EDGES OF REGRESSION AND LIMIT NORMAL POINT OF CONJUGATE SURFACES

摘要

The present paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line and the contact boundary line on the conjugate surfaces. It is proved that the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively. Two groups of equations for the undercutting and the contact boundary lines of the conjugate surfaces are developed based on the definition of the edges of regression in differential geometry. The geometric meaning of Wildhaber's concept of the limit normal point is explained. Numerical examples are taken for illustration of the above-mentioned concepts and equations.