The cutter is a fundamental machine tool used extensively throughout manufacturing industries. The performance and quality of the cutter have a direct influence upon the cutting precision, product quality and production rate. Invigorating the domestic cutter industry and establishing a characteristic syscxtem of cutter technology requires that new technology be imported, the constraints of previous experience be overcome, a fundamental research and development capability be developed and new machine tool materials be adopted Two basic approaches exist when considering geometrical models of the cutter. In the first approach, developing new cutters and establishing an optimal set of cutter design parameters is performed in accordance with general cutting theory and the operational functions of the machine tool. Meanwhile, in the second approach, the structural requirements and design parameters of an ideal cutter are used to establish a geometrical cutter model which describes the various contours of the cutter. Developing an accurate geometrical model is an essential prerequisite to realizing the com-puter-aided design of a cutter, and is necessary in order to apply the theory of cutter design and manufacturing theory to the practical manufacturing proc-ess. Moreover, the geometrical model provides the basis for interference checking and manufacturing error analysis. Modern cutter design and manufacturing technologies integrate the results from a diverse range of previous studies, including those performed within the fields of fundamental mathematical theory, computer-aided ap-plication technology, modern design technology, material science and manufacturing technology. In each field, technological progress is reliant upon the development of mathematical theory. In the present study, differen-tial geometry, conjugate theory, engagement relationship theory, coordinate transfer and numerical methods are used to develop a systematic method for the design, simulation, manufacturing and compensation of special revolving cutters. Using the proposed mathematical models, this paper presents real-izable and effective manufacturing models for these revolving cutters. Fur-thermore, the Taguchi method and power signal analysis techniques are em-ployed to investigate the effects of different cutting-edge curves on the cut-ting characteristics of Inconel tool material. The basic research activities performed within the present study can be summarized as follows: 1.The study develops geometrical models for the cutting-edge curves and flute designs of ball-end cutters, truncated-cone ball-end cutters and toroid-cone shape cutters. Applying the inverse-envelope theory, a geometrical model for the cross-section of the grinding wheel used to grind the required helical groove on the cutter is developed. Further-more, the relative positions and velocities of the grinding wheel and workpiece during the NC manufacturing of the cutter are developed and investigated via a process of computer simulation. Finally, a compensation method is developed which resolves the problems of residual revolution surface and localized non-existence of the cutting-edge. The theoretical models and results provide a valuable source of reference for the NC manufacturing of revolving cutters. 2.A series of experiments are performed to investigate the effects of the cutting-edge geometry on the machining performance when machining Inconel 718. The Taguchi method is adopted to determine the set of optimal machining parameters for a variety of cutting-edge types, in-cluding those of the truncated-cone ball-end cutter, the plane type, the S type and the traditional type. The results of these experiments serve as a valuable reference for the automated machining of aero-materials. 3.Study the design and manufacture of the cutting-edge curve, flute sur-face and the coning angle of the grinding wheel for both the rotating burr and the revolving cutter, and discuss the difference of the related geometrical models. Also, the practical cutting-edge curve and the feeding rate of the relative movement for the cutter of the two and half axes processes of the NC machine have been discussed.