Abstract: A universal envelope-approximation theory was presented to generate the sculptured surface by strip-width-maximization machining with single point contact using non-ball-end cutters,formulating the problem of multi-axis sculptured surface machining as that of approximating the cutter surface to the design surface under the movement transform.The speed equation and the movement transform matrix is deduced to determine the relative motion between the tool and the workpiece by intrinsic differential geometry based on the idea of the moving frame.The functional optimized model of the tool positioning was established to enable the relative motion between the tool and the workpiece to be smooth and continuous,aiming at the highest machining efficiency and machining accuracy respectively.Simulated examples demonstrate the improved machining efficiency and precision of the envelope-approximation Theory over current published methods.