Abstract
A special place in the theory of shaping is occupied by the method of compiling mathematical models of technological processes for obtaining surfaces of parts using cutting. The mathematical model includes a description of the shape of the cutting tool and the law of its movement relative to the workpiece. In this case, several reference systems are used, and the entire calculation is carried out taking into account the complex movement of bodies. The matrix expression of the laws of motion of bodies can be the basis for creating a model of the forming process. In many cases, the envelope surface can serve as a model of the surface treated with a cutting tool. From these positions, the envelope theory is an integral part of the theory of shaping. The mathematical description of the envelope depends on the type of task for the surface family. The mathematical model of the technological process of forming includes a description of the shape of the producing surface and the law of its movement relative to the workpiece, as well as obtaining the equation of the processed surface as the envelope of the family of producing surfaces.
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