Methods of digital differential analyzers in the implementation of the geometrical problem in CNC metal cutting machine

Abstract

The article deals with methods for the implementation of a geometric problem in CNC machines using digital differential analyzers. The advantages and disadvantages of the implementation of interpolation in CNC systems by various methods are considered, special attention is paid to the general methods of digital differential analyzers in the implementation of the interpolation of the movement of the working organs of the machine tool. Interpolation methods are analyzed in which the Euler method is used for numerical integration, based on the expansion of the function in a Taylor series with discarding the highest (second and higher) degrees of expansion. The mathematical formalization of the construction of complex curves is shown by the methods of digital differential analyzers - plane curves of the second order, such as parabola, hyperbola, ellipse.