Crank

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.

Examples

A crank

Hand crank on a pencil sharpener

Familiar examples include:

Using a hand

• mechanical pencil sharpener
• fishing reel and other reels for cables, wires, ropes, etc.
• manually operated car window
• the crank set that drives a trikke through its handles.

Using the feet

• the crankset that drives a bicycle via the pedals.
• treadle sewing machine

Engines

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.

Mechanics

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.

History

Crank

Tibetan operating a quern (1938). The perpendicular handle of such rotary handmills works as a crank.

It was thought that evidence of the earliest true crank handle was found in a Han era glazed-earthenware tomb model of an agricultural winnowing fan dated no later than 200 AD, but since then a series of similar pottery models with crank operated winnowing fans were unearthed, with one of them dating back to the Western Han dynasty (202 BC - 9 AD).

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). A crank is later also described in an early 15th century Arabic manuscript of Hero of Alexandria's Mechanics.

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 cranks and gear wheels. 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).

Crank and connecting rod

The Chinese used not just the crank, but the crank and connecting rod for operating querns as far back as the Western Han dynasty (202 BC - 9 AD). Eventually crank-and-connecting rods were used in the inter-conversion or rotary and reciprocating motion for other applications such as flour-sifting, treadle spinning wheels, water-powered furnace bellows, and silk-reeling machines. 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.

Hierapolis sawmill from 3rd century Asia Minor, the earliest known machine to combine a crank with a connecting rod.

Evidence for the crank in combination with a connecting rod appears in the Hierapolis sawmill from 3rd century Asia Minor (modern Turkey), while two stone sawmills from the 6th century have also been found at Ephesus, Syria, and Gerasa, Asia Minor (modern Turkey).

Crankshaft

Main article: Crankshaft

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. 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.

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. His twin-cylinder pump incorporated the earliest known crankshaft, while his other machine incorporated the first known crank-slider mechanism.

20th century

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.

See also

• Winch
• Piston motion equations
• Nothing grinder
• Sun and planet gear

References

Bibliography

• 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{{citation}}: CS1 maint: location missing publisher (link)
• 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

External links

• Crank highlight: Hypervideo of construction and operation of a four cylinder internal combustion engine courtesy of Ford Motor Company
• Kinematic Models for Design Digital Library (KMODDL) - Movies and photos of hundreds of working mechanical-systems models at Cornell University. Also includes an e-book library of classic texts on mechanical design and engineering.