Abstarct: Four-bar mechanisms are among the most widely used and important mechanisms used in the industry. The design and analysis of these mechanisms to perform a predetermined task has always been one of the long-standing and fundamental problems in the kinematics of mechanisms. In the past, the design of these mechanisms was done using a calculation algorithm and a simple mathematical formula known as drawing or geometric methods. These methods have accurate solutions only for a small number of points. This means that if the number of accuracy points exceeds a certain limit, these methods will lose their effectiveness. Today, with the invention of numerical optimization methods, mexta-heuristic algorithms have replaced traditional methods and can solve the problem for a high number of accuracy points by minimizing the error. Defining a suitable objective function is always one of the challenges in solving optimization problems. To design the mechanism, the error function is usually used for this purpose. But in this thesis, the goal is to include the effect of the speed of error change in the objective function baxsed on the use of some control relations and to investigate its effect on the optimization process. The problem of designing four-bar mechanism in different problems with different number of accuracy points has been investigated and optimized with particle swarm algorithm. The results show that the use of control relations in the objective function has a good effect on reducing the path generation error.