On the optimum synthesis of a four-bar linkage using differential evolution and method of variable controlled deviations

Alternative Constraint Handling Technique for Four-Bar Linkage Path Generation

“…One task for designing a four-bar linkage is a path generation problem. This synthesis problem is aimed at finding significant link lengths of the mechanism to achieve a point on a coupler link moving along the desired path [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The problem is usually converted to be an optimization problem, which is posed to find the dimensions of a mechanism and some other parameters.…”

“…The path generation problem is of interest by many researchers due to the advantage of using such a mechanism such as work reported by Sleesongsom and Bureerat [16]. Almost all of the previous work tried to improve the design performance of the path synthesis problem in both the constraint handling [10][11]16] and the performance of an optimizer [1][2][3][4][5][6][7][8][9]16]. The path synthesis optimization problem normally composes of two types of constraints.…”

“…The second constraint is set to obtain unknown timings of the crank in a sequential order. From the literature, it is found that a simple exterior penalty function technique is the most popular technique used to deal with constraints [1][2][3][4][5][6][7][9][10][11], but it still lacks in efficiency as reported in [8,11,13,16]. Very recent work in [16] proposed a new technique to neglect the second constraint from the optimization problem and a first constraint is still tackle with the traditional penalty technique, which is found to give the considerably better results than the traditional exterior penalty technique.…”

A Specific Problem of Mechanism Synthesis

“…The effectiveness of the method depends essentially on the number of design parameters, therefore mechanism synthesis addresses also the techniques minimizing the number of design parameters (Buśkiewicz, 2014;Buśkiewicz, 2010;McGarva and Mullineux, 1994;Ullah and Kota, 1997;Wen-Yi, 2010). Other techniques focus on developing algorithms minimizing an objective function and constructing new error functions (Penunuri et al, 2011;Sanchez Marin and Gonzalez, 2004;Matekar and Gogate, 2012;Bulatovic and Dordevic, 2009;Chao and Jorge, 2008).…”

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.…”