Edges of Regression and Limit Normal Point of Conjugate Surfaces1

Abstract

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]