A mechanical calculator was a device used to perform the basic operations of arithmetic. Mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator.
The mechanical calculator was invented in 1642[1] by Blaise Pascal, it was called Pascal's Calculator or Pascaline. The first commercially successful device, Thomas' arithmometer, was manufactured from 1851. The first machine with columns of keys, the comptometer, was introduced in 1887 while 10 key calculators and electric motors appeared in 1902.[2] The use of electric motors allowed for the design of very powerful machines during the first half of the 20th century. In 1961, A full-keyboard machine, the Anita from Sumlock comptometer LTD, 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 last mechanical calculators were built in the middle of the 1970s.
The mechanical engines of Charles Babbage were the first automatic mechanical calculators in the world. Babbage started work on his analytical engine in 1834. "In less than two years he had scketched 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".[3] Babbage never built his steam powered mechanical calculators but Howard Aiken mentioned Babbage extensively when he convinced IBM to build the Harvard Mark I in 1937 ; when the machine was finished some hailed it as "Babbage's dream come true".[4]
The mechanical calculator was preceded by and competed with clerical aids such as abaci, Napier's bones and slide rules, and various books of mathematical tables. The true precursors to the mechanical calculator were machines made of toothed gears linked by carry mechanisms like odometers, astrolabes, clocks and pedometers.[5]
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Devices have been used to aid computation for thousands of years, using one-to-one correspondence with our fingers.[6] The earliest counting device was probably a form of tally stick. Later record keeping aids throughout the Fertile Crescent included clay shapes, which represented counts of items, probably livestock or grains, sealed in containers.[7]
The first clerical aids were abathia, and were often constructed as a wooden frame with beads sliding on wires. Abathias were in use centuries before the adoption of the written Arabic numerals system and are still used by some merchants, fishermen and clerks in Africa, Asia, and elsewhere. As well, "counting boards", with parallel grooves to hold beads, were used like the abacus.
The counter abacus was devised by Egyptian mathematicians in Egypt in 2000 BC. It was used for arithmetic tasks. The Roman abacus was used in Babylonia as early as 2400 BC. Since then, many other forms of reckoning boards or tables have been invented. In a medieval counting house, a checkered cloth would be placed on a table, and markers moved around on it according to certain rules, as an aid to calculating sums of money (this is the origin of "Exchequer" as a term for a nation's treasury).
A number of analog computers were constructed in ancient and medieval times to perform astronomical calculations. These include the Antikythera mechanism and other astrolabes from ancient Greece (c. 150-100 BC), which are generally regarded as the first mechanical analog computers.[8] Other early versions of mechanical devices used to perform some type of calculations include the planisphere and other mechanical computing devices invented by Abū Rayhān al-Bīrūnī (c. AD 1000); the equatorium and universal latitude-independent astrolabe by Abū Ishāq Ibrāhīm al-Zarqālī (c. AD 1015); the astronomical analog computers of other medieval Muslim astronomers and engineers; and the astronomical clock tower of Su Song (c. AD 1090) during the Song Dynasty. The "castle clock", an astronomical clock invented by Al-Jazari in 1206, is considered to be the earliest programmable analog computer.[9]
The 17th century marks the beginning of the history of mechanical calculators, as it saw the invention of the adding machine by Blaise Pascal[1][10] followed by Gottfried Leibniz who invented the Leibniz wheel and who was also the first person to describe a pinwheel calculator[11]. Pascal was the only one to produce working mechanical calculators (about twenty), but neither of them were successful in commercializing their machines.
It also saw the invention of some very powerful calculating tools like logarithms, 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 calculators[12] until the production release of the arithmometer in the mid 19th century.
In 1642, Blaise Pascal invented the mechanical calculator while looking for a way to help his father who had been assigned the task of reorganizing the tax revenues of the French province of Haute-Normandie.[13] After three years of effort and 50 prototypes[14] he introduced his machine to the public. He built twenty of these machines (called the Pascaline) in the following ten years.[15] This machine could add and subtract two numbers directly and multiply and divide by repetition.
