USE OF STRUCTURAL-PARAMETRIC MODELING IN MEASURING THE SIZE OF ANGLES RELATED TO A CIRCLE

Abstract

The article considers the possible cases of the position of the magnitude of the angles relative to the circle and formulates the basics and principles of the method of structural - parametric modeling in measuring the magnitude of the angles associated with the circle. The method of structural-parametric modeling allows at the first stage, which is the location of the vertex of the angle, to determine its value on the basis of generalized principles of dependences, which is determined by the previously published theorem on measuring the magnitude of angles associated with a circle. The cases of the position of the vertex of the angles relative to the circle were reduced to the following three possible placements, namely: - in the circle: - on the circle and outside it. Separately, there were cases of position of the vertex of the angle in the center of the circle (central angle) and outside the circle, provided that the vertex of the angle goes to infinity (secant vertices of the angle - parallel to each other). This method should be used when constructing geometric dependences on the scheme of the modified kinematic screw, because to construct conjugate surfaces it is necessary to accurately determine the geometric parameters of the magnitude of the angles in the circle. This approach is also important when constructing angles on the wheel, which is of great importance in kinematics. By determining the structural-parametric dependences, based on the considered cases, it is convenient to model a set of complex geometrically conjugate helical surfaces with similar characteristics, changing only the corresponding analytical values. Accordingly, the cases described above allow us to solve certain problems of geometric modeling, and due to the variability of the value of the angle (from zero to 180 °) at its apex make it true for all possible cases. Therefore, for further modeling of complex geometric surfaces it is expedient to use these structural-parametric dependences in a circle (wheel).

Keywords: a magnitude of angles, circle, a wheel, modeling, difficult geometrical surfaces, a central angle, an inscribed angle, a tangent, secant.