An Analytical Stress–Deflection Model for Fixed-Clamped Flexures Using a Pseudo-Rigid-Body Approach

Abstract

Fixed-clamped flexures are one common component of compliant mechanisms which remain difficult to design due to their unique force– and stress–deflection profiles. In this work, an analytical stress-deflection model for fixed-clamped flexures is proposed that utilizes a modified pseudo-rigid-body model. Proof-of-concept mechanical testing and finite element analysis demonstrate that the model can predict forces and stresses within 3.5% for a range of steel flexure topologies. Special analysis is carried out on the characteristic radius factor, a parameter to which model accuracy is particularly sensitive. For slender flexures or large deflection scenarios, a dynamic characteristic radius factor is required to capture the resulting nonlinear axial strain. By evaluating the effects of loading, geometry, and material properties, an analytical equation that can predict an optimal value is proposed. When integrated into our model, this equation for an appropriate characteristic radius factor can predict the optimal parameter value within 0.45 ± 0.47%, resulting in average model error of 3.45 ± 2.09% across a large range of flexure thicknesses and deflections. The distinct combination of axial and bending stresses experienced in fixed-clamped flexures has made mechanisms that use these members challenging to design. This work provides a model that designers, engineers, and researchers can draw from to understand stress profiles present in these flexible members.