A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or a simulation like an analog computer or a slide rule. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator and the digital computer.
In 1642, Blaise Pascal invented the first operational mechanical calculator with better tens-carry.Prof. René Cassin, Pascal tercentenary celebration, London, (1942), Magazine Nature Concerned about his father's exhausting work as tax collector in Rouen, Pascal designed the Pascaline to help with the large amount of tedious arithmetic required.Jean Marguin (1994), p. 48
In 1672, Gottfried Leibniz started designing an entirely new machine called the Stepped Reckoner. It used a stepped drum, built by and named after him, the Leibniz wheel, was the first two-motion design, the first to use cursors (creating a memory of the first operand) and the first to have a movable carriage. Leibniz built two Stepped Reckoners, one in 1694 and one in 1706.Jean Marguin, pp. 64-65 (1994) The Leibniz wheel was used in many calculating machines for 200 years, and into the 1970s with the Curta hand calculator, until the advent of the electronic calculator in the mid-1970s. Leibniz was also the first to promote the idea of a pinwheel calculator.
During the 18th century, several inventors in Europe were working on mechanical calculators for all four species. Philipp Matthäus Hahn, Johann Helfreich Müller and others constructed machines that worked flawlessly, but due to the enormous amount of manual work and high precision needed for these machines they remained singletons and stayed mostly in cabinets of curiosity of their respective rulers. Only Müller's 1783 machine was put to use tabulating lumber prices; it later came into possession of the landgrave in Darmstadt.
Thomas' arithmometer, the first commercially successful machine, was manufactured in 1851; it was the first mechanical calculator strong enough and reliable enough to be used daily in an office environment. For forty years the arithmometer was the only type of mechanical calculator available for sale until the industrial production of the more successful Odhner Arithmometer in 1890.Beside two arithmometer clone makers from Germany and England, the only other company selling calculators was Felt & Tarrant in the United States, which started selling their comptometer in 1887 but had only sold 100 machines by 1890.
The comptometer, introduced in 1887, was the first machine to use a keyboard that consisted of columns of nine keys (from 1 to 9) for each digit. The Dalton adding machine, manufactured in 1902, was the first to have a 10 key keyboard.Ernst Martin p. 133 (1925) Electric motors were used on some mechanical calculators from 1901.Ernst Martin p. 23 (1925) In 1961, a comptometer type machine, the Anita Mk VII from Sumlock, became the first desktop mechanical calculator to receive an all-electronic calculator engine, creating the link in between these two industries and marking the beginning of its decline. The production of mechanical calculators came to a stop in the middle of the 1970s closing an industry that had lasted for 120 years.
Charles Babbage designed two kinds of mechanical calculators, which were too sophisticated to be built in his lifetime, and the dimensions of which required a steam engine to power them. The first was an automatic mechanical calculator, his difference engine, which could automatically compute and print mathematical tables. In 1855, Georg Scheutz became the first of a handful of designers to succeed at building a smaller and simpler model of his difference engine.#MARG,Jean Marguin p. 171, (1994) The second one was a programmable mechanical calculator, his analytical engine, which Babbage started to design in 1834; "in less than two years he had sketched out many of the salient features of the modern computer. A crucial step was the adoption of a punched card system derived from the Jacquard loom" making it infinitely programmable."The introduction of punched cards into the new engine was important not only as a more convenient form of control than the drums, or because programs could now be of unlimited extent, and could be stored and repeated without the danger of introducing errors in setting the machine by hand; it was important also because it served to crystallize Babbage's feeling that he had invented something really new, something much more than a sophisticated calculating machine." Bruce Collier, 1970 In 1937, Howard Aiken convinced IBM to design and build the ASCC/Mark I, the first machine of its kind, based on the architecture of the analytical engine;I. Bernard Cohen, pp. 66–67, (2000) when the machine was finished some hailed it as "Babbage's dream come true".Brian Randell, pp. 187, 1975
Ancient history
A short list of other precursors to the mechanical calculator must include a group of mechanical analog computers which, once set, are only modified by the continuous and repeated action of their actuators (crank handle, weight, wheel, water...). Before the common era, there are odometers and the Antikythera mechanism, a seemingly out of place, unique, geared astronomical clock, followed more than a millennium later by early mechanical clocks, geared astrolabes and followed in the 15th century by pedometers. These machines were all made of toothed gears linked by some sort of carry mechanisms. These machines always produce identical results for identical initial settings unlike a mechanical calculator where all the wheels are independent but are also linked together by the rules of arithmetic.
