Profile determination of a tube-straightening roller by envelope theory

A simple method by applying envelope theory to determine the profile of a t ube-straightening roller has been studied. The roller profile is defined as the envelope of a three-parameter family of spatial curves. the three para meters are translation and rotation, which generate by their motions the sp atial curves. The envelope theory is utilized by an implicit function. To a void undercutting of the surface of the straightening roller, principal cur vatures and contact lines are analyzed. It is found that a spherical-end cu tter is needed in making the roller. The radius of the spherical-end cutter is similar to that of the radius of the tube. Due to available mathematica l software, the complete contour of the tube-straightening roller can be si mulated using a personal computer, as shown in this paper. (C) 1999 Elsevie r Science S.A. All rights reserved.