Wheel and axle
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The wheel and axle is a
simple machine A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refer ...
consisting of a
wheel A wheel is a circular component that is intended to rotate on an axle Bearing (mechanical), bearing. The wheel is one of the key components of the wheel and axle which is one of the Simple machine, six simple machines. Wheels, in conjunction wi ...
attached to a smaller
axle An axle or axletree is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the wheels rotating around the axle. In the former case, bearing ...
so that these two parts rotate together in which a force is transferred from one to the other. The wheel and axle can be viewed as a version of the lever, with a drive force applied tangentially to the perimeter of the wheel, and a load force applied to the axle supported in a bearing, which serves as a fulcrum.


History

The
Halaf Tell Halaf ( ar, تل حلف) is an archaeological site in the Al Hasakah governorate of northeastern Syria, a few kilometers from the city of Ra's al-'Ayn near the Turkish border. The site, which dates to the 6th millennium BCE, was the fir ...
culture of 6500–5100 BCE has been credited with the earliest depiction of a wheeled vehicle, but this is doubtful as there is no evidence of Halafians using either wheeled vehicles or even pottery wheels. One of the first applications of the wheel to appear was the
potter's wheel In pottery, a potter's wheel is a machine used in the shaping (known as throwing) of clay into round ceramic ware. The wheel may also be used during the process of trimming excess clay from leather-hard dried ware that is stiff but malleable, a ...
, used by prehistoric cultures to fabricate clay pots. The earliest type, known as "tournettes" or "slow wheels", were known in the
Middle East The Middle East ( ar, الشرق الأوسط, ISO 233: ) is a geopolitical region commonly encompassing Arabian Peninsula, Arabia (including the Arabian Peninsula and Bahrain), Anatolia, Asia Minor (Asian part of Turkey except Hatay Pro ...
by the 5th millennium BCE. One of the earliest examples was discovered at Tepe Pardis,
Iran Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...
, and dated to 5200–4700 BCE. These were made of stone or clay and secured to the ground with a peg in the center, but required significant effort to turn. True potter's wheels, which are freely-spinning and have a wheel and axle mechanism, were developed in
Mesopotamia Mesopotamia ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن or ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the F ...
(
Iraq Iraq,; ku, عێراق, translit=Êraq officially the Republic of Iraq, '; ku, کۆماری عێراق, translit=Komarî Êraq is a country in Western Asia. It is bordered by Turkey to Iraq–Turkey border, the north, Iran to Iran–Iraq ...
) by 4200–4000 BCE. The oldest surviving example, which was found in Ur (modern day
Iraq Iraq,; ku, عێراق, translit=Êraq officially the Republic of Iraq, '; ku, کۆماری عێراق, translit=Komarî Êraq is a country in Western Asia. It is bordered by Turkey to Iraq–Turkey border, the north, Iran to Iran–Iraq ...
), dates to approximately 3100 BCE. Evidence of wheeled vehicles appeared by the late 4th millennium BCE. Depictions of wheeled
wagon A wagon or waggon is a heavy four-wheeled vehicle pulled by draught animals or on occasion by humans, used for transporting goods, commodities, agricultural materials, supplies and sometimes people. Wagons are immediately distinguished from ...
s found on
clay tablet In the Ancient Near East, clay tablets (Akkadian ) were used as a writing medium, especially for writing in cuneiform, throughout the Bronze Age and well into the Iron Age. Cuneiform characters were imprinted on a wet clay tablet with a stylu ...
pictographs A pictogram, also called a pictogramme, pictograph, or simply picto, and in computer usage an icon, is a graphic symbol that conveys its meaning through its pictorial resemblance to a physical object. Pictographs are often used in writing and gr ...
at the Eanna district of
Uruk Uruk, also known as Warka or Warkah, was an ancient city of Sumer (and later of Babylonia) situated east of the present bed of the Euphrates River on the dried-up ancient channel of the Euphrates east of modern Samawah, Al-Muthannā, Iraq.Harm ...
, in the
Sumer Sumer () is the earliest known civilization in the historical region of southern Mesopotamia (south-central Iraq), emerging during the Chalcolithic and early Bronze Ages between the sixth and fifth millennium BC. It is one of the cradles of c ...
ian civilization of Mesopotamia, are dated between 3700–3500 BCE. In the second half of the 4th millennium BCE, evidence of wheeled vehicles appeared near-simultaneously in the
Northern Caucasus The North Caucasus, ( ady, Темыр Къафкъас, Temır Qafqas; kbd, Ишхъэрэ Къаукъаз, İṩxhərə Qauqaz; ce, Къилбаседа Кавказ, Q̇ilbaseda Kavkaz; , os, Цӕгат Кавказ, Cægat Kavkaz, inh, ...
(
Maykop culture The Maykop culture (, , scientific transliteration: ''Majkop,''), c. 3700 BC– 3000 BC, was a major Bronze Age archaeological culture in the western Caucasus region. It extends along the area from the Taman Peninsula at the Kerch Strait to ne ...
) and
