An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

Abstract

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that govern its performance as a basic constituent of flexure mechanisms. This paper presents a new modeling approach for obtaining insight into the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear, and torsion deformation. The approach is based on the use of a discretized version of a finite (i.e., nonlinear) strain spatial beam formulation for extracting analytical expressions that describe deformation and stiffness characteristics of a flexure strip in a parametric format. This particular way of closed-form modeling exploits the inherent finite-element assumptions on interpolation and also lends itself for numeric implementation. As a validating case study, a closed-form parametric expression is derived for the lateral support stiffness of a flexure strip and a parallelogram flexure mechanism. This captures a combined torsion–bending dictated geometrically nonlinear effect that undermines the support bearing stiffness when the mechanism moves in the intended degree of freedom (DoF). The analytical result is verified by simulations and experimental measurements.