In this paper, a dimensional synthesis method for a four-bar (4R) path generator mechanism having revolute joints with clearance is presented. Joint clearances are considered as virtual massless links. The proposed method uses a neural network (NN) to define the characteristics of joints with clearance with respect to the position of the input link, and a genetic algorithm (GA) to implement the optimization of link parameters using an appropriate objective function based on path and transmission angle errors. Training and testing data sets for network weights are obtained from mechanism simulation, and Grashof's rule is used during the optimization process as constraint. The results show that the proposed method is very efficient for the purpose of modeling the joint variables and also adjusting the link dimensions to optimize planar mechanisms with clearances.