Two-Step Approach for Optimizing Flexure-Based Mechanisms: A Displacement Amplifier Case Study

A flexure-based compliant mechanism achieves its motion from the deflection of its flexure hinges, offering many advantages, such as increased precision and reduced wear and backlash. In a flexure-based mechanism, flexure hinges at different positions may be subject to significantly different loads and undergo diverse deflections, thus different load-deflection properties are preferred for each of the flexure hinges. To optimize a flexure-based mechanism for better performances always leads to a high-dimensional optimization problem involving the dimensions of the mechanism, the geometric parameters, and the orientations of each of the flexure hinges, which could be computationally prohibitive for optimization. To address this challenge, we propose a two-step optimization approach, in which the problem is divided into two relatively independent subproblems, i.e., a kinematic optimization and a kinetostatic optimization. The tensural displacement amplifier is taken as a case study to demonstrate the effectiveness of the proposed two-step optimization approach. As compared with the original design, both the transmission efficiency and the output stiffness are significantly improved after the two-step optimization with almost the same amplification ratio. The optimized design is further verified by a finite element model (FEM) and a physical prototype. In general, the two-step optimization approach can be easily tailored for improving the performances of various flexure-based mechanisms.