Gottfried Leibniz invented the first calculator that could perform all four arithmetic operations automatically while adding direct multiplication and division to the Pascaline ; it was called the Stepped Reckoner. He built it around 1672, but careful examination at the end of the 19th century showed a problem with the carry mechanism. It used his Leibniz wheels which, a century and a half later, will be at the heart of the arithmometer, the first calculator to be commercialized. He also was the first to describe a pinwheel calculator in 1685[11]. Leibniz 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."[16]
Wilhelm Schickard, a German polymath, designed a calculating clock in 1623; a fire destroyed it during its construction in 1624 and Schickard abandoned his project. This machine had been described in various publications over the centuries[17] but in 1957 it was presented for the first time as a long lost mechanical calculator by Dr. Franz Hammer. The building of the first replica in the 1960s showed that Schickard's machine had an unfinished design and therefore wheels and springs were added to make it work.[18] The use of these replicas showed that the single tooth wheel, when used within Shickard's design, was an inadequate carry mechanism.[19] Schickard's work had no impact on the development of mechanical calculators[20] (see Pascal versus Schickard).
Scottish mathematician and physicist John Napier noted multiplication and division of numbers could be performed by addition and subtraction, respectively, of logarithms of those numbers. While producing the first logarithmic tables Napier needed to perform many multiplications, and it was at this point that he designed Napier's bones, a device consisting of square rods positioned side by side, marked with digits, used for multiplication and division.[21]
In 1622 William Oughtred invented the slide rule, which was revealed by his student Richard Delamain in 1630.[22] Since real numbers can be represented as distances or intervals on a line, the slide rule allows multiplication and division operations to be carried out significantly faster than was previously possible.[23] The devices were used by generations of engineers and other mathematically inclined professional workers, until the invention of the pocket calculator. The engineers in the Apollo program that sent a man to the moon made many of their calculations on slide rules, which were accurate to three or four significant figures.[24]
The 18th century saw the first fully functional, four operations, mechanical calculators. Both pinwheel calculators and Leibniz wheel calculators were built with a few unsuccessful attempts at their commercialization.
In 1851, the 19th century saw the birth of the mechanical calculator industry when Thomas de Colmar released his simplified Arithmomètre. For 40 years, the arithmometer was the only mechanical calculator available for sale. By then, in 1890, about 2,500 arithmometers had been sold[25] plus a few more from two arithmometer clone makers (Burkhardt, Germany, 1878 and Layton, UK, 1883) and Felt and Tarrant, the only other competitor in true commercial production, had sold 100 comptometers.[26].
It also saw the designs of Charles Babbage calculating machines which gave the blueprint of the mainframe computers built in the middle of the 20th century.[27]
Although this is an old machine, nevertheless it represents how one operates any basic rotary calculator. Facits have a pinwheel cylinder that shifts internally, instead of a moving carriage, but the principles still hold.
Two different classes of mechanisms had become established by this time, reciprocating and rotary. The former type of mechanism was operated typically by a limited-travel hand crank; some internal detailed operations took place on the pull, and others on the release part of a complete cycle. The illustrated 1914 machine is this type; the crank is vertical, on its right side. Later on, some of these mechanisms were operated by electric motors and reduction gearing that operated a crank and connecting rod to convert rotary motion to reciprocating.
The latter, type, rotary, had at least one main shaft that made one [or more] continuous revolution[s], one addition or subtraction per turn. Numerous designs, notably European calculators, had handcranks, and locks to ensure that the cranks were returned to exact positions once a turn was complete.
The first half of the 20th century saw the gradual development of the mechanical calculator mechanism.
The Dalton adding-listing machine introduced in 1902 was the first of its type to use only ten keys, and became the first of many different models of "10-key add-listers" manufactured by many companies.
In 1948 the miniature Curta calculator, which was held in one hand for operation, was introduced after being developed by Curt Herzstark in 1938. This was an extreme development of the stepped-gear calculating mechanism. It subtracted by adding complements; between the teeth for addition were teeth for subtraction.
From the early 1900s through the 1960s, mechanical calculators dominated the desktop computing market (see History of computing hardware). Major suppliers in the USA included Friden, Monroe, and SCM/Marchant. (Some comments about European calculators follow below.) These devices were motor-driven, and had movable carriages where results of calculations were displayed by dials. Nearly all keyboards were full — each digit that could be entered had its own column of nine keys, 1..9, plus a column-clear key, permitting entry of several digits at once. (See the illustration below of a Marchant Figurematic.)One could call this parallel entry, by way of contrast with ten-key serial entry that was commonplace in mechanical adding machines, and is now universal in electronic calculators. (Nearly all Friden calculators, as well as some rotary (German) Diehls had a ten-key auxiliary keyboard for entering the multiplier when doing multiplication.) Full keyboards generally had ten columns, although some lower-cost machines had eight. Most machines made by the three companies mentioned did not print their results, although other companies, such as Olivetti, did make printing calculators.
