Abstract
A simple method by applying envelope theory to determine the profile of a tube-straightening roller has been studied. The roller profile is defined as the envelope of a three-parameter family of spatial curves. The three parameters are rotation, translation and rotation, which generate by their motions the spatial curves. The envelope theory is utilized by an implicit function. To avoid undercutting of the surface of the straightening roller, principal curvatures and contact lines are analyzed. It is found that a spherical-end cutter 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 mathematical software, the complete contour of the tube-straightening roller can be simulated using a personal computer, as shown in this paper.
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