Optimal synthesis of four-bar linkages for path generation using the individual repairing method

Constraints are one of the main factors that hinder the optimal synthesis of linkages to obtain the global optimum. At present, the most commonly used constraint handling method is called the penalty function (PF) method, but this technique has proven to be inefficient and unreliable in path synthesis. In this paper, a novel and effective constraint handling method called the individual repairing (IR) method is developed for the optimization model of four-bar mechanisms for path synthesis. The function of the IR method is to check the conformity of each individual to the Grashof condition, the sequence condition, and the variable range condition after population initialization and each iteration as well as to repair all unreasonable individuals according to the corresponding repairing technique to make them all satisfy the constraint conditions. In other words, the new constraint handling method establishes a transformation method so that each infeasible point in the search space uniquely corresponds to a feasible point. Based on the IR method, the optimization of path synthesis can be effectively carried out. Finally, the validity and reliability of the new constraint handling method are verified using three examples.