Abstract: A workpiece executes a rotation movement about a longitudinal axis and is machined by a tool in a multitude of reshaping engagements, in which an active region of the tool comes into contact with the machining region. The tool is held by a tool holder. The tool holder is mounted in an orbiting body so as to be rotatable about a rotation axis and is driven to carry out a rotating movement about the rotation axis, and is driven to carry out an orbiting movement by the orbiting body. Rotation movement of the workpiece is synchronised with the orbiting movement of the tool holder and the rotating movement of the first tool holder is synchronised with the orbiting movement of the tool holder.