Generalization of Archimedes' Trammel?

[nomadreid]

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.

 

[haruspex]

A vague reference to three lanes appears in

It does? I couldn't find it. And the animation at the Larroy link only uses two lanes. Both generalizations are merely to two non-orthogonal lanes.
To go to 3 lanes you could consider a circle constrained to have its perimeter lying on three tracks.

 

[nomadreid]

Thanks, haruspex. I stand corrected; I no longer know where I thought (apparently mistakenly, now that I re-read the article) the stated reference was. So, after my own scan of the on-line literature turned up nothing on such generalizations, and throwing this out to the PhysicsForums community also turned up no explicit working out of the generalization that you suggest, I am going to assume that such a generalization has not been published, or at least not recently.