“…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.…”