A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation

Abstract

To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form parametric load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates a wide range of loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified by nonlinear finite elements analysis.