# Crank (mechanism)

### Crank (mechanism)

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 convert circular motion into reciprocating motion, or vice versa. The arm may be a bent portion of the shaft, or a separate arm or disk 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.

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. There is usually a bar perpendicular to the other end of the arm, often with a freely rotatable handle or pedal attached.

A compound crank

## Contents

• Examples 1
• Hand-powered cranks 1.1
• Foot-powered cranks 1.2
• Engines 1.3
• Mechanics 2
• History 3
• Western World 3.1
• Classical Antiquity 3.1.1
• Middle Ages 3.1.2
• Renaissance 3.1.3
• Far East 3.2
• Middle East 3.3
• 20th Century 3.4
• Crank axle 4
• References 6
• Bibliography 6.1
• External links 7

## Examples

Hand crank on a pencil sharpener

Familiar examples include:

### Engines

Animation showing piston and crankshaft motion in an internal combustion engine such as an automobile engine

Almost all reciprocating engines use cranks (with connecting rods) 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 (TDC). So the reciprocating motion created by a steadily rotating crank and connecting rod is approximately simple harmonic motion:

x = r \cos \alpha + l

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 from sinusoidal motion due to the changing angle of the connecting rod during the cycle, and is expressed (see Piston motion equations) as:

x = r \cos \alpha + \sqrt{l^2 - r^2\sin^2 \alpha}

This difference becomes significant in high-speed engines, which may need balance shafts to reduce the vibration due to this "secondary imbalance".

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. But in reality, the torque is maximum at crank angle of less than α = 90° from TDC for a given force on the piston. One way to calculate this angle is to find out when the conrod smallend (piston) speed becomes the fastest in downward direction given a steady crank rotational velocity. Piston speed x' is expressed as:

x' = -r\sin \alpha - \frac{r^2\sin \alpha \cos \alpha}{\sqrt{l^2-r^2\sin^2 \alpha}}

For example, for rod length 6" and crank radius 2", numerically solving the above equation finds the velocity minima (maximum downward speed) to be at crank angle of 73.17615° after TDC. Then, using the triangle sine law, it is found that the crank to conrod angle is 88.21738° and the conrod angle is 18.60647° from vertical (see Piston motion equations#Example).

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 connecting rods are attached to the wheels at points separated by some angle, 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

### Western World

#### Classical Antiquity

Roman crank handle from Augusta Raurica, dated to the 2nd century AD[1]

The eccentrically mounted handle of the rotary handmill which appeared in 5th century BC Celtiberian Spain and ultimately spread across the Roman Empire constitutes a crank.[2][3][4] A Roman iron crankshaft of yet unknown purpose dating to the 2nd century AD was excavated in Augusta Raurica, Switzerland. The 82.5 cm long piece has fitted to one end a 15 cm long bronze handle, the other handle being lost.[1][5]

A ca. 40 cm long true iron crank was excavated, along with a pair of shattered mill-stones of 50−65 cm diameter and diverse iron items, in Aschheim, close to Munich. The crank-operated Roman mill is dated to the late 2nd century AD.[6] An often cited modern reconstruction of a bucket-chain pump driven by hand-cranked flywheels from the Nemi ships has been dismissed though as "archaeological fantasy".[7]

Roman Hierapolis sawmill from the 3rd century AD, the earliest known machine to combine a crank with a connecting rod.[8]

The earliest evidence, anywhere in the world, for the crank combined with a connecting rod in a machine appears in the late Roman Hierapolis sawmill from the 3rd century AD and two Roman stone sawmills at Gerasa, Roman Syria, and Ephesus, Asia Minor (both 6th century AD).[8] On the pediment of the Hierapolis mill, a waterwheel fed by a mill race is shown powering via a gear train two frame saws which cut rectangular blocks by the way of some kind of connecting rods and, through mechanical necessity, cranks. The accompanying inscription is in Greek.[9]

The crank and connecting rod mechanisms of the other two archaeologically attested sawmills worked without a gear train.[10][11] In ancient literature, there is a reference to the workings of water-powered marble saws close to Trier, now Germany, by the late 4th century poet Ausonius;[8] about the same time, these mill types seem also to be indicated by the Christian saint Gregory of Nyssa from Anatolia, demonstrating a diversified use of water-power in many parts of the Roman Empire[12] The three finds push back the date of the invention of the crank and connecting rod mechanism by a full millennium;[8] for the first time, all essential components of the much later steam engine were assembled by one technological culture:

With the crank and connecting rod system, all elements for constructing a steam engine (invented in 1712) — Hero's aeolipile (generating steam power), the cylinder and piston (in metal force pumps), non-return valves (in water pumps), gearing (in water mills and clocks) — were known in Roman times.[13]

#### Middle Ages

Vigevano's war carriage

A rotary grindstone − the earliest representation thereof −[14] which is operated by a crank handle is shown in the Carolingian manuscript Utrecht Psalter; the pen drawing of around 830 goes back to a late antique original.[15] A musical tract ascribed to the abbot Odo of Cluny (ca. 878−942) describes a fretted stringed instrument which was sounded by a resined wheel turned with a crank; the device later appears in two 12th century illuminated manuscripts.[14] There are also two pictures of Fortuna cranking her wheel of destiny from this and the following century.[14]

The use of crank handles in trepanation drills was depicted in the 1887 edition of the Dictionnaire des Antiquités Grecques et Romaines to the credit of the Spanish Muslim surgeon Abu al-Qasim al-Zahrawi; however, the existence of such a device cannot be confirmed by the original illuminations and thus has to be discounted.[16] The Benedictine monk Theophilus Presbyter (c. 1070−1125) described crank handles "used in the turning of casting cores".[17]

The Italian physician Guido da Vigevano (c. 1280−1349), planning for a new crusade, made illustrations for a paddle boat and war carriages that were propelled by manually turned compound cranks and gear wheels (center of image).[18] The Luttrell Psalter, dating to around 1340, describes a grindstone which was rotated by two cranks, one at each end of its axle; the geared hand-mill, operated either with one or two cranks, appeared later in the 15th century;[19]

Medieval cranes were occasionally powered by cranks, although more often by windlasses.[20]

#### Renaissance

15th century paddle-wheel boat whose paddles are turned by single-throw crankshafts (Anonymous of the Hussite Wars)

The crank became common in Europe by the early 15th century, often seen in the works of those such as the German military engineer Konrad Kyeser.[19] Devices depicted in Kyeser's Bellifortis include cranked windlasses (instead of spoke-wheels) for spanning siege crossbows, cranked chain of buckets for water-lifting and cranks fitted to a wheel of bells.[19] Kyeser also equipped the Archimedes' screws for water-raising with a crank handle, an innovation which subsequently replaced the ancient practice of working the pipe by treading.[21] The earliest evidence for the fitting of a well-hoist with cranks is found in a miniature of c. 1425 in the German Hausbuch of the Mendel Foundation.[22]

German crossbowman cocking his weapon with a cranked rack-and-pinion device (ca. 1493)

The first depictions of the compound crank in the carpenter's brace appear between 1420 and 1430 in various northern European artwork.[23] The rapid adoption of the compound crank can be traced in the works of the Anonymous of the Hussite Wars, an unknown German engineer writing on the state of the military technology of his day: first, the connecting-rod, applied to cranks, reappeared, second, double compound cranks also began to be equipped with connecting-rods and third, the flywheel was employed for these cranks to get them over the 'dead-spot'.

One of the drawings of the Anonymous of the Hussite Wars shows a boat with a pair of paddle-wheels at each end turned by men operating compound cranks (see above). The concept was much improved by the Italian

• 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.