. Therefore, it is preferred to use linear models, which admit analytical solutions. The purpose of this paper is to show what is lost in terms of accuracy in reducing a nonlinear bending stiffness model associated with a flexure hinge when simplifications are made to obtain an analytical solution. An analysis of the simplification process leading to a linear stiffness model and its analytical solution is presented. From this study arises an increased awareness of flexure joints in terms of the accuracy obtained with their stiffness models, suggesting important information to the user in choosing the level of complexity required to model them in a specific application. A comparison between analytical and numerical results is provided in the form of maps and tables so as to make that choice as clear as possible.