Static and Dynamic Compliance Analyses of Curved-Axis Flexure Hinges: A Discrete Beam Transfer Matrix

Abstract

A discrete beam transfer matrix method is introduced to enhance the existing approaches for the static and dynamic compliance solutions of curved-axis flexure hinges with variable curvatures and nonuniform profiles. An idea of discretizing curved-axis flexure hinges as a series of constant beam segments parallel to the centroidal axis is developed. As a result, only a concise beam transfer matrix with decoupled longitudinal and transverse components is needed to establish the compliance model. A step-by-step modeling procedure with simple formulas is provided as well qualifying for curved-axis and folded hinges. With this modeling idea, the small-deflection compliance matrix in the common sense of statics and particularly in a viewpoint of frequency-dependent dynamics can be simultaneously obtained. A typical curved-axis flexure hinge available in the literature is analyzed and compared as a study case. In addition, the static and dynamic design for a compliant guiding mechanism composed of folded flexure hinges is efficiently implemented with the presented method.