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This paper presents a new vibration control device by which the equivalent mass and damping of a structure are increased simultaneously. The vibration control system, rotational inertia dampers combined with toggles, can be utilized effectively even in structures with small drift. Numerical analysis shows that the performance of the rotational inertia damper is further enhanced with the addition of a viscous or friction damping mechanism. It is also observed that as the lead of the ball-screw decreases the equivalent mass and damping of the structure and consequently the vibration control effect of the rotational inertia damper increases significantly.