This paper presents a mechanism design optimization for actuating the horizontal stabilizers of an aircraft using a rotating empennage without a vertical stabilizer. Birds do not have vertical stabilizers and rotate their tail feathers to control agile maneuvers. A rotating empennage concept will mimic this motion and enable the bio-inspired flight of a fixed wing aircraft. To maintain control, the bio-inspired rotating empennage will incorporate three degrees of freedom: independent rotation of each horizontal stabilizer and rotation of the empennage relative to the main axis of the fuselage. The primary benefits of an aircraft without a vertical stabilizer are reduced drag and weight which, in turn, results in a more efficient operation. In order to reduce inertia of the rotating empennage, the linear actuators that position the horizontal stabilizers will be placed within the fuselage. Mechanisms that couple the linear translation of the actuators with the rotation of the horizontal stabilizers ideally require a low peak force and short stroke from the actuator. With two conflicting objectives, a Pareto front optimization was conducted to determine appropriate link lengths of candidate solutions and to understand the effectiveness of alternate mechanisms. The study considers rack & pinon, scotch-yoke, slider-crank, inverted slider-crank, Watt II, and Stephenson III mechanisms.