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

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. Keywords: pipe welding, cylinders, intersections, geometrical modeling Introduction: A welding problem Many problems arising in engineering and physics have a mathematical description that is too complicated for consideration in lower--level mathematics courses. It is often possible to make simplifyingassumptions that reduce the problem to manageable proportions, but it is often the case that these simplificati...