In these machines, addition and subtraction were performed in a single operation, as on a conventional adding machine, but multiplication and division were accomplished by repeated mechanical additions and subtractions. Friden made a calculator that also provided square roots, basically by doing division, but with added mechanism that automatically incremented the number in the keyboard in a systematic fashion. The last of the mechanical calculators were likely to have short-cut multiplication, and some ten-key, serial-entry types had decimal-point keys. However, decimal-point keys required significant internal added complexity, and were offered only in the last designs to be made. The Marchant (Model SKA) also offered square root calculation. Handheld mechanical calculators such as the 1948 Curta continued to be used until they were displaced by electronic calculators in the 1970s.
Typical European four-operations machines use the Odhner mechanism, or variations of it. This kind of machine included the Original Odhner, Brunsviga and several following imitators, starting from Triumphator, Thales, Walther, Facit up to Toshiba. Although most of these were operated by handcranks, there were motor-driven versions. Hamann calculators externally resembled pinwheel machines, but the setting lever positioned a cam that disengaged a drive pawl when the dial had moved far enough.
Although Dalton introduced in 1902 first ten-key printing adding (two operations, the other being subtraction) machine, these feature were not present in computing (four operations) machines for many decades. Facit-T (1932) was the first 10-key computing machine sold in large numbers. Olivetti Divisumma-14 (1948) was the first computing machine with both printer and a 10-key keyboard.
Full-keyboard machines, including motor-driven ones, were also built until the 1960s. Among the major manufacturers were Mercedes-Euklid, Archimedes, and MADAS in Europe; in the USA, Friden, Marchant, and Monroe were the principal makers of rotary calculators with carriages. Reciprocating calculators (most of which were adding machines, many with integral printers) were made by Remington Rand and Burroughs, among others. All of these were key-set. Felt & Tarrant made Comptometers, as well as Victor, which were key-driven.
The basic mechanism of the Friden and Monroe, described above, was a modified Leibniz wheel (better known, perhaps informally, in the USA as a "stepped drum" or "stepped reckoner"). The Friden had an elementary reversing drive between the body of the machine and the accumulator dials, so its main shaft always rotated in the same direction. The Swiss MADAS was similar. The Monroe, however, reversed direction of its main shaft to subtract.
The earliest Marchants were pinwheel machines, but most of them were remarkably-sophisticated rotary types. They ran at 1,300 addition cycles per minute if you held down the [+] bar. Others were limited to 600 cycles per minute, because their accumulator dials started and stopped for every cycle; Marchant dials moved at a steady and proportional speed for continuing cycles. Most Marchants had a row of nine keys on the extreme right, as shown in the photo of the Figurematic. These simply made the machine add for the number of cycles corresponding to the number on the key, and then shifted the carriage one place. Even nine add cycles took only a short time.
In a Marchant, near the beginning of a cycle, the accumulator dials moved downward "into the dip", away from the openings in the cover. They engaged drive gears in the body of the machine, which rotated them at speeds proportional to the digit being fed to them, with added movement (reduced 10:1) from carries created by dials to their right. At the completion of the cycle, the dials would be misaligned like the pointers in a traditional watt-hour meter. However, as they came up out of the dip, a constant-lead disc cam realigned them by way of a (limited-travel) spur-gear differential. As well, carries for lower orders were added in by another, planetary differential. (The machine shown has 39 differentials in its (20-digit) accumulator!).
In any mechanical calculator, in effect, a gear, sector, or some similar device moves the accumulator by the number of gear teeth that corresponds to the digit being added or subtracted — three teeth changes the position by a count of three. The great majority of basic calculator mechanisms move the accumulator by starting, then moving at a constant speed, and stopping. In particular, stopping is critical, because to obtain fast operation, the accumulator needs to move quickly. Variants of Geneva drives typically block overshoot (which, of course, would create wrong results).
However, two different basic mechanisms, the Mercedes-Euklid and the Marchant, move the dials at speeds corresponding to the digit being added or subtracted; a [1] moves the accumulator the slowest, and a [9], the fastest. In the Mercedes-Euklid, a long slotted lever, pivoted at one end, moves nine racks ("straight gears") endwise by distances proportional to their distance from the lever's pivot. Each rack has a drive pin that's moved by the slot. The rack for [1] is closest to the pivot, of course. For each keyboard digit, a sliding selector gear, much like that in the Leibniz wheel, engages the rack that corresponds to the digit entered. Of course, the accumulator changes either on the forward or reverse stroke, but not both. This mechanism is notably simple and relatively easy to manufacture.
