The Geometry of Intersecting Tubes Applied to Controlling a Robotic Welding Torch

by John M. Stockie

MapleTech (Special Issue on Maple in Industry), vol. 5, no. 2/3, pp. 58-66.

Abstract

The question of how to control a robotic welding torch to trace the joint between two cylindrical pipes can be reduced to a problem in algebra. Maple can be utilised to derive the parametric equations describing the curve of intersection between the two cylinders, and then to explore the solution graphically for various physical parameters. This problem can serve as an excellent introduction to the use of Maple for simplifying and solving systems of equations, and offers several straightforward extensions that increase its applicability to more advanced mathematics courses.

You can obtain the following files related to this paper:

the full text of the article.
the Maple worksheet forming the bulk of this paper.
a much improved version of the worksheet in the Maple Application Center
the Maple code for the elliptic integral routines "evalf/EllipticE" and "evalf/EllipticK", which is also available from the Maple share library.