Multi-objective Optimal Design of a 2-DOF Flexure-Based Mechanism Using Hybrid Approach of Grey-Taguchi Coupled Response Surface Methodology and Entropy Measurement

Abstract

A large displacement and a high first natural frequency are two main concerns for any flexure-based positioning system. A two-degree-of-freedom (DOF) flexure-based mechanism (FBM) with a modified double-lever amplification mechanism is first designed. This study then proposes a multi-objective optimal design of the 2-DOF FBM using the hybrid approach of grey-Taguchi coupled response surface methodology and entropy measurement. The design variables of the 2-DOF FBM include the thickness of the flexure hinges and the length of lever amplification, both of which play vital roles in determining quality responses. The quality responses of the 2-DOF FBM are assessed by measuring the displacement and first natural frequency. The experimental plan is carried out using the Taguchi \({L_{25}}\) orthogonal array. An integrated approach of grey-Taguchi- based response surface methodology and entropy measurement is then applied for the multi-objective optimization of the 2-DOF FBM. To illustrate the relation between the design variables and the output responses, mathematical regression models are developed. The entropy measurement technique is applied to calculate the weight factor corresponding to each response. Then, an analysis of variance (ANOVA) is conducted to determine the significant parameters affecting the responses. In addition, the ANOVA and experimental validations are conducted to validate the statistical adequacy and the prediction accuracy of the developed mathematical models, respectively. The results reveal that the regression models have good statistical adequacy and excellent prediction accuracy. The confirmation results of the grey relational grade fall within 95 % of the confidence interval. It is strongly believed that the proposed approach has great potential for the optimal design of related flexure-based mechanisms.