Optimization of a two degrees of freedom compliant mechanism using Taguchi method-based grey relational analysis

This paper presents a multi-response optimal design for new two degrees of freedom compliant mechanism (TDCM) by the use of the hybrid statistical optimization techniques such as Taguchi method, response surface methodology, grey relational analysis and entropy weighting measurement technique. The design parameters like various thicknesses of flexure hinges play a vital role in determining its quality characteristics of TDCM. The quality characteristics of TDCM are assessed by measuring the displacement and first natural frequency. The experimental trials are designed by the Taguchi’s L ₂₅ orthogonal array. A hybrid approach of grey-Taguchi based response surface methodology and entropy measurement is then combined to maximize both the displacement and first natural frequency simultaneously. Response surface methodology is utilized for modeling the relationship between design parameters and two responses with grey relational grade. Entropy measurement technique is employed for calculating the weight corresponding to each of quality characteristics. Analysis of variance (ANOVA) is conducted to determine the significant parameters affecting the responses. ANOVA and confirmation tests are conducted to validate the prediction accuracy and the statistical adequacy of the developed mathematical models. The experimental results were in a good agreement with the simulation results from ANSYS. The proposed methodology is expected to use for related micropositioning compliant mechanisms.