The Marchant, however, has, for every one of the its ten columns of keys, a nine-ratio "preselector transmission" with its output spur gear at the top of the machine's body; that gear engages the accumulator gearing. When one tries to work out the numbers of teeth in such a transmission, a straightforward approach leads one to consider a mechanism like that in mechanical gasoline pump registers, used to indicate the total price. However, this mechanism is seriously bulky, and utterly impractical for a calculator; 90-tooth gears are likely to be found is the gas. pump. Practical gears in the computing parts of a calculator can't have 90 teeth. They would be either too big, or too delicate.
Given that nine ratios per column implies significant complexity, a Marchant contains a few hundred individual gears in all, many in its accumulator. Basically, the accumulator dial has to rotate 36 degrees (1/10 of a turn) for a [1], and 324 degrees (9/10 of a turn) for a [9], not allowing for incoming carries. At some point in the gearing, one tooth needs to pass for a [1], and nine teeth for a [9]. There's no way to develop the needed movement from a driveshaft that rotates one revolution per cycle with few gears having practical (relatively small) numbers of teeth.
The Marchant, therefore, has three driveshafts to feed the little transmissions. For one cycle, they rotate 1/2, 1/4, and 1/12 of a revolution. [2]. The 1/2-turn shaft carries (for each column) gears with 12, 14, 16, and 18 teeth, corresponding to digits 6, 7, 8, and 9. The 1/4-turn shaft carries (also, each column) gears with 12, 16, and 20 teeth, for 3, 4, and 5. Digits [1] and [2] are handled by 12 and 24-tooth gears on the 1/12-revolution shaft. Practical design places the 12th-rev. shaft more distant, so the 1/4-turn shaft carries freely-rotating 24 and 12-tooth idler gears. For subtraction, the driveshafts reversed direction.
In the early part of the cycle, one of five pendants moves off-center to engage the appropriate drive gear for the selected digit. If possible, see John Wolff's Web site [3] for a superb collection of photos with some accompanying explanations. He has similar sets of photos for several other notable calculators.
Some machines had as many as 20 columns in their full keyboards. The monster in this field was the Duodecillion made by Burroughs for exhibit purposes.
For sterling currency, £/s/d (and even farthings), there were variations of the basic mechanisms, in particular with different numbers of gear teeth and accumulator dial positions. To accommodate shillings and pence, extra columns were added for the tens digit[s], 10 and 20 for shillings, and 10 for pence. Of course, these functioned as radix-20 and radix-12 mechanisms.
A variant of the Marchant, called the Binary-Octal Marchant, was a radix-8 (octal) machine. It was sold to check very early vacuum-tube (valve) binary computers for accuracy. (Back then, the mechanical calculator was much more reliable than a tube/valve computer.)
As well, there was a twin Marchant, comprising two pinwheel Marchants with a common drive crank and reversing gearbox.[4] The article at the link describes them and shows a twin Brunsviga (side-by-side machines). Twin machines were relatively rare, and apparently were used for surveying calculations (The CORDIC algorithm was invented later, but these machine might be able to execute it.) At least one triple machine (Brunsviga(?)) was made. It's likely that a given accumulator could be engaged with either half of the twin.
The Facit calculator, and one similar to it, are basically pinwheel machines, but the array of pinwheels moves sidewise, instead of the carriage. The pinwheels are biquinary; digits 1 through 4 cause the corresponding number of sliding pins ot extend from the surface; digits 5 through 9 also extend a five-tooth sector as well as the same pins for 6 through 9.
The keys operate cams that operate a swinging lever to first unlock the pin-positioning cam that's partof the pinwheel mechanism; further movement of the lever (by an amount determined by the key's cam) rotates the pin-positioning cam to extend the necessary number of pins. [5]
Stylus-operated adders with circular slots for the stylus, and side-by -side wheels, as made by Sterling Plastics (USA), had an ingenious anti-overshoot mechanism to ensure accurate carries.
Mechanical calculators continued to be sold, though in rapidly decreasing numbers, into the early 1970s, with many of the manufacturers closing down or being taken over. Comptometer type calculators were often retained for much longer to be used for adding and listing duties, especially in accounting, since a trained and skilled operator could enter all the digits of a number in one movement of the hands on a Comptometer quicker than was possible serially with a 10-key electronic calculator. In fact, it was quicker to enter larger digits in two strokes using only the lower-numbered keys; for instance, a 9 would be entered as 4 followed by 5. Some key-driven calculators had keys for every column, but only 1 through 5; they were correspondingly compact. The spread of the computer rather than the simple electronic calculator put an end to the Comptometer. Also, by the end of the 1970s, the slide rule had become obsolete.