Eastern Europe Eastern Europe is a subregion of the Europe, European continent. As a largely ambiguous term, it has a wide range of geopolitical, geographical, ethnic, cultural, and socio-economic connotations. The vast majority of the region is covered by Russ ...
( Cucuteni–Trypillian culture). Depictions of a wheeled vehicle appeared between 3500 and 3350 BCE in the Bronocice clay pot excavated in a
Funnelbeaker culture The Funnel(-neck-)beaker culture, in short TRB or TBK (german: Trichter(-rand-)becherkultur, nl, Trechterbekercultuur; da, Tragtbægerkultur; ) was an archaeological culture in north-central Europe. It developed as a technological merger of lo ...
settlement in southern
Poland Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populous ...
. In nearby Olszanica, a 2.2 m wide door was constructed (2.2 wide doors were constructed) for wagon entry; this barn was 40 m long and had 3 doors. Surviving evidence of a wheel–axle combination, from Stare Gmajne near Ljubljana in Slovenia (
Ljubljana Marshes Wooden Wheel The Ljubljana Marshes Wheel is a wooden wheel that was found in the Ljubljana Marsh some south of Ljubljana, the capital of Slovenia, in 2002. Radiocarbon dating, performed in the VERA laboratory (Vienna Environmental Research Accelerator) in Vi ...
), is dated within two
standard deviations In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
to 3340–3030 BCE, the axle to 3360–3045 BCE. Two types of early Neolithic European wheel and axle are known; a circumalpine type of wagon construction (the wheel and axle rotate together, as in Ljubljana Marshes Wheel), and that of the
Baden culture The Baden culture was a Chalcolithic archaeological culture, culture from 3520–2690 BC. It was found in Central Europe, Central and Southeast Europe, and is in particular known from Moravia (Czech Republic), Hungary, southern Poland, Slovakia, ...
in Hungary (axle does not rotate). They both are dated to c. 3200–3000 BCE. Historians believe that there was a diffusion of the wheeled vehicle from the
Near East The ''Near East''; he, המזרח הקרוב; arc, ܕܢܚܐ ܩܪܒ; fa, خاور نزدیک, Xāvar-e nazdik; tr, Yakın Doğu is a geographical term which roughly encompasses a transcontinental region in Western Asia, that was once the hist ...
to Europe around the mid-4th millennium BCE. An early example of a wooden wheel and its axle was found in 2002 at the Ljubljana Marshes some 20 km south of
Ljubljana Ljubljana (also known by other historical names) is the capital and largest city of Slovenia. It is the country's cultural, educational, economic, political and administrative center. During antiquity, a Roman city called Emona stood in the ar ...
, the capital of Slovenia. According to
radiocarbon dating Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon. The method was dev ...
, it is between 5,100 and 5,350 years old. The wheel was made of
ash Ash or ashes are the solid remnants of fires. Specifically, ''ash'' refers to all non-aqueous, non- gaseous residues that remain after something burns. In analytical chemistry, to analyse the mineral and metal content of chemical samples, ash ...
and
oak An oak is a tree or shrub in the genus ''Quercus'' (; Latin "oak tree") of the beech family, Fagaceae. There are approximately 500 extant species of oaks. The common name "oak" also appears in the names of species in related genera, notably ''L ...
and had a
radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
of 70 cm and the axle was 120 cm long and made of oak. In
China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...
, the earliest evidence of spoked wheels comes from
Qinghai Qinghai (; alternately romanized as Tsinghai, Ch'inghai), also known as Kokonor, is a landlocked province in the northwest of the People's Republic of China. It is the fourth largest province of China by area and has the third smallest po ...
in the form of two wheel hubs from a site dated between 2000 and 1500 BCE. In
Roman Egypt , conventional_long_name = Roman Egypt , common_name = Egypt , subdivision = Province , nation = the Roman Empire , era = Late antiquity , capital = Alexandria , title_leader = Praefectus Augustalis , image_map = Roman E ...
,
Hero of Alexandria Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greece, Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egy ...
identified the wheel and axle as one of the
simple machine A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refer ...
s used to lift weights. This is thought to have been in the form of the
windlass The windlass is an apparatus for moving heavy weights. Typically, a windlass consists of a horizontal cylinder (barrel), which is rotated by the turn of a crank or belt. A winch is affixed to one or both ends, and a cable or rope is wound arou ...
which consists of a crank or
pulley A pulley is a wheel on an axle or shaft that is designed to support movement and change of direction of a taut cable or belt, or transfer of power between the shaft and cable or belt. In the case of a pulley supported by a frame or shell that ...
connected to a cylindrical barrel that provides mechanical advantage to wind up a rope and lift a load such as a bucket from the well. The wheel and axle was identified as one of six simple machines by Renaissance scientists, drawing from Greek texts on technology.


