CONDITIONS DETERMINATION OF EXISTENCE OF TANGENT CURVE TO FAMILY OF EQUIDISTANT CURVES OF THE SHORTENED EPICYCLOIDS IN EPICYCLIC TRANSMISSION INTERNAL GEAR

Abstract

This article describes the production of single equations that describe the profiles of parts in cycloidal transmission internal gear. Profile wheel with internal tooth, outlined of the curve, wherein different parts are described by different equations. This creates difficulties in the design and calculation of transmission. Thus, the search for common equations is an important scientific and practical problem. On the basis of positions of differential geometry were shown out a two-parameter system of equations describing tangent curve to family of equidistant curves of the shortened epicycloids. Similarly shown out equalization of connection between parameter that determines position of point on a profile and by a parameter that determines a profile from the great number of family, similarly investigated the conditions when there is a curve. Also examined a technique of designing the so-called β-function. This is a specific component of a mathematical model of the cycloidal transmission, which determines the conditions for the existence of the envelope curve. The research result can be used as an engineering method for designing and manufacturing epicyclic transmission gear.