Abstract: The invention relates to servo-driven computer-numerically-controlled systems of the type adapted to receive part program instructions defining a desired path of relative movement between a tool and a workpiece, wherein the path may include an interior or exterior curved portion to be effected by coordinated linear movement of machine members along at least two orthogonal linear axes. The invention provides apparati and methods for correcting path radius errors to facilitate rapid and accurate movement along the curve. In a preferred embodiment, such path radius correction is applied to a fixed cycle for machining inside circles preferably incorporating such path radius correction and providing substantially tangential engagement between the tool and a machining locus orbited by the tool to avoid abrupt accelerations or decelerations while the tool is in contact with the workpiece.