Kinetostatic Modeling of Bridge-Type Amplifiers Based on Timoshenko Beam Constraint Model

Abstract

In this paper, we develop an accurate kinetostatic modeling method for bridge-type amplifiers by incorporating the impacts of nonlinear shear effect, center-shifting and load-stiffening. To account for the nonlinear stress-stiffening and shear effects, a Timoshenko Beam Constraint Model (TBCM) is first investigated to accurately predict the deformations of the short beam flexure hinges popularly employed in the bridge-type amplifiers. Accordingly, a flexible branched chain model is established for bridge-type amplifiers, where the input and output displacements, as well as the displacement amplification ratio and the input stiffness, are derived. The results indicate significant nonlinearities of the amplification ratio and the input stiffness with respect to the driving forces, which are further verified by the finite element analysis (FEA) results. The proposed modeling method can derive a more accurate model of the bridgetype amplification mechanism to capture its kinetostatic behaviors, which can better support the design and control of flexure mechanism based nano-manipulating systems.