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The paper describes a physical control method for rotating an object that has no support from below. Conventionally, physical correction of the rotational center of an unsupported object while maintaining rotation around an axis that is located outside the object is difficult. In particular, for the case in which the object is soft and pliable, control is more difficult because gravity can easily affect the shape of the object. As an example, we selected a task in which a robot turns a rope using an end effector. In order to accomplish this task, we propose a novel control method. To control the rotational center to a target position while fixing the shape by centrifugal force, we formulated a method whereby a compensator is added to a control rule that enables the trajectory of the end effector to converge to a limit-cycle within a fixed radius. We applied the proposed control method to a simplified rope simulator. The results of the simulation revealed that the end effector of the robot and the center of mass of the simplified rope converge to a limit-cycle attractor. This result indicates that the system applies the forces that stabilize the shape of the rope and the location of the rotational center. In addition, we applied the proposed method to a rope turning task performed by a humanoid robot. The robot was able to turn a rope with one fixed end and could collaborate with a human. Both tasks could be realized by the same control method.