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A crank is an arm attached at right angles to a rotating shaft by which reciprocating motion is imparted to or received from the shaft. It is used to change circular into reciprocating motion, or reciprocating into circular motion. The arm may be a bent portion of the shaft, or a separate arm attached to it. Attached to the end of the crank by a pivot is a rod, usually called a connecting rod. The end of the rod attached to the crank moves in a circular motion, while the other end is usually constrained to move in a linear sliding motion, in and out.

The term often refers to a human-powered crank which is used to manually turn an axle, as in a bicycle crankset or a brace and bit drill. In this case a person's arm or leg serves as the connecting rod, applying reciprocating force to the crank. Often there is a bar perpendicular to the other end of the arm, often with a freely rotatable handle on it to hold in the hand, or in the case of operation by a foot (usually with a second arm for the other foot), with a freely rotatable pedal.

## HistoryEdit

An eccentric crank-like mechanism appeared in China from the 4th century BC.[3] Hand-operated cranks were in use during the Han Dynasty (202 BC - 220 AD), as Han era glazed-earthenware tomb models from the 1st century BC portray, and was used thereafter in China for silk-reeling and hemp-spinning, for the agricultural winnowing fan, in the water-powered flour-sifter, for hydraulic-powered metallurgic bellows, and in the well windlass.[4][5] The earliest use of the crank in a machine occurs in the crank-driven winnowing machine in Han China.[6]

A Roman iron crank handle was excavated in Augusta Raurica, Switzerland. The 82.5 cm long piece with a 15 cm long handle is of yet unknown purpose and dates to no later than ca. 250 AD.[7] Evidence of a crank appears in the late Hierapolis (Asia Minor) sawmill from the 3rd century, while two stone sawmills from the 6th century have also been found at Ephesus, Asia Minor, and Gerasa, Jordan.[8] In China, a crank and connecting rod machine appeared in the 5th century, followed by a crank and connecting rod machine with a piston rod in the 6th century.[3]

A device shown in the early 9th century Carolingian manuscript Utrecht Psalter is a crank handle used with a rotary grindstone.[9] Scholars point to the use of crank handles in trepanation drills in a 10th century work by the Spanish Muslim surgeon Abu al-Qasim al-Zahrawi (936–1013).[9] The Benedictine monk Theophilus Presbyter (c. 1070–c.1125) described crank handles "used in the turning of casting cores" according to Needham.[10]

In the Muslim world, the non-manual crank appears in the mid-9th century in several of the hydraulic devices described by the Banu Musa brothers in their Book of Ingenious Devices.[11] These automatically-operated cranks appear in several devices described in the book, two of which contain an action which approximates to that of a crankshaft. The Banu Musa brothers' automatic crank would not have allowed a full rotation, but only a small modification was required to convert it to a crankshaft.[12] The Arabic inventor, Al-Jazari (1136–1206), described a crank and connecting rod system in a rotating machine in two of his water-raising machines.[13] His twin-cylinder pump incorporated the earliest known crankshaft,[14] while his other machine incorporated the first known crank-slider mechanism.[15] The Italian physician and inventor Guido da Vigevano (c. 1280–1349) made illustrations for a paddle boat and a war carriages that were propelled by manually turned crankshafts and gear wheels.[16] The crank became common in Europe by the early 15th century, seen in the works of those such as the military engineer Konrad Kyeser (1366–after 1405).[16]

Cranks were formerly common on some machines in the early 20th century; for example almost all phonographs before the 1930s were powered by clockwork motors wound with cranks, and internal combustion engines of automobiles were usually started with cranks (known as starting handles in the UK), before electric starters came into general use.

## ExamplesEdit

Familiar examples include:

### EnginesEdit

Almost all reciprocating engines use cranks to transform the back-and-forth motion of the pistons into rotary motion. The cranks are incorporated into a crankshaft.

