The wonky trammel of Archimedes

This article examines the ellipsograph of Archimedes, also known as the locus problem of Franciscus van Schooten, and related mechanisms. We not only solve the algebraic system explicitly, but we also reverse engineer the problem and find configurations that provide a particular solution. Using the modern techniques of polynomial Gröbner Bases we show this can be used as a traditional compass, as a straight edge (to draw a straight line) and as an ellipsograph to trace ellipses.