Elastic mechanisms with clearances have extensive applications in a series of mechanism-based devices such as vehicles, aircraft, spacecraft, robots, and precision machinery. Small-sized mechanisms are of great significance for the research and manufacturing of prototype mechanisms under the guidance of appropriate similarity criteria. Based on the equation analysis method and dimensional analysis method, the kinematic and dynamic similarity criteria of the gap-free mechanism were established, and the dynamic similarity criterion of the gap-free mechanism was obtained. For the rudder surface actuator of the aircraft, physical models with different clearance values were established using the ADAMS simulation software and simulation calculations were carried out. It was found that the change of the similarity coefficient of the clearance would only cause oscillation in the angular velocity output of the mechanism, but would not lead to a corresponding proportional change in the angular velocity, which verifying the research conclusion of the kinematic and dynamic similarity criterion of the mechanism with clearance.