Differential (mechanics)
Encyclopedia
A differential is a device, usually, but not necessarily, employing gear
Gear
A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine....

s, capable of transmitting torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

and rotation through three shafts, almost always used in one of two ways: in one way, it receives one input and provides two outputs—this is found in most automobiles—and in the other way, it combines two inputs to create an output that is the sum, difference, or average, of the inputs.

In automobile
Automobile
An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...

s and other wheeled vehicles, the differential allows each of the driving roadwheels
Wheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...

to rotate at different speeds.

## Purpose

A vehicle's wheels rotate at different speeds, mainly when turning corners. The differential is designed to drive a pair of wheels while allowing them to rotate at different speeds. In vehicles without a differential, such as kart
Kart racing
Kart racing or karting is a variant of open-wheel motorsport with small, open, four-wheeled vehicles called karts, go-karts, or gearbox/shifter karts depending on the design. They are usually raced on scaled-down circuits...

s, both driving wheels are forced to rotate at the same speed, usually on a common axle
Axle
An axle 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 its surroundings, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle...

driven by a simple chain-drive mechanism. When cornering, the inner wheel needs to travel a shorter distance than the outer wheel, so with no differential, the result is the inner wheel spinning and/or the outer wheel dragging, and this results in difficult and unpredictable handling, damage to tire
Tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...

s and roads, and strain on (or possible failure of) the entire drivetrain
Powertrain
In a motor vehicle, the term powertrain or powerplant refers to the group of components that generate power and deliver it to the road surface, water, or air. This includes the engine, transmission, drive shafts, differentials, and the final drive...

.

## History

There are many claims to the invention of the differential gear but it is possible that it was known, at least in some places, in ancient times. Some historical milestones of the differential include:
• 1050 BC–771 BC: The Book of Song
Book of Song
The Book of Song , also called "The History of the Song," is a historical text of the Liu Song Dynasty of the Southern Dynasties of China. It covers history from 420 to 479, and is one of the Twenty-Four Histories, a traditional collection of historical records. It was authored by Shen Yue from...

(which itself was written between 502 and 557 A.D.) makes the assertion that the South Pointing Chariot
South Pointing Chariot
The south-pointing chariot was an ancient Chinese two-wheeled vehicle that carried a movable pointer to indicate the south, no matter how the chariot turned. Usually, the pointer took the form of a doll or figure with an outstretched arm...

, which may have used a differential gear, was invented during the Western Zhou Dynasty in China.
• 150 - 100 BC: Hypothesized use, now discredited, in the Greek
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....

Antikythera mechanism
Antikythera mechanism
The Antikythera mechanism is an ancient mechanical computer designed to calculate astronomical positions. It was recovered in 1900–1901 from the Antikythera wreck. Its significance and complexity were not understood until decades later. Its time of construction is now estimated between 150 and 100...

• 30 BC - 20 BC: Differential gear systems possibly used in China
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...

• 227–239 AD: Despite doubts from fellow ministers at court, Ma Jun
Ma Jun
Ma Jun , style name Deheng , was a Chinese mechanical engineer and government official during the Three Kingdoms era of China...

from the Kingdom of Wei in China
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...

invents the first historically verifiable South Pointing Chariot
South Pointing Chariot
The south-pointing chariot was an ancient Chinese two-wheeled vehicle that carried a movable pointer to indicate the south, no matter how the chariot turned. Usually, the pointer took the form of a doll or figure with an outstretched arm...

, which provided cardinal direction
Cardinal direction
The four cardinal directions or cardinal points are the directions of north, east, south, and west, commonly denoted by their initials: N, E, S, W. East and west are at right angles to north and south, with east being in the direction of rotation and west being directly opposite. Intermediate...

as a non-magnetic, mechanized compass
Compass
A compass is a navigational instrument that shows directions in a frame of reference that is stationary relative to the surface of the earth. The frame of reference defines the four cardinal directions – north, south, east, and west. Intermediate directions are also defined...

