This paper reports a technique for constructing a geometric shape of the surface of contact between the interacting conjugated machine elements using computer technology. A subprogram has been developed in the MATLAB software package. The comprehensive solution to such problems is a certain scientific challenge and is of great importance when designing the kinematic pairs in mechanical engineering. The main systemic drawback in the construction of complex mechanisms is that the design process does not take into consideration the geometric characteristics of the contact spatial engagement surface in the screw kinematic pairs. As a result, during the manufacture of a kinematic pair, conventionally designed structural elements demonstrate defects that shorten their lifespan. Solving the set task could reduce the time to design toothing, cutting tools, would ensure the required estimation and graphic accuracy, as well as improve the efficiency of the manufacture of parts. The study of existing procedures for designing screw conjugated surfaces has made it possible to note their unsatisfactory compliance with modern design requirements. Therefore, the manufacture of a kinematic pair that provides for technological accuracy implies the assignment of the curvilinear shapes for a contact spatial engagement surface under the predefined conditions. The proposed geometric technique for determining the shape of a contact spatial surface of the kinematic pairs of toothing and cutting tools could make it possible to design and manufacture components and mechanisms with the required accuracy

This paper has proposed improving the methods of circular and screw conversion, to be used in the design of cutting tools and toothing that include complex mated surfaces. Underlying the improvement of both methods is the construction of a mathematical base and the development of a computer subprogram, based on it, in the MATLAB system. During the research, the original screw-type curved surface and the curvilinear generatrix axis were formed on the basis of improved methods, taking into consideration the exclusion of interference at the design stage. A comprehensive solution to this problem is important for the manufacture of products by rolling. Given this, the original instrumental surface of the cutting tool takes into consideration the pairing condition between the article’s and tool’s points. The result, when designing gears and cutting tools using the proposed improved methods, assigns the curvilinear surface parametrically, represented by two-dimensional arrays characterizing its coordinates. To avoid interference at the design stage, it is necessary to analyze the intersection of the axis of the curvilinear generatrix with horizontal planes. That would make it possible, when machining an article, to avoid cutting, jamming, as well as the dangerous concentration of stresses. The accuracy and reliability of a wide range of articles in machines and machinery and other kinematic pairs also improve. The proposed improvement of circular and screw conversion methods to simulate curvilinear mated surfaces that exclude interference at the design stage is of practical interest in machine building