On the Optimum Synthesis of Four-bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions

Abstract

Mechanism synthesis, the identification of the parameters of a mechanism, has been extensively studied especially for four-bar linkages using graphical and numerical optimization approaches. Graphical techniques follow a number of predefined steps and rely heavily on the user. Numerical optimization techniques that require the user to provide ''good initial guesses'' or bounds for the design variables have also been applied. In general, a linkage is synthesized for function generation, motion generation, and path generation. This article studies four-bar mechanism synthesis by combining Differential Evolution, an evolutionary optimization scheme that can search outside the initial defined bounds for the design variables, and a newly developed novel technique called the Geometric Centroid of Precision Points (GCPP) and the distant precision point in defining the initial bounds for the design variables. The developed methodology has been applied to the synthesis of four-bar linkages for path generation with prescribed timing, where the coupler point is required to pass through a number of precision points within a prescribed accuracy level and in the correct order, and for the generation of families of coupler curves. Two penalty functions were used, one for constraint violation and one for relative accuracy. The results of the application of this approach could also be used as ''good initial guesses'' for improving the desired accuracy level. Examples demonstrating the successful application of the developed methodology are presented.

Reduced number of design parameters in optimum path synthesis with timing of four-bar linkage

“…The prevalent techniques are based on the genetic/evolutionary algorithms and other heuristic methods patterned upon biological systems and social behaviours (Avilés et Shiakolas et al 2002Shiakolas et al , 2005. Frequently, the methods are devoted to a single specific path-synthesis task: synthesis of open-path generators, synthesis of closed-path generators, path synthesis with and without timing (time prescription).…”

On the optimum synthesis of six-bar linkages using differential evolution and the geometric centroid of precision positions technique

“…Four-bar mechanisms synthesis is broadly reviewed in [4,5]. The review of literature relating to six-bar mechanism synthesis is presented next.…”

“…The graphical techniques are limited to a finite number of precision points. Numerical techniques are commonly combined with various optimization schemes such as genetic algorithms [2][3][4], evolutionary techniques [5], interior-point method [6] and gauss constrained method [7].…”

Optimum Path Synthesis of a Geared Five-Bar Mechanism

“…Several optimization algorithms, including exact gradient [9], simulated annealing [13], genetic algorithm (GA) and modified GA [7,8,10,11,19,23,25], ant-gradient [6,17,26], genetic algorithmfuzzy logic [24], differential evolution (DE) and modified DE [14-16, 18, 19, 21, 22, 27], particle swarm optimization [19], GA-DE [20,28], and hybrid optimizer [29], are used to solve the optimization problems of path synthesis. In the one-phase synthesis method, the error function in [9][10][11][14][15][16][17][18][19][20][21][22] is based on the sum of the square of Euclidean distance error (termed the square deviation in this study) between the target points and the corresponding coupler points. The error function in [23,24] is based on the orientation structural error of the fixed link.…”