Straight-axis folded flexure hinges: In-plane elastic response

This research generalizes the serpentine hinge design and concept by studying the straight-axis folded flexure hinge as a large-displacement counterpart of shape-similar, solid notch hinges. A folded hinge is formed of several unit segments that repeat periodically along the axial direction and are inscribed in a region defined by various geometric envelope curves. The envelope curves are identical to the curves defining the outer profile of the parent solid flexure hinges. This concept increases the number of design parameters of a solid notch hinge by including the geometry and dimensions of the envelope curve, the number of unit segments, the distance between segments, and the geometric configuration of each segment. Two categories of folded hinges are studied here: one category is defined by a rectangular envelope with all unit segments being identical; the other category uses curved-line envelopes and the unit segments scale along the transverse direction. For both categories generic in-plane analytical compliance models are formulated. A particular design is analyzed from each category with the unit segment serially combining straight- and elliptic-line portions. The validity of the analytical compliance model is verified by means of experimental testing and finite element analysis of some simple translation stages that include either rectangular- or circular-envelope folded hinges. The analytical compliance model is subsequently utilized to assess the quasi-static response sensitivity of the folded hinges to the geometric parameters, and to compare the folded configurations with their parent, notch designs.