Leibniz wheel

A Leibniz wheel or stepped drum is a special cylinder with teeth of different lengths. When connected to a counting wheel, it can be used in the calculating engine of a class of mechanical calculators. This clever invention was created by Gottfried Wilhelm Leibniz in 1673. For over three hundred years, it helped people do math before electronic calculators were invented.

Leibniz built a machine called the stepped reckoner using this design in 1694. Much later, a man named Thomas de Colmar used the same idea in his Arithmometer, which was the first calculating machine made for many people to use. The Leibniz wheel was also a key part of the Curta calculator, a popular portable calculator made in the second half of the 1900s.

Concept

A Leibniz wheel is a special cylinder with teeth of different lengths. When you connect it to a counting wheel that can move up and down, the counting wheel can fit with any number of teeth on the Leibniz wheel.

The picture shows a Leibniz wheel with nine teeth connected to a red counting wheel. It is set to use three teeth for each turn, so it adds or takes away 3 from the counter each time it turns. In some old machines, several Leibniz wheels are linked together and turned by a handle. By moving sliders, you can choose which teeth to use, and the wheels work together to keep the numbers correct.

Later, some machines used a different part called pinwheels, which worked in a similar way but took up less space. But Leibniz wheels were still used in many machines until electronic calculators were invented.

Machines built using this principle

• Germany – Gottfried Leibniz built his first stepped reckoner in 1694 and another one in 1706.
• Germany – Philipp Matthäus Hahn, a German pastor, built two circular machines in 1770.
• Germany – J.C. Schuster, Hahn's brother in law, built a few machines of Hahn's design into the early 19th century.
• United Kingdom – Lord Stanhope designed a machine using Leibniz wheels in 1777. He also designed a pinwheel calculator in 1775.
• Germany – Johann-Helfrich Müller built a machine very similar to Hahn's machine in 1783.
• France – Thomas de Colmar invented his Arithmometer in 1820 but it took him 30 years of development before it was commercialized in 1851. It was manufactured until 1915. Louis Payen, Veuve L. Payen and Darras were successive owners and distributors of the Arithmometer.
• France – Timoleon Maurel invented his Arithmaurel in 1842. The complexity of its design limited its capacity and doomed its production, but it could multiply two numbers by the simple fact of setting them on its dials.
• Europe – About twenty clones of the Arithmometer were manufactured in Europe starting with Burkhardt in 1878 then came Layton, Saxonia, Gräber, Peerless, Mercedes-Euklid, Archimedes, TIM, Bunzel, Austria, Tate, Madas etc. These clones, often more sophisticated than the original arithmometer, were built until the beginning of World War II.
• United Kingdom – Joseph Edmondson invented and manufactured a circular calculator in 1885.
• United States – Friden and Monroe calculators used a biquinary variant of this mechanism. Both were made in large numbers; Monroe started early in the 20th century; Friden in the 1930s. (The Marchant used a radically different and unique mechanism.) The variant mechanism worked with digits from 1 through 4 as shown in the animation; digits larger than 4 engaged a five-tooth gear as well as the teeth of the Leibniz wheel. This made it unnecessary for the sliding gear to travel longer distances for the higher-number digits. Otherwise, pressing a 5..9 key would require either a longer stroke (as in a Comptometer) or excessive force combined with a gently sloping cam surface.
• Austria – Curt Herzstark introduced his Curta portable calculator in 1948, which remained popular until the introduction of electronic calculators in the 1970s.