Comparative Study on the Synthesis of Path-Generating Four-Bar Linkages Using Metaheuristic Optimization Algorithms

Abstract

Four-bar linkages are one of the most widely used mechanisms in industries. This paper presents a comparative study on the accuracy and efficiency of the optimum synthesis of path-generating four-bar linkages using five metaheuristic optimization algorithms. The utilized metaheuristic methods included two swarm intelligence-based algorithms, i.e., particle swarm optimization and hybrid particle swarm optimization, and three evolutionary-based algorithms, i.e., differential evolution, ensemble of parameters and mutation strategies in differential evolution, and linearly ensemble of parameters and mutation strategies in differential evolution. The objective function to be minimized is the sum of squares of the distance between the generated points and the precision points of a coupler point. The optimal design of four-bar linkages must meet the Grashof’s criteria and exhibit sequential constraints that can prevent the occurrence of order defect. This study investigated five representative cases of the dimensional synthesis of four-bar path generators with and without prescribed timing and compared the optimal solutions of the utilized five metaheuristic methods to those of previously reported algorithms in literature. The improved metaheuristic methods exhibited superior optimal solution and enhanced reliability compared to the original methods. Moreover, three improved metaheuristic methods were not only easy implemented, but also more efficient for solving the optimal synthesis problems, particularly for high dimensional problems.

Optimal Design and Dynamic Analysis of a Spring-Actuated Cam-Linkage Mechanism in a Vacuum Circuit Breaker

“…(4) Optimal design results Table 5 displays the parameter settings for the optimal VCB mechanism design. This study employed the DE-gr method, which involved using a specified proportion of the crossover rate to the mutation factor, referred to as a golden ratio (0.618:0.382) [19]. Twentyfive numerical experiments were performed to obtain the best optimal solution, and each experiment had 300 generations.…”

“…Ortiz et al [18] used an improved DE algorithm with self-adaptive control parameters (called IOA s-at method). Recently, Kang et al [19] applied the DE algorithm with a specified golden ratio (0.618:0.382) as the cross rate and mutation factor; the method is called the DE-gr method, to effectively optimize the dimensional synthesis problem of path-generating four-bar linkages. They reported that the efficiency and accuracy of the DE-gr algorithm was superior to those of the PSO, DE [16], DE-GE [17] and IOA s-at [18] methods.…”

Application of the path-repairing technique and virus optimization algorithm for the dimensional synthesis of four-bar mechanisms

“…In 2022, Qaiyum and Mohammad applied the improved harmony search algorithm [ 17 ], while Huang et al used the repellency evolutionary algorithm [ 18 ]. Kang et al compared various metaheuristic optimization algorithm for path synthesis of four-bar mechanisms [ 19 ].…”

Study of Differential Evolution Variants in the Dimensional Synthesis of Four-Bar Grashof-Type Mechanisms

“…The first three methods are helpful for synthesizing four-bar mechanisms when the trajectories (paths) are relatively simple. As trajectories become more complicated, the optimization method turns out to be more effective, so its use is now widespread [22][23][24][25][26].…”

“…Hence, optimization problems related to the dimensional synthesis of four-bar Grashoftype mechanisms are complex, and classical optimizers such as Sequential Quadratic Programming or the least square optimization technique may have difficulties in finding appropriate solutions, as reported in the specialized literature [22]. It is difficult for practitioners to execute the classical optimizers because of the challenges in defining the initial conditions and the algorithms' reliance on gradient information.…”