In Plane Compliances of Planar Flexure Hinges With Serially Connected Straight and Circular Axis Segments

Abstract

The paper introduces a new category of planar flexure hinges that are formed by serially connecting variable crosssectional segments of straight longitudinal axes with segments of circular longitudinal axes. The smalldisplacement compliance analytical model is derived for a general hinge configuration using a matrix approach that sums the transformed localframe compliance matrices of individual component segments. The particular class of antisymmetric flexure hinges is studied using the general model and the corresponding globalframe compliance matrix is calculated as a linear combination of compliances defining the halfhinge configuration. A serpentine (folded) flexure hinge is introduced to illustrate the generic antisymmetric design and model. Finite element simulation is used to validate the analytic compliances of this particular configuration and the compliance sensitivity to geometric parameters variation is further analyzed. The translation stiffnesses of a planarmotion stage with two identical serpentine hinges are calculated based on hinge compliances. The optimum hinge design is subsequently identified, which realizes minimumresistance motion along the stage axial motion direction.