. Some such chariots may have used differential gears.
• 658, 666 AD: two Chinese Buddhist monks and engineers create South Pointing Chariots for Emperor Tenji
Emperor Tenji
, also known as Emperor Tenchi, was the 38th emperor of Japan, according to the traditional order of succession.Tenji's reign spanned the years from 661 through 671.-Traditional narrative:...

of Japan.
• 1027, 1107 AD: Documented Chinese reproductions of the South Pointing Chariot by Yan Su and then Wu Deren, which described in detail the mechanical functions and gear ratios of the device much more so than earlier Chinese records. See article on the South Pointing Chariot
South Pointing Chariot
The south-pointing chariot was an ancient Chinese two-wheeled vehicle that carried a movable pointer to indicate the south, no matter how the chariot turned. Usually, the pointer took the form of a doll or figure with an outstretched arm...

for further information.
• 1720: Joseph Williamson uses a differential gear in a clock.
• 1810: Rudolph Ackermann
Rudolph Ackermann
Rudolph Ackermann was an Anglo-German bookseller, inventor, lithographer, publisher and businessman.- Biography :...

of Germany invents a four-wheel steering system for carriages, which some later writers mistakenly report as a differential.
• 1827: modern automotive differential patented by watchmaker Onésiphore Pecqueur (1792–1852) of the Conservatoire des Arts et Métiers in France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

for use on a steam cart. (Sources: Britannica Online and)
• 1832: Richard Roberts
Richard Roberts (engineer)
Richard Roberts was a British engineer whose development of high-precision machine tools contributed to the birth of production engineering and mass production.-Early life:...

of England patents 'gear of compensation', a differential for road locomotives.
• 1876: James Starley
James Starley
James Starley was an English inventor and father of the bicycle industry. He was one of the most innovative and successful builders of bicycles and tricycles. His inventions include the differential gear and the perfection of chain-driven bicycles.-Early life:Starley was born in 1831 at Albourne,...

of Coventry
Coventry
Coventry is a city and metropolitan borough in the county of West Midlands in England. Coventry is the 9th largest city in England and the 11th largest in the United Kingdom. It is also the second largest city in the English Midlands, after Birmingham, with a population of 300,848, although...

invents chain-drive differential for use on bicycle
Bicycle
A bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist....

s; invention later used on automobiles by Karl Benz
Karl Benz
Karl Friedrich Benz, was a German engine designer and car engineer, generally regarded as the inventor of the gasoline-powered car, and together with Bertha Benz pioneering founder of the automobile manufacturer Mercedes-Benz...

.
• 1897: first use of differential on an Australian steam car
Steam car
A steam car is a light car powered by a steam engine.Steam locomotives, steam engines capable of propelling themselves along either road or rails, developed around one hundred years earlier than internal combustion engine cars although their weight restricted them to agricultural and heavy haulage...

by David Shearer.
• 1913: Packard
Packard
Packard was an American luxury-type automobile marque built by the Packard Motor Car Company of Detroit, Michigan, and later by the Studebaker-Packard Corporation of South Bend, Indiana...

introduces the spiral-gear differential, which cuts gear noise.
• 1926: Packard introduces the hypoid differential, which enables the propeller shaft and its hump in the interior of the car to be lowered.
• 1958: Vernon Gleasman patents the Torsen
Torsen
Torsen is a type of differential used in automobiles. It was invented by American Vernon Gleasman and manufactured by the Gleason Corporation. Torsen is a contraction of Torque-Sensing...

dual-drive differential, a type of limited slip differential
Limited slip differential
A limited slip differential is a type of differential gear arrangement that allows for some difference in angular velocity of the output shafts, but imposes a mechanical bound on the disparity...

that relies solely on the action of gearing instead of a combination of clutches and gears.

Note: The Antikythera mechanism
Antikythera mechanism
The Antikythera mechanism is an ancient mechanical computer designed to calculate astronomical positions. It was recovered in 1900–1901 from the Antikythera wreck. Its significance and complexity were not understood until decades later. Its time of construction is now estimated between 150 and 100...

(150 BC
150 BC
Year 150 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Flamininus and Balbus...

100 BC
100 BC
Year 100 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Marius and Flaccus...

), discovered on an ancient shipwreck near the Greek
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....

island of Antikythera
Antikythera
Antikythera or Anticythera is a Greek island lying on the edge of the Aegean Sea, between Crete and Peloponnese. Since the 2011 local government reform it is part of the municipality of Kythira island....