The 17th century
Overview The 17th century marked the beginning of the history of mechanical calculators, as it saw the invention of its first machines, including Pascal's calculator, in 1642.Please see Pascaline#Pascal versus Schickard Blaise Pascal had invented a machine which he presented as being able to perform computations that were previously thought to be only humanly possible."The arithmetical machine produces effects which approach nearer to thought than all the actions of animals. But it does nothing which would enable us to attribute will to it, as to the animals.", Pascal, Pensées Bartleby.com, Great Books online, Blaise Pasdcal, Thoughts
The 17th century also saw the invention of some very powerful tools to aid arithmetic calculations like Napier's bones, logarithmic tables and the slide rule which, for their ease of use by scientists in multiplying and dividing, ruled over and impeded the use and development of mechanical calculatorsScripta Mathematica, p. 128 (1932) until the production release of the arithmometer in the mid 19th century.
Invention of the mechanical calculator
In 1623 and 1624 Wilhelm Schickard, in two letters that he sent to Johannes Kepler, reported his design and construction of what he referred to as an “arithmeticum organum” (“arithmetical instrument”), which would later be described as a Rechenuhr (calculating clock). The machine was designed to assist in all the four basic functions of arithmetic (addition, subtraction, multiplication and division). Amongst its uses, Schickard suggested it would help in the laborious task of calculating astronomical tables. The machine could add and subtract six-digit numbers, and indicated an overflow of this capacity by ringing a bell. The adding machine in the base was primarily provided to assist in the difficult task of adding or multiplying two multi-digit numbers. To this end an ingenious arrangement of rotatable Napier's bones were mounted on it. It even had an additional "memory register" to record intermediate calculations. Whilst Schickard noted that the adding machine was working, his letters mention that he had asked a professional, a clockmaker named Johann Pfister, to build a finished machine. Regrettably it was destroyed in a fire either whilst still incomplete, or in any case before delivery. Schickard abandoned his project soon after. He and his entire family were wiped out in 1635 by bubonic plague during the Thirty Years' War.
Schickard's machine used clock wheels which were made stronger and were therefore heavier, to prevent them from being damaged by the force of an operator input. Each digit used a display wheel, an input wheel and an intermediate wheel. During a carry transfer all these wheels meshed with the wheels of the digit receiving the carry.
Blaise Pascal invented a mechanical calculator with a sophisticated carry mechanism in 1642. After three years of effort and 50 prototypes(fr) La Machine d’arithmétique, Blaise Pascal, Wikisource he introduced his calculator to the public. He built twenty of these machines in the following ten years.Guy Mourlevat, p. 12 (1988) This machine could add and subtract two numbers directly and multiply and divide by repetition. Since, unlike Schickard's machine, the Pascaline dials could only rotate in one direction zeroing it after each calculation required the operator to dial in all 9s and then (method of ) propagate a carry right through the machine.Courrier du CIBP, N°8, p. 9, (1986) This suggests that the carry mechanism would have proved itself in practice many times over. This is a testament to the quality of the Pascaline because none of the 17th and 18th century criticisms of the machine mentioned a problem with the carry mechanism and yet it was fully tested on all the machines, by their resets, all the time."...et si blocage il y avait, la machine était pratiquement inutilisable, ce qui ne fut jamais signalé dans les textes du XVIIIe siecle parmi ses défaults" Guy Mourlevat, p. 30 (1988)
In 1672, Gottfried Leibniz started working on adding direct multiplication to what he understood was the working of Pascal's calculator. However, it is doubtful that he had ever fully seen the mechanism and the method could not have worked because of the lack of reversible rotation in the mechanism. Accordingly, he eventually designed an entirely new machine called the Stepped Reckoner; it used his Leibniz wheels, was the first two-motion calculator, the first to use cursors (creating a memory of the first operand) and the first to have a movable carriage. Leibniz built two Stepped Reckoners, one in 1694 and one in 1706. Only the machine built in 1694 is known to exist; it was rediscovered at the end of the 19th century having been forgotten in an attic in the University of Göttingen.
Leibniz had invented his namesake wheel and the principle of a two-motion calculator, but after forty years of development he wasn't able to produce a machine that was fully operational; this makes Pascal's calculator the only working mechanical calculator in the 17th century. Leibniz was also the first person to describe a pinwheel calculator.David Smith, p. 173-181 (1929) He once said "It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used."As quoted in
Other calculating machines Schickard, Pascal and Leibniz were inevitably inspired by the role of clockwork which was highly celebrated in the seventeenth century.See http://things-that-count.net However, simple-minded application of interlinked gears was insufficient for any of their purposes. Schickard introduced the use of a single toothed "mutilated gear" to enable the carry to take place. Pascal improved on that with his famous weighted sautoir. Leibniz went even further in relation to the ability to use a moveable carriage to perform multiplication more efficiently, albeit at the expense of a fully working carry mechanism.