Boundary-Evolved Optimization for Compliant Mechanism Design: Principles, Verification, and Applications

Abstract

A boundary-evolved optimization (BEO) method is proposed for designing compliant mechanisms. In the BEO, the initial structure with a predefined configuration is remodeled using a level set function, which is then evolved based on the gradient information of the design objectives and constraints. Utilizing prior knowledge of existing mechanisms allows for flexible adjustments of structural shapes and dimensions while ensuring convergence stability, even in complex static and dynamic hybrid optimization tasks. To validate the BEO method, two numerical cases including a microgripper and a stage with multistage amplification were optimized and compared to results optimized by conventional methods. The significantly improved performance well demonstrated the effectiveness and superiority of the proposed BEO method. As a practical application, the BEO method was successfully applied to design a piezo-actuated fast tool servo (FTS). The prototype was tested to have a stroke of 20.75 $\boldsymbol {\mu }$m and a first-order resonant frequency of 4947 Hz, exhibiting a good agreement with the desired performance. By implementing a feedback control system, the FTS was coordinated with an ultra-precision machine tool to generate a typical microlens array, achieving a peak-to-valley form error of 0.35 $\boldsymbol {\mu }$m and a surface roughness of Sa = 7.64 nm.