This work presents an approach based on Genetic Algorithms (GA) for the dimensional synthesis of planar mechanisms as path generators. The study case deals with the development of a four-bar mechanism with application to lower limb prosthesis, specifically the knee joint. The optimization algorithm contains the objective function defined by the synthesis problem and the representation of a set of mathematical relationships that describe the kinematic restrictions of the planar mechanism. The objective function is a given numerical value for every solution that corresponds to the best possible mechanism. In other words, this objective function is the determinant to minimize the error between the desired and the generated points and can be affected by the lengths of the links, the transmission angles, the Grashof conditions, type of mechanisms, etc. The population, crossover or mutation in the GA determines the exactitude in the results. The first goal of this work is to find the optimal dimensions of the links to minimize the error between the actual coupler curve and the desired path.