Compliance and Dynamic Modeling of General Notch Flexure Hinges Using a Beam Transfer Matrix

Abstract

Kinetostatics and dynamics are two key aspects in designing flexure hinges for use in compliant mechanisms. We introduce a unified method employing the transfer matrix of Timoshenko beams and finite-discrete idea for quickly predicting the kinetostatic and dynamic behaviors of general single/multi-axis notch flexure hinges. The closed-form equations of compliance, rotational precision and natural frequencies are derived targeting for arbitrary contours with a step-by-step modeling procedure. These new formulas have a concise form with the same degrees of freedom as the existing analytical ones. It is easy to operation for efficiently comparing and synthesizing different notch flexure hinges under a unified modeling framework. All a designer has to do is to prepare the concerned shape function without the need to be caught into the laborious and even unsolvable derivation of mechanics. The presented method is numerically and experimentally verified by applying to several groups of typical notch flexure hinges. Except for contributing a straightforward modeling technique, our results provide insights into the dynamic characteristic of flexure hinges which was less studied previously.

Keywords: Compliant mechanisms, Flexure hinge/pivot, Transfer matrix method, Timoshenko beam theory