A Timeless History
Cut in metal long before plastic. By the 1800s craftsmen were making these curves with a 'geometric chuck' on the lathe — gear rolling on gear to engrave watch cases and, from 1862, the fine-line patterns on U.S. banknotes. John Holt Ibbetson printed specimens of his chuck in 1833. In 1965 the British engineer Denys Fisher turned the idea into the century's best-known drawing toy; within a year it was in American homes.
SourceIbbetson, A Brief Account of Ibbetson's Geometric Chuck, 1833 · U.S. Bureau of Engraving and Printing, History (1862) · Image: Ibbetson 1833, frontispiece plate — Internet Archive (PD)
Science In Action
Teeth — ring and wheel are counted in teeth; their ratio alone decides the shape of the curve • Loops — a 96-tooth ring and a 32-tooth wheel give three loops: the wheel turns three times per circuit • The hole — a pen near the wheel's edge draws pointed loops; nearer the centre, they round off • Closing — the line meets itself once both counts have run out; the curve is a hypotrochoid
SourceWolfram MathWorld, Hypotrochoid · MacTutor, Hypotrochoid · Ibbetson 1833, pp. 32–34 · Image: Ibbetson 1833, plate — Internet Archive (PD)
Arts
Guilloché: the pattern as jewellery. Engine-turned gold — hundreds of fine lines cut on a rose engine so they catch the light — dressed snuffboxes, watch cases and dials. The back of Robert Roskell's pocket watch of 1820–21, in the Met, is a whole family of these curves drawn in gold; later jewellers laid translucent enamel over the same engraved waves.
SourceThe Metropolitan Museum of Art, Pocket watch, Robert Roskell, 1820–21, 44.18 · Image: the same watch, back — The Met (CC0)
Applications Today
Banknotes — fine-line rosettes were a security feature; the Bank of Canada Museum redraws them with toy gears • Screens — two short equations, x and y in cosines and sines, draw the same curve on any computer • Toy shops — gear-drawing sets have never left production in the sixty years since
SourceBank of Canada Museum, The art of guilloche · Wolfram MathWorld, Hypotrochoid · Image: gear-drawn curves, 2018 — Wikimedia Commons (CC0)
One more thingIn 1864 a French army officer, Peaucellier, built the first linkage that draws an exactly straight line: seven bars, no ruler. Curves had been easy for ages.
SourceKempe, How to Draw a Straight Line, 1877 · MacTutor, Alfred Kempe
Americans could order a gear-drawing toy, the Wondergraph, from the Sears catalog as early as 1908.
Diagrams illustrating the epicycloidal cutting frame — frontispiece plate (central medallion crop) — John Holt Ibbetson — 1833 — A Brief Account of Ibbetson's Geometric Chuck, manufactured by Holtzapffel & Co., London, printed for the author; scan University of California Libraries (Bern Dibner copy) on the Internet Archive — archive.org identifier briefaccountofib00ibbeiala, page image _0010.jp2 (1856 × 3152)
