A system for reprofiling a wheel set of a railway vehicle allows the center of rotation of the wheel set to move relative to supporting rollers. A cutting tool used to reprofile the wheel profile on a wheel set is moved relative to the center of rotation of the wheel set to maintain a constant distance between the center of rotation and the cutter. The rollers are maintained in a fixed position during the cutting process. The system avoids mechanically forcing a constant location of the wheel set relative to the center of rotation.