Abstract: A device for machining a surface of a workpiece includes a workpiece holder configured to rotate the workpiece about a workpiece rotational axis, a tool having a tool rotational axis and at least one blade having a blade radius of curvature and a tool holder configured to position the tool such that an active point of the blade comes into engagement with the workpiece and configured to pivot the tool about the tool rotational axis and to configured to move the tool with an advancing motion such that the active point of the blade shifts along the blade. The advancing motion is defined by a curve having at least a first radius of curvature and a second radius of curvature.