The Trammel of Archimedes has been around for a long time, but it is usually with two "lanes", or shuttles. Some variations on the classical one are covered nicely in "A New Look at the So-Called. Trammel of Archimedes" byTom M. Apostol and Mamikon A. Mnatsakanian (http://www.jstor.org/stable/27642689), but still restricted to two lanes. A vague reference to three lanes appears in "A wonky Trammel of Archimedes' (web.mat.bham.ac.uk/C.J.Sangwin/Publications/WonkyTrammel.pdf) , and pictures of three-laned ones abound (e.g., at the bottom of https://plus.google.com/+PedroLarroy/posts/7HKvcjiUGPH). However, nowhere (at least on the Internet) do I find a good treatment of a generalization to n lanes, for example that would allow me to calculate the area of the envelope of the ellipse traced out by such a mechanism. Can anyone point me in the right direction (preferably something freely accessible on-line)? Thanks in advance.