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A pinwheel calculator is a class of
mechanical calculator
A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators wer ...
described as early as 1685, and popular in the 19th and 20th century, calculating via wheels whose number of teeth were adjustable. These wheels, also called pinwheels, could be set by using a side lever which could expose anywhere from 0 to 9 teeth, and therefore when coupled to a counter they could, at each rotation, add a number from 0 to 9 to the result. By linking these wheels with carry mechanisms a new kind of calculator engine was invented. Turn the wheels one way and one performs an addition, the other way a subtraction.
As part of a redesign of the
arithmometer
The arithmometer (french: arithmomètre) was the first digital mechanical calculator strong enough and reliable enough to be used daily in an office environment. This calculator could add and subtract two numbers directly and could perform lon ...
, they reduced by an order of magnitude the cost and the size of mechanical calculators on which one could easily do the four basic operations (add, subtract, multiply and divide).
Pinwheel calculators became extremely popular with the success of
Thomas' Arithmometer (manufactured 1850s) and
Odhner Arithmometer
The Odhner Arithmometer was a very successful pinwheel calculator invented in Russia in 1873 by W. T. Odhner, a Swedish immigrant. Its industrial production officiallyTrogemann G., Nitussov A.: ''Computing in Russia'', page 39-45, GWV-Vieweg, ...
(manufactured 1890s).
History
![Sprossenrad leibniz](https://upload.wikimedia.org/wikipedia/commons/d/d8/Sprossenrad_leibniz.png)
* - In "Machina arithmetica in qua non additio tantum et subtractio sed et multiplicatio nullo, diviso vero paene nullo animi labore peragantur", written in 1685,
Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...
described an arithmetic machine he had invented that was made by linking two separate machines, one to perform additions/subtractions and one for multiplications/divisions.
Pascal's calculator was to be used for additions and subtractions (he called it the calculating box of Pascal) and a machine using wheels with movable teeth was to be used for multiplications and divisions. There is no evidence that Leibniz constructed this pinwheel machine, but his
Leibniz wheel
A Leibniz wheel or stepped drum is a cylinder with a set of teeth of incremental lengths which, when coupled to a counting wheel, can be used in the calculating engine of a class of mechanical calculators. Invented by Leibniz in 1673, it was used ...
, which, when coupled to a sliding counting wheel, can mesh with a variable number of teeth, seems to have been his way of implementing a variable number of teeth design.
* -
Giovanni Poleni
Giovanni Poleni (b. Venice, around 1683; d. Padua, Nov., 1761) was a Marquess, physicist, mathematician and antiquarian.
Early life
He was the son of Marquess Jacopo Poleni and studied the classics, philosophy, theology, mathematics, and physics ...
by 1709 had built a wooden ''calculating clock'' calculator that used a pinwheel design; he destroyed it after hearing that Antonius Braun had received 10,000
Guldens for dedicating a pinwheel machine of his own design to the emperor
Charles VI of Vienna. Poleni described his machine in his ''Miscellanea'' in 1709, but it was also described by
Jacob Leupold
Jacob Leupold (22 July 1674 – 12 January 1727) was a German physicist, mathematician, instrument maker, mining commissioner and engineer. He wrote the seminal book ''Theatrum Machinarum Generale'' ("The General Theory of Machines").
Early lif ...
in his ''Theatrum Machinarum Generale'', ("The General Theory of Machines") which was published in 1727.
* - Antonius Braun was a native of
Swabia
Swabia ; german: Schwaben , colloquially ''Schwabenland'' or ''Ländle''; archaic English also Suabia or Svebia is a cultural, historic and linguistic region in southwestern Germany.
The name is ultimately derived from the medieval Duchy of ...
; his machine, which he presented to the emperor in 1727, was cylindrical in shape and was made of steel, silver and brass; it was finely decorated and looked like a renaissance table clock. It could perform all four operations. His dedication to the emperor engraved on the top of the machine also reads "..to make easy to ignorant people, addition, subtraction, multiplication and even division".
* -
Lord Stanhope of the United Kingdom designed a pinwheel machine in 1775. It was set in a rectangular box with a handle on the side. He also designed a machine using
Leibniz wheel
A Leibniz wheel or stepped drum is a cylinder with a set of teeth of incremental lengths which, when coupled to a counting wheel, can be used in the calculating engine of a class of mechanical calculators. Invented by Leibniz in 1673, it was used ...
s in 1777.
