Abstract: A fly-cutting system is disclosed, and in particular one that comprises a dynamically-controllable actuator for controlling the position, orientation, or both position and orientation of a cutting element carried by a fly-cutting head. In certain embodiments, the actuator can adjust the position or orientation of a cutting element, or both, hundreds or thousands of times per second, enabling precise control over the shape of features formed by the cutting element in a surface of a workpiece.