A trammel of Archimedes is a mechanism that generates the shape of an ellipse.^[1] It consists of two shuttles which are confined ("trammelled") to perpendicular channels or rails, and a rod which is attached to the shuttles by pivots at fixed positions along the rod. As the shuttles move back and forth, each along its channel, the end of the rod moves in an elliptical path. The semi-axes a and b of the ellipse are the distances between the end of the rod and the two pivots. An ellipsograph is a trammel of Archimedes intended to draw, cut, or machine ellipses, e.g. in wood or other sheet materials. An ellipsograph has the appropriate instrument (pencil, knife, router, etc.) attached to the rod. Usually the distances a and b are adjustable, so that the size and shape of the ellipse can be varied.

The history of such ellipsographs is not certain, but they are believed to date back to Proclus and perhaps even to the time of Archimedes.^[2]

 

An animation of a Trammel of Archimedes in action.

Wooden versions of the trammel of Archimedes have been produced also as toys or novelty items, and sold under the name of Kentucky do-nothings, nothing grinders or do nothing machines. In these toys the drafting instrument is replaced by a crank handle, and the position of the sliding shuttles is usually fixed.