, was once suggested to have employed a differential gear. This has since been disproved. Other possible uses of differentials prior to Joseph Williamson's clock of 1720 are hypothetical.

## Functional description

The following description of a differential applies to a "traditional" rear-wheel-drive car or truck with an "open" or limited slip differential combined with a reduction gearset:

Torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

is supplied from the engine, via the transmission
Transmission (mechanics)
A machine consists of a power source and a power transmission system, which provides controlled application of the power. Merriam-Webster defines transmission as: an assembly of parts including the speed-changing gears and the propeller shaft by which the power is transmitted from an engine to a...

, to a drive shaft (British term: 'propeller shaft', commonly and informally abbreviated to 'prop-shaft'), which runs to the final drive unit that contains the differential. A spiral bevel
Spiral bevel gear
A spiral bevel gear is a bevel gear with helical teeth. The main application of this is in a vehicle differential, where the direction of drive from the drive shaft must be turned 90 degrees to drive the wheels...

pinion
Pinion
A pinion is a round gear used in several applications:*usually the smallest gear in a gear drive train, although in the case of John Blenkinsop's Salamanca, the pinion was rather large...

gear takes its drive from the end of the propeller shaft, and is encased within the housing of the final drive unit. This meshes with the large spiral bevel ring gear, known as the crown wheel. The crown wheel and pinion may mesh in hypoid orientation, not shown. The crown wheel gear is attached to the differential carrier or cage, which contains the 'sun' and 'planet' wheels or gears, which are a cluster of four opposed bevel gears in perpendicular plane, so each bevel gear meshes with two neighbours, and rotates counter to the third, that it faces and does not mesh with. The two sun wheel gears are aligned on the same axis as the crown wheel gear, and drive the axle half shaft
Half shaft
The term half shaft is another name for a front-wheel drive shaft, which is also called the constant velocity axle or CV axle. There is one half shaft per wheel. Some may further to this part as a CV shaft....

s connected to the vehicle's driven wheels
Drive wheel
A drive wheel is a roadwheel in an automotive vehicle that receives torque from the powertrain, and provides the final driving force for a vehicle. A two-wheel drive vehicle has two driven wheels, and a four-wheel drive has four, and so-on....

. The other two planet gears are aligned on a perpendicular axis which changes orientation with the ring gear's rotation. In the two figures shown above, only one planet gear (green) is illustrated, however, most automotive applications contain two opposing planet gears. Other differential designs employ different numbers of planet gears, depending on durability requirements. As the differential carrier rotates, the changing axis orientation of the planet gears imparts the motion of the ring gear to the motion of the sun gears by pushing on them rather than turning against them (that is, the same teeth stay in the same mesh or contact position), but because the planet gears are not restricted from turning against each other, within that motion, the sun gears can counter-rotate relative to the ring gear and to each other under the same force (in which case the same teeth do not stay in contact).

Thus, for example, if the car is making a turn to the right, the main crown wheel may make 10 full rotations. During that time, the left wheel will make more rotations because it has further to travel, and the right wheel will make fewer rotations as it has less distance to travel. The sun gears (which drive the axle half-shafts) will rotate in opposite directions relative to the ring gear by, say, 2 full turns each (4 full turns relative to each other), resulting in the left wheel making 12 rotations, and the right wheel making 8 rotations.

The rotation of the crown wheel gear is always the average of the rotations of the side sun gears. This is why, if the driven roadwheels are lifted clear of the ground with the engine off, and the drive shaft is held (say leaving the transmission 'in gear', preventing the ring gear from turning inside the differential), manually rotating one driven roadwheel causes the opposite roadwheel to rotate in the opposite direction by the same amount.

When the vehicle is traveling in a straight line, there will be no differential movement of the planetary system of gears other than the minute movements necessary to compensate for slight differences in wheel diameter, undulations in the road (which make for a longer or shorter wheel path), etc.

## Loss of traction

One undesirable side effect of a conventional differential is that it can limit traction under less than ideal conditions. The amount of traction required to propel the vehicle at any given moment depends on the load at that instant—how heavy the vehicle is, how much drag and friction there is, the gradient of the road, the vehicle's momentum, and so on.

