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A new method for manipulation of a rigid body with a flexible sheet is presented, and the method is applied to repositioning of bedridden patients. A key feature of the proposed system is that the body is not securely connected to the sheet and the contact region between the body and the sheet changes dynamically during manipulation. The use of a soft flexible sheet and the untethered nature of manipulation, makes the system particularly well suited to handling the human body. We present an application to a rehabilitation bed for repositioning a bedridden patient to alleviate secondary ailments such as bedsores. In order to prevent injury to the patient's fragile skin, it must be ensured that the patient does not slip on the sheet during repositioning. We model the system and present a no-slip condition based on system parameters. The model is used to develop a closed loop control strategy for coordinating the motions of multiple actuators of the prototype bed. The prototype bed can successfully reposition test subjects using the control strategy developed.