* - Dr. Didier Roth, a French inventor, patented and built a machine based on that design in 1842.
* -
Izrael Staffel, a polish clockmaker introduced his pinwheel machine in 1845 at an industrial exposition in
Warsaw, Poland
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-cen ...
and won a gold medal in 1851 at
The Great Exhibition
The Great Exhibition of the Works of Industry of All Nations, also known as the Great Exhibition or the Crystal Palace Exhibition (in reference to the temporary structure in which it was held), was an international exhibition which took pl ...
in London.
* -
Frank S. Baldwin invented a pinwheel calculator in the United States in 1872.
* - In
St. Petersburg
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
, Russia,
Wilgott Theophil Odhner
Willgodt Theophil Odhner (in Cyrillic, Вильгодт Теофил Однер) was a Swedish engineer and entrepreneur, working in St. Petersburg, Russia. He was the inventor of the Odhner Arithmometer, which by the 1940s was one of the most pop ...
invented his arithmometer in 1874 and in 1890 it became the first pinwheel calculator to be mass-manufactured. Its industrial production started in Odhner's workshop: ''W.T. Odhner, Maschinenfabrik & Metallgiesserei'' and then moved to the Odhner-Gill factory (фабрика Однера-Гиля) in 1891. Odhner type calculators were more popular in
Europe
Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a Continent#Subcontinents, subcontinent of Eurasia ...
(particularly in Germany) than in the United States.
* - ''Grimme, Natalis & Co.'' bought the rights to Odhner's patents in 1892 and soon after started production in Brunswick, Germany. They sold their machines under the Brunsviga brand name (Brunsviga is the Latin name of the town of Brunswick, just as Braunschweig is its name in German
); they became very successful on their own and were the first of a long line of Odhner clone makers.
* - In 1924,
Felix Dzerzhinsky
Felix Edmundovich Dzerzhinsky ( pl, Feliks Dzierżyński ; russian: Фе́ликс Эдму́ндович Дзержи́нский; – 20 July 1926), nicknamed "Iron Felix", was a Bolshevik revolutionary and official, born into Poland, Polish n ...
, the head of the Russian
Cheka
The All-Russian Extraordinary Commission ( rus, Всероссийская чрезвычайная комиссия, r=Vserossiyskaya chrezvychaynaya komissiya, p=fsʲɪrɐˈsʲijskəjə tɕrʲɪzvɨˈtɕæjnəjə kɐˈmʲisʲɪjə), abbreviated ...
, initiated the manufacturing of arithmometers. Later they were named ''arithmometer Feliks'' and served in the
Soviet Union
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...
well into the 1970s, popularly known under the name "
Iron Feliks".
Operation
"The operation of machines of this type was accomplished by means of pulling
lever
A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or ''fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is div ...
s or
knobs to set up the desired number. Addition, subtraction,
multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...
, and
division
Division or divider may refer to:
Mathematics
*Division (mathematics), the inverse of multiplication
*Division algorithm, a method for computing the result of mathematical division
Military
*Division (military), a formation typically consisting ...
were accomplished by means of revolving
drum
The drum is a member of the percussion group of musical instruments. In the Hornbostel-Sachs classification system, it is a membranophone. Drums consist of at least one membrane, called a drumhead or drum skin, that is stretched over a she ...
s. For addition they revolved in one direction, and for subtraction the direction was reversed. For multiplication the revolutions were repeated in the same direction as for addition, and for division they were repeated in the same direction as for subtraction. Two sets of dials provided a means of reading totals. In one the accumulation of totals appeared; in the other, there appeared the figure which was added, subtracted, multiplied, or divided." (The Office Appliance Manual, p. 88)
References
Sources
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External links
Images of the Odhner's pinwheel calculators*
*MechanicalComputing A detailed animation describing the design and workings of pinwheel calculators.
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*Mařík, Robert
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*{{cite web , title=Pinwheel Calculators , publisher=UK Science Museum Group Collection , url=http://collection.sciencemuseum.org.uk/search/object_type/calculating-machine-(pinwheel)
Mechanical calculators