The device comprises a main body, a fixing member affording fixing of a door leaf to the main body, a ball socket able to drive the main body under the effect of a motor, a roller able to move between (a) an active locking position in which the roller locks the ball socket with respect to the main body, in a closed position of the door leaf and (b) an inactive unlocking position in which a the roller allows displacement of the ball socket with respect to the main body. The device also includes a sleeve that allows a small movement of the fixing member with respect to the ball socket in a displacement direction from the closed position of the door leaf. The device further comprises a tooth that inhibits sleeve to immobilize the fixing member with respect to the ball socket, at least in translation in the displacement direction, when the roller is in the inactive position.