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This paper proposes an efficient hybrid methodology for multi-objective optimization design of a compliant rotary joint (CRJ). A combination of the Taguchi method (TM), finite element analysis (FEA), the response surface method (RSM), and particle swarm optimization (PSO) algorithm is developed to solving the optimization problem. Firstly, the TM is applied to determine the number of numerical experiments. And then, 3D models of the CRJ is built for FEA simulation, and mathematical models are formed using the RSM. Subsequently, the suitability of the regression equation is assessed. At the same time, the calculation of weight factors is identified based on the series of statistical equations. Based on the well-established equations, a minimum mass and a maximum rotational angle are simultaneously optimized through the PSO algorithm. Analysis of variance is used to analyze the contribution of design variables. The behavior of the proposed method is compared to the adaptive elitist differential evolution and cuckoo search algorithm through the Wilcoxon signed rank test and Friedman test. The results determined the weight factors of the mass and rotational angle are about 0.4983 and 0.5017, respectively. The results found that the optimum the mass and rotational angle are 0.0368 grams and 59.1928 degrees, respectively. It revealed that the maximum stress of 335 MPa can guarantee a long working time. The results showed that the proposed hybrid method outperforms compared to other evolutionary algorithms. The predicted results are close to the validation results. The proposed method is useful for related engineering fields.

mathematical problems in engineering

Efficient Hybrid Method of FEA-Based RSM and PSO Algorithm for Multi-Objective Optimization Design for a Compliant Rotary Joint for Upper Limb Assistive Device