Wheel And Axle
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The wheel and axle is a
simple machine A simple machine is a machine, mechanical device that changes the Direction (geometry) , direction or Magnitude_(mathematics) , magnitude of a force. In general, they can be defined as the simplest Mechanism (engineering) , mechanisms that use ...
, consisting of a
wheel A wheel is a rotating component (typically circular in shape) that is intended to turn 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 machin ...
attached to a smaller
axle An axle or axletree is a central shaft for a rotation, rotating wheel and axle, 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 ...
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 A lever is a simple machine consisting of a beam (structure), beam or rigid rod pivoted at a fixed hinge, or '':wikt:fulcrum, fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, l ...
, 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 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, 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 (term originally coined in English language) is a geopolitical region encompassing the Arabian Peninsula, the Levant, Turkey, Egypt, Iran, and Iraq. The term came into widespread usage by the United Kingdom and western Eur ...
by the 5th millennium BCE. One of the earliest examples was discovered at Tepe Pardis,
Iran Iran, officially the Islamic Republic of Iran (IRI) and also known as Persia, is a country in West Asia. It borders Iraq to the west, Turkey, Azerbaijan, and Armenia to the northwest, the Caspian Sea to the north, Turkmenistan to the nort ...
, 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 is a historical region of West Asia situated within the Tigris–Euphrates river system, in the northern part of the Fertile Crescent. Today, Mesopotamia is known as present-day Iraq and forms the eastern geographic boundary of ...
(
Iraq Iraq, officially the Republic of Iraq, is a country in West Asia. It is bordered by Saudi Arabia to Iraq–Saudi Arabia border, the south, Turkey to Iraq–Turkey border, the north, Iran to Iran–Iraq border, the east, the Persian Gulf and ...
) by 4200–4000 BCE. The oldest surviving example, which was found in Ur (modern day
Iraq Iraq, officially the Republic of Iraq, is a country in West Asia. It is bordered by Saudi Arabia to Iraq–Saudi Arabia border, the south, Turkey to Iraq–Turkey border, the north, Iran to Iran–Iraq border, the east, the Persian Gulf and ...
), 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 Working animal#Draft animals, draft animals or on occasion by humans, used for transporting goods, commodities, agricultural materials, supplies and sometimes people. Wagons are i ...
s found on
clay tablet In the Ancient Near East, clay tablets (Akkadian language, 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 t ...
pictographs A pictogram (also pictogramme, pictograph, or simply picto) is a graphical symbol that conveys meaning through its visual resemblance to a physical object. Pictograms are used in systems of writing and visual communication. A pictography is a wri ...
at the Eanna district of
Uruk Uruk, the archeological site known today as Warka, was an ancient city in the Near East, located east of the current bed of the Euphrates River, on an ancient, now-dried channel of the river in Muthanna Governorate, Iraq. The site lies 93 kilo ...
, in the
Sumer Sumer () is the earliest known civilization, located in the historical region of southern Mesopotamia (now south-central Iraq), emerging during the Chalcolithic and Early Bronze Age, early Bronze Ages between the sixth and fifth millennium BC. ...
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 ( Maykop culture) 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. Its eastern boundary is marked by the Ural Mountain ...
( 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 (, ; ; ), was an archaeological culture in north-central Europe. It developed as a technological merger of local neolithic and mesolithic techno-complexes between the lower Elbe and middle V ...
settlement in southern
Poland Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukrai ...
. In nearby Olszanica, a 2.2 m wide door was 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), is dated within two standard deviations 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 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 () is a transcontinental region around the Eastern Mediterranean encompassing the historical Fertile Crescent, the Levant, Anatolia, Egypt, Mesopotamia, and coastal areas of the Arabian Peninsula. The term was invented in the 20th ...
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 {{Infobox settlement , name = Ljubljana , official_name = , settlement_type = Capital city , image_skyline = {{multiple image , border = infobox , perrow = 1/2/2/1 , total_widt ...
, the capital of Slovenia. According to
radiocarbon dating Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for Chronological dating, determining the age of an object containing organic material by using the properties of carbon-14, radiocarbon, a radioactive Isotop ...
, it is between 5,100 and 5,350 years old. The wheel was made of ash and oak and had a
radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...
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. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...
, the earliest evidence of spoked wheels comes from
Qinghai Qinghai is an inland Provinces of China, province in Northwestern China. It is the largest provinces of China, province of China (excluding autonomous regions) by area and has the third smallest population. Its capital and largest city is Xin ...
in the form of two wheel hubs from a site dated between 2000 and 1500 BCE. In
Roman Egypt Roman Egypt was an imperial province of the Roman Empire from 30 BC to AD 642. The province encompassed most of modern-day Egypt except for the Sinai. It was bordered by the provinces of Crete and Cyrenaica to the west and Judaea, ...
,
Hero of Alexandria Hero of Alexandria (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimental ...
identified the wheel and axle as one of the
simple machine A simple machine is a machine, mechanical device that changes the Direction (geometry) , direction or Magnitude_(mathematics) , magnitude of a force. In general, they can be defined as the simplest Mechanism (engineering) , mechanisms that use ...
s used to lift weights. This is thought to have been in the form of the windlass which consists of a crank or
pulley Sheave without a rope A pulley is a wheel on an axle or shaft enabling a taut cable or belt passing over the wheel to move and change direction, or transfer power between itself and a shaft. A pulley may have a groove or grooves between flan ...
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 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 ...
. When used as the
wheel A wheel is a rotating component (typically circular in shape) that is intended to turn 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 machin ...
of a wheeled vehicle the smaller cylinder is the axle of the wheel, but when used in a windlass,
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 (physics), tension of a rope or wire rope (also called "cable" or "wire cable"). In its simplest form, it consists of a Bobb ...
, 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. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...
or elasticity, the power 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 ...
, 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 or gearwheel is a rotating machine part typically used to transmit rotational motion and/or torque by means of a series of teeth that engage with compatible teeth of another gear or other part. The teeth can be integral saliences or ...
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. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...
is called the ideal mechanical advantage (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
preview online
{{Authority control Historic machinery Simple machines Vehicle technology