Geometric modeling of conjugated kinimatic surfaces

Abstract

The paper proposes geometric modeling of conjugate kinematic surfaces for practical use in mechanical engineering, having a spatially complex surface that is closely associated with the formation of mutually enveloping conjugate surfaces.At the present stage of rapid development of complex designs of machines and apparatuses with the complex interaction of their parts, descriptive geometry methods are widely used in solving various complex technical problems. One of the common methods for the formation of geometric objects is geometric modeling, which allows the desired geometry of the product during the creative creation of machines, even at the design stage, to determine the conjugation of the kinematic surfaces of systems of complex movements and solve many other problems. Since the surface of the machining part and the cutting tool is conjugated, each of these surfaces can be represented as an envelope with respect to the second movable surface.The paper proposes to optimize the process by creating universal graphic tools, which essentially represents a graphic image of the parameters of kinematic conjugate pairs, changing one of which leads to a change in the other, opens up the possibility of obtaining shapes of parts with predetermined parameters. The wish should be attached to expand the capabilities of the propeller diagram, taking into account the real picture of the kinematics of engagement, which, when the distance between the ages of the screws changes, would give a real idea of the change in the geometry of the engagement in each instant wheel movement.The theory of envelope surfaces was further developed in matters of profiling of a cutting tool. Concerning the design of a cutting tool by the graph analytic method of profiling, it follows that from graphical constructions at any stage of design, it is easy to go over to the calculation by the analytical method, if necessary, checking or accurately determining the parametersGraphic methods allow you to visualize the process of obtaining the profile of the part, to analyze the influence of each parameter on the profile and structural dimensions, where it is easy to identify the profiling errors of the conjugate kinematic surfaces. For accurate design, it is necessary to perform quite a number of geometric constructions, where it is accompanied by the introduction of completely objective errors, which can be avoided and also requires substantial creative preparation, which this article is devoted to.