Keuffel and Esser Trammel

This drawing device is 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.
This device was used by professionals who needed to draw ellipses in engineering drawings or blueprints. It is made of nickel-plated brass and moves very smoothly. Small points on the underside of the device hold it securely to the drawing surface. A reversible writing tip or pencil-lead holder screws onto the adjustable bracket at the end of the top beam. The two screws on each slider allow them to be positioned along the top beam. As the top beam is rotated, the sliders move in opposite directions along their tracks--as one moves inward, the other moves outward--and an ellipse is drawn on the writing surface. The closer the sliders are to each other on the beam, the more circular the ellipse becomes, and the eccentricity of the ellipse approaches zero. The eccentricity of an ellipse is a number between zero and one that describes how far from circular an ellipse is. A circle has eccentricity zero. As an ellipse becomes longer and thinner, the eccentricity approaches one.
This model was manufactured (or imported) in approximately 1930 by the Keuffel and Esser Company of New York. It is marked “Keuffel & Esser Co N.Y. Switzerland.” This device first appears as item 1181 in their 1921 catalogue, which states that “This instrument draws ellipses of any shape, from 6 inches to 18 inches major axis, with great accuracy.” It remains available into the 1950s. Two other ellipsographs (items 1178 and 1180) were available prior to this item being offered, but appear to have no longer been available once this item was added to the listing. The “Switzerland” mark may indicate that this device was imported for sale by K&E. The top beam is 22 cm (8 1/2 in) long and can be extended an additional 2.5 cm (1 in). The two tracks are 10 cm (3 7/8 in) long.
K&E, was a drafting instruments and supply company that was founded in New York City in 1867 by Wilhelm J. D. Keuffel (1838--1908) and Herman Esser (1845--1908), immigrants from Prussia (what is now far northeastern Germany). Over time the company grew, expanding its products to include surveying instruments and a wide variety of drafting devices, and became well known for its slide rules. In 1987 the company was bought by AZON Corporation. This device was a gift of Brown University in 1973.
Immigrant Entrepreneurship: German-American Business Biographies, 1720 to Present,
K&E, Catalogue, 1921
Currently not on view
date made
ca 1930
Keuffel & Esser Co.
place made
United States: New York, New York
Physical Description
paper (overall material)
nickelplated brass (overall material)
overall: 6 cm x 23.8 cm x 10 cm; 2 3/8 in x 9 3/8 in x 3 15/16 in
ID Number
accession number
catalog number
Credit Line
Gift of Brown University Department of Mathematics
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History, Kenneth E. Behring Center


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