Some Exercises with Equations of Meshing: Review of Fundamental Manuscript

Abstract

The manuscript by Professor V. I. Goldfarb discusses approaches to obtaining the equation of the enveloping surface for a one-parameter family of surfaces, which is usually called in the theory of gearing “the equation of meshing”. Professor V. I. Goldfarb shows, through relatively simple transformations (exercises in the author's terms), the generality of this condition and the internal relation between the concepts and techniques used, obtained and used by different authors, who worked in different eras and in different fields of science—differential geometry, higher geometry, theory of gearing and theory of generating. The manuscript is of both fundamental and educational importance and serves to form a general concept of the processes of meshing and generating and to better understand these processes.