The torque applied to each driving wheel
Wheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...

is a result of the engine
Engine
An engine or motor is a machine designed to convert energy into useful mechanical motion. Heat engines, including internal combustion engines and external combustion engines burn a fuel to create heat which is then used to create motion...

, transmission
Transmission (mechanics)
A machine consists of a power source and a power transmission system, which provides controlled application of the power. Merriam-Webster defines transmission as: an assembly of parts including the speed-changing gears and the propeller shaft by which the power is transmitted from an engine to a...

and drive axles applying a twisting force against the resistance of the traction
Traction (engineering)
Traction refers to the maximum frictional force that can be produced between surfaces without slipping.The units of traction are those of force, or if expressed as a coefficient of traction a ratio.-Traction:...

at that roadwheel. In lower gears and thus at lower speeds, and unless the load is exceptionally high, the drivetrain can supply as much torque as necessary, so the limiting factor becomes the traction under each wheel. It is therefore convenient to define traction as the amount of torque that can be generated between the tire
Tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...

and the road surface, before the wheel starts to slip. If the torque applied to drive wheels does not exceed the threshold of traction, the vehicle will be propelled in the desired direction; if not, then one or more wheels will simply spin.

A conventional "open" (non-locked or otherwise traction-aided) differential always supplies close to equal (because of internal friction) torque to each side. To illustrate how this can limit torque applied to the driving wheels, imagine a simple rear-wheel drive vehicle, with one rear roadwheel on asphalt with good grip, and the other on a patch of slippery ice. It takes very little torque to spin the side on slippery ice, and because a differential splits torque equally to each side, the torque that is applied to the side that is on asphalt is limited to this amount.

Based on the load, gradient, et cetera, the vehicle requires a certain amount of torque applied to the drive wheels to move forward. Since an open differential limits total torque applied to both drive wheels to the amount utilized by the lower traction wheel multiplied by a factor of 2, when one wheel is on a slippery surface, the total torque applied to the driving wheels may be lower than the minimum torque required for vehicle propulsion.

A proposed way to distribute the power to the wheels, is to use the concept of gearless differential, of which a review has been reported by Provatidis, but the various configurations seem to correspond either to the "sliding pins and cams" type, such as the ZF B-70 available for early VWs, or are a variation of the ball differential
Ball differential
A ball differential is a type of differential typically used on radio-controlled cars. It differs from a geared differential by using several small ball bearings rotating between two plates, instead of bevel gears.- History :...

.

Many newer vehicles feature traction control
Traction control system
A traction control system , also known as anti-slip regulation , is typically a secondary function of the anti-lock braking system on production motor vehicles, designed to prevent loss of traction of driven road wheels...

, which partially mitigates the poor traction characteristics of an open differential by using the anti-lock braking system
Anti-lock braking system
An anti-lock braking system is a safety system that allows the wheels on a motor vehicle to continue interacting tractively with the road surface as directed by driver steering inputs while braking, preventing the wheels from locking up and therefore avoiding skidding.An ABS generally offers...

to limit or stop the slippage of the low traction wheel, increasing the torque that can be applied to both wheels. While not as effective in propelling a vehicle under poor traction conditions as a traction-aided differential, it is better than a simple mechanical open differential with no electronic traction assistance.

## Traction-aiding devices

There are various devices for getting more usable traction from vehicles with differentials.
• One solution is the Positive Traction (Posi), the most well-known of which is the clutch-type. With this differential, the side gears are coupled to the carrier via a multi-disc clutch which allows extra torque to be sent to the wheel with higher resistance than available at the other driven roadwheel when the limit of friction is reached at that other wheel. Below the limit of friction more torque goes to the slower (inside) wheel.

• A limited slip differential
Limited slip differential
A limited slip differential is a type of differential gear arrangement that allows for some difference in angular velocity of the output shafts, but imposes a mechanical bound on the disparity...

(LSD) or anti-spin is another type of traction aiding device that uses a mechanical system that activates under centrifugal force to positively lock the left and right spider gears together when one wheel spins a certain amount faster than the other. This type behaves as an open differential unless one wheel begins to spin and exceeds that threshold. While positraction units can be of varying strength, some of them with high enough friction to cause an inside tire to spin or outside tire to drag in turns like a spooled differential, the LSD will remain open unless enough torque is applied to cause one wheel to lose traction and spin, