In a method for machining a workpiece, a cutting tool is guided relative to the workpiece, with a vibration being superposed, the amplitude of which is at least 5 m. A supply circuit for a piezo actuator of a vibrating tool generates a voltage at the voltage output, which has a direct component and an alternating component. A supply system for a piezo actuator of a vibrating tool has the above-mentioned supply circuit which is connected to a secondary coil that is coupled to a primary coil.

A machine tool having a monolithic base is disclosed. The monolithic base includes at least two flat surfaces that are mutually orthogonal and that are convex with respect to each other. The machine tool includes at least two moveable stages, each mounted to one of the flat surfaces, and each stage also being mutually orthogonal.