Beam Constraint Model: Generalized Nonlinear Closed-form Modeling of Beam Flexures for Flexure Mechanism Design.

Abstract

Flexure mechanisms, also known as compliant mechanisms, provide guided motion via elastic deformation. Their ability to produce repeatable/precise frictionless motion makes them a common choice in precision positioning devices, frictionless bearings, biomedical devices and prosthetics. Traditionally, design of flexure mechanisms has been conducted in an intuitive manner using simplistic linear models. For flexure mechanisms where nonlinear effects that contribute to error motions and stiffness variations are present, designers have had to use computational methods such as finite elements modeling, which provides relatively limited design insight. This dissertation aims to create an alternative modeling tool that captures nonlinear effects in a simple closed form manner, so that the parametric variation of various performance attributes in flexure mechanisms can be easily studied. In order to make the design process more systematic, this approach breaks down flexure mechanisms to its building blocks that are referred to as flexure elements. The deformation mechanics of the two most common flexure elements, the flexure strip and the wire flexure, are analyzed in detail and the relations between the loads and displacements, applied and measured at the elements’ end points, are determined. To ensure accuracy at an elemental level, pertinent geometric nonlinearities are captured. The effects of initial alignment errors, which are often present in flexure mechanisms in practice, are also studied in detail at the elemental as well as overall mechanism level. Furthermore, an analytical framework is provided in this dissertation that illustrates Newtonian and energy methods to analyze flexure mechanisms constructed using multiple flexure elements. Overall, the novelty of this modeling technique lies in its ability to represent the relations between fully generalized spatial loads and spatial end-displacements (both translational and rotational displacement) over a relatively large range in a simple yet accurate manner. As a result, several complex mechanisms can be analyzed accurately without resorting to computational/numerical techniques or restricting the loading conditions. Given the generality of the analytical models of the flexure elements, this formulation can be used in the future for optimization of flexure mechanisms in terms of shape/type/number of flexure elements as well as their spatial arrangement.