The surface shape of mechanical parts is nothing more than the surface of several basic shapes: plane, cylinder, cone and various forming surfaces, any surface can be regarded as a line (called the bus) along another line (called the wire) movement track, the formation of the surface of the bus and wire collectively referred to as the occurrence line. When the accuracy and surface roughness requirements are high, they need to be formed by cutting tools on machine tools.

The occurrence line in cutting process is obtained by the relative motion of the cutting edge of the tool and the workpiece. Due to the different shape of the cutting edge of the tool used and the different processing methods taken, the method of forming the occurrence line can be summarized as follows:

(1) Trajectory method It is the use of the tool for a certain law of the trajectory of the workpiece processing method. The cutting edge and the machined surface are point contacts, and the occurrence line is the track line of the contact point. A forming motion is required to form the generation line by the trajectory method.

(2) Forming method It is the use of forming tools to process the workpiece. The shape and length of the cutting edge exactly coincide with the generation line (bus) that is required to be formed.

(3) Tangential method It is a method of machining the workpiece by using the rotating edge of the tool for trajectory motion. In order to obtain the generating line by tangential method, two forming motions are needed, namely the rotating motion of the tool and the center of the tool moving according to a certain law.

(4) Developing method It is a method of processing by using the workpiece and the tool for developing cutting motion. When cutting, the tool and the workpiece are relative to each other according to the defined motion relationship (developed motion or fan motion), the cutting edge is tangential to the machined surface (point contact), and the envelope of the instantaneous position of the cutting edge is the required line of occurrence. Forming a generation line by the generative method requires a forming motion (generative motion).