Analytical modeling and analysis of rhombus-type amplifier based on beam flexures

Abstract

In order to accurately reveal the kinematic characteristics, the nonlinearities of load-equilibrium equations associated with the deflection of the flexible elements cannot be neglected, especially for the distributed-compliance compliant mechanisms. The object of this paper is to present a nonlinear analytical model of rhombus-type amplifier based on the beam flexures and to evaluate the effect of forces so as to offer helpful for initial parametric design studies. Based on the beam constraint model (BCM), the nonlinear analytical models of the one-stage and two-stage rhombus-type amplifiers are established respectively with some permissible approximations. Then, the input stiffness and off-axis stiffness models are formulated respectively, and the stiffness characteristic analysis is also carried out. Additionally, finite element analysis (FEA) is conducted to evaluate responses of the model with various parameters under the action of different forces. Finally, experimental studies of the performances are carried out, and the experimental results are compared with the theoretical models and FEA results. The nonlinear behaviors in the displacement, amplification ratio and input stiffness are revealed accurately, and the reason why the amplification ratio of the two-stage amplifier is different from the expected value is explained.