Mechanical advantage

The
simple machine A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refer ...
called a ''wheel and axle'' refers to the assembly formed by two disks, or cylinders, of different diameters mounted so they rotate together around the same axis. The thin rod which needs to be turned is called the axle and the wider object fixed to the axle, on which we apply force is called the wheel. A tangential force applied to the periphery of the large disk can exert a larger force on a load attached to the axle, achieving
mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for t ...
. When used as the
wheel A wheel is a circular component that is intended to rotate on an axle Bearing (mechanical), bearing. The wheel is one of the key components of the wheel and axle which is one of the Simple machine, six simple machines. Wheels, in conjunction wi ...
of a
wheeled vehicle A wheel is a circular component that is intended to rotate on an axle bearing. The wheel is one of the key components of the wheel and axle which is one of the six simple machines. Wheels, in conjunction with axles, allow heavy objects to be ...
the smaller cylinder is the axle of the wheel, but when used in a
windlass The windlass is an apparatus for moving heavy weights. Typically, a windlass consists of a horizontal cylinder (barrel), which is rotated by the turn of a crank or belt. A winch is affixed to one or both ends, and a cable or rope is wound arou ...
,
winch A winch is a mechanical device that is used to pull in (wind up) or let out (wind out) or otherwise adjust the tension of a rope or wire rope (also called "cable" or "wire cable"). In its simplest form, it consists of a spool (or drum) attache ...
, and other similar applications (see medieval mining lift to right) the smaller cylinder may be separate from the axle mounted in the bearings. It cannot be used separately. Assuming the wheel and axle does not dissipate or store energy, that is it has no
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...
or
elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...
, the
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
input by the force applied to the wheel must equal the power output at the axle. As the wheel and axle system rotates around its bearings, points on the circumference, or edge, of the wheel move faster than points on the circumference, or edge, of the axle. Therefore, a force applied to the edge of the wheel must be less than the force applied to the edge of the axle, because power is the product of force and velocity. Let ''a'' and ''b'' be the distances from the center of the bearing to the edges of the wheel ''A'' and the axle ''B.'' If the input force ''FA'' is applied to the edge of the wheel ''A'' and the force ''FB'' at the edge of the axle ''B'' is the output, then the ratio of the velocities of points ''A'' and ''B'' is given by ''a/b'', so the ratio of the output force to the input force, or
mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for t ...
, is given by :MA = \frac = \frac. The mechanical advantage of a simple machine like the wheel and axle is computed as the ratio of the resistance to the effort. The larger the ratio the greater the multiplication of force (torque) created or distance achieved. By varying the radii of the axle and/or wheel, any amount of mechanical advantage may be gained.Bowser, Edward Albert, 1890
An elementary treatise on analytic mechanics: with numerous examples.
(Originally from the University of Michigan) D. Van Nostrand Company, pp. 190
In this manner, the size of the wheel may be increased to an inconvenient extent. In this case a system or combination of wheels (often toothed, that is,
gear A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic pr ...
s) are used. As a wheel and axle is a type of lever, a system of wheels and axles is like a compound lever.Baker, C.E. The Principles and Practice of Statics and Dynamics... for the Use of Schools and Private Students. London: John Weale, 59, High Holborn. 1851 pp. 26–2
read online or download full text"> read online or download full text
/ref> On a powered wheeled vehicle the transmission exerts a force on the axle which has a smaller radius than the wheel. The mechanical advantage is therefore much less than 1. The wheel and axle of a car are therefore not representative of a simple machine (whose purpose is to increase the force). The friction between wheel and road is actually quite low, so even a small force exerted on the axle is sufficient. The actual advantage lies in the large rotational speed at which the axle is rotating thanks to the transmission.


Ideal mechanical advantage

The mechanical advantage of a wheel and axle with no
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...
is called the
ideal mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for t ...
(IMA). It is calculated with the following formula: :\mathrm = =


Actual mechanical advantage

All actual wheels have friction, which dissipates some of the power as heat. The actual mechanical advantage (AMA) of a wheel and axle is calculated with the following formula: :\mathrm = = \eta \cdot where :\eta = is the efficiency of the wheel, the ratio of power output to power input


References


Additional resources

Basic Machines and How They Work, United States. Bureau of Naval Personnel, Courier Dover Publications 1965, pp. 3–1 and followin
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