## MechanicsEdit

The displacement of the end of the connecting rod is approximately proportional to the cosine of the angle of rotation of the crank, when it is measured from top dead center. So the reciprocating motion created by a steadily rotating crank and connecting rod is approximately simple harmonic motion:

$x = l + r \cos \alpha \,$

where x is the distance of the end of the connecting rod from the crank axle, l is the length of the connecting rod, r is the length of the crank, and α is the angle of the crank measured from top dead center (TDC). Technically, the reciprocating motion of the connecting rod departs slightly from sinusoidal motion due to the changing angle of the connecting rod during the cycle.

The mechanical advantage of a crank, the ratio between the force on the connecting rod and the torque on the shaft, varies throughout the crank's cycle. The relationship between the two is approximately:

$\tau = Fr \sin \alpha \,$

where $\tau\,$ is the torque and F is the force on the connecting rod. For a given force on the crank, the torque is maximum at crank angles of α = 90° or 270° from TDC. When the crank is driven by the connecting rod, a problem arises when the crank is at top dead centre (0°) or bottom dead centre (180°). At these points in the crank's cycle, a force on the connecting rod causes no torque on the crank. Therefore if the crank is stationary and happens to be at one of these two points, it cannot be started moving by the connecting rod. For this reason, in steam locomotives, whose wheels are driven by cranks, the two connecting rods are attached to the wheels at points 90° apart, so that regardless of the position of the wheels when the engine starts, at least one connecting rod will be able to exert torque to start the train.

## ReferencesEdit

1. Ritti, Grewe & Kessener 2007, p. 159
2. Lucas 2005, p. 5, fn. 9
3. 3.0 3.1 Joseph Needham (1975), "History and Human Values: a Chinese Perspective for World Science and Technology", Philosophy and Social Action II (1-2): 1-33 [4], retrieved on 13 March 2010
4. Needham 1986, pp. 118–119.
5. Temple, Robert. (1986). The Genius of China: 3,000 Years of Science, Discovery, and Invention, p. 46. With a forward by Joseph Needham. New York: Simon and Schuster, Inc. ISBN 0671620282.
6. N. Sivin (August 1968), "Review: Science and Civilisation in China by Joseph Needham", Journal of Asian Studies (Association for Asian Studies) 27 (4): 859-864 [862]
7. Laur-Belart 1988, p. 51–52, 56, fig. 42
8. Ritti, Grewe & Kessener 2007, p. 161
9. 9.0 9.1 Needham 1986, p. 112.
10. Needham 1986, pp. 112–113.
11. A. F. L. Beeston, M. J. L. Young, J. D. Latham, Robert Bertram Serjeant (1990), The Cambridge History of Arabic Literature, Cambridge University Press, p. 266, ISBN 0521327636
12. Banu Musa, Donald Routledge Hill (1979), The book of ingenious devices (Kitāb al-ḥiyal), Springer, pp. 23-4, ISBN 9027708339
13. Sally Ganchy, Sarah Gancher (2009), Islam and Science, Medicine, and Technology, The Rosen Publishing Group, p. 41, ISBN 1435850661
14. Lotfi Romdhane & Saïd Zeghloul (2010), "Al-Jazari (1136–1206)", History of Mechanism and Machine Science (Springer) 7: 1-21, doi:10.1007/978-90-481-2346-9, ISBN 978-90-481-2346-9, ISSN 1875-3442
15. 16.0 16.1 Needham 1986, p. 113.

### BibliographyEdit

• Lucas, Adam Robert (2005), "Industrial Milling in the Ancient and Medieval Worlds. A Survey of the Evidence for an Industrial Revolution in Medieval Europe", Technology and Culture 46: 1–30
• Laur-Belart, Rudolf (1988), Führer durch Augusta Raurica (5th ed.), Augst
• Needham, Joseph (1991), Science and Civilisation in China: Volume 4, Physics and Physical Technology: Part 2, Mechanical Engineering, Cambridge University Press, ISBN 0521058031 .
• Ritti, Tullia; Grewe, Klaus; Kessener, Paul (2007), "A Relief of a Water-powered Stone Saw Mill on a Sarcophagus at Hierapolis and its Implications", Journal of Roman Archaeology 20: 138–163

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