A reactionless mechanism is one in which no reaction forces nor moments are transmitted to the base for any arbitrary motion. This interesting property often requires to increase the total mass and the moments of inertia, leading to reduced dynamical performances. Therefore, this paper presents an optimization approach to synthesize and improve the dynamical performance of a reactionless three-degree-of-freedom planar mechanism. The three legs of this original mechanism are composed of reactionless four-bar mechanisms dynamically balanced with only one counter-rotation at the base. The optimization variables are the geometric and inertial parameters, whereas the goal is to minimize the global moment of inertia of each leg. This will reduce the power consumption of the three actuators and increase the agility. To meet physical and realistic requirements, the optimization problem is also constrained with bounds on the parameters, with the reachability of a given workspace and with a given range on a kinematic sensitivity index. Since different initial guesses of the optimization process lead to similar objective results, it is proposed to search for several local solutions (morphologies). A methodology is therefore developed to explore the design space and group the results after refinement. The final choice among the obtained solutions is made using additional design criteria based on the sensitivity in terms of dynamic balancing and power consumption with respect to the design parameters.