Complementary theorems of surface enwrapping expressed in graphical form

Abstract

In this paper it is presented the issue of surface enwrapping, associated with a pair of rolling centrodes, based on the complementary theorems as “substituting
circles family” and “minimum distance” theorem. The profiling issues are presented for rack gear and gear shaped tools. The solving of these problems is based on the complementary theorems of surface enwrapping, expressed in analytical form. Using the capabilities of the CATIA design environment are presented specific methods for graphical profiling of rack gear and gear shaped tools. Examples based on both complementary theorems are presented, establishing the profiles of the tools specifically for the analysed generating types. The examples refer to surfaces composed of line segments and circle arcs. It is emphasized the basic quality of the graphical method – the accuracy of the obtained profile and the intuitive form in which this problem is solved.