Elliptic Trammel

This wooden model is a prime example of an elliptic trammel, often referred to as the Trammel of Archimedes. An oval shape, the ellipse is one of the four conic sections, the others being the circle, the parabola, and the hyperbola. Ellipses are important curves used in the mathematical sciences. For example, the planets follow elliptical orbits around the sun. Ellipses are required in surveying, engineering, architectural, and machine drawings for two main reasons. First, any circle viewed at an angle will appear to be an ellipse. Second, ellipses were common architectural elements, often used in ceilings, staircases, and windows, and needed to be rendered accurately in drawings. Several types of drawing devices that produce ellipses, called ellipsographs or elliptographs, were developed and patented in the late 19th and early 20th centuries.

As one of the sliders travels toward the center along its track, the other slider travels outward along its track. By placing a pencil in the bracket at the end of the top beam, a complete ellipse can be drawn. The location of the sliders can be adjusted along the top beam by removing the carved pegs securing the sliders. This changes how far each of the sliders can travel along its track and thus changes the eccentricity of the ellipse. The eccentricity is a number between zero and one that describes how far from circular an ellipse is. A circle has eccentricity zero and an ellipse that is so long and thin that it becomes a line segment has eccentricity one.

Trammels are the most common type of ellipsograph and were often made for use in teaching and as children’s toys. Videos of trammels in use and even designs for making your own can easily be found on the Internet. This trammel is fairly large---the beam measures 36 cm (14 ¼ in) long while the tracks measure 19 cm (7 ½ in) each. The opening for a writing device is fairly large and has a white residue, so this model may well have been used as a teaching device, possibly held against a blackboard to draw an ellipse using chalk. It has no markings and its maker is unknown, but it was most likely made in the late 19th century. It was a gift of Wesleyan University in Connecticut in 1984.

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