Optimal design of a novel three-stage displacement amplifying mechanism with curved-axis flexure hinges

Abstract

A novel three-stage displacement amplifying mechanism is proposed by integrating the lever-type, Scott-Russell and double-arm elliptical mechanisms with red blood cell inspired flexure hinges that well balances the displacement amplification ratio and main resonance frequency. Flexure hinges are loaded in tension and bending instead of compression and bending, which can be free from potential buckling problems due to the stress stiffening effects. The combination of the dynamic stiffness matrix method and the discrete-beam transfer matrix method is utilized to rapidly forecast the kinetostatic and dynamic performances of the proposed compliant amplifier, including the curved-axis flexure hinges with complex contour profiles. Then, the Pareto multi-objective optimization strategy, taking those key geometric parameters obtained by the sensitivity analysis into account, is represented based on NSGA-II and a linear frequency solution strategy to accelerate the calculation efficiency and parameter optimization iteration. Based on the application requirement, a point on the Pareto curve is chosen as the optimal configuration for operating conditions. At last, experiments of the piezoelectric compliant amplifier under two types of external mass loads are exhibited. A displacement amplification ratio of 12.2 and main resonance frequency of 1380.5 Hz are achieved for the piezoelectric compliant amplifier under no external mass load.