In this work we present a genetic algorithm based method to design a mechatronic system. First, we present the sequential approach where we optimize the geometry of the mechanism, for a given path, and then solve the dynamic problem where we take into account the characteristics of the motor along with the inertia of the different links of the mechanism. Several types of objective functions are tested. We show, however, that this sequential method does not yield acceptable results for the dynamic behavior due to the fact that the geometry is assumed fixed when optimizing the dynamics. This led us to formulate a global optimization problem where all the parameters of the mechanism are considered simultaneously. The problem is then presented as a multi-objective optimization one where the geometry and the dynamics are considered simultaneously. The obtained solutions form what is called a "Pareto front" and they are analyzed for several different design conditions. This paper also shows the advantages of a multi-objective optimization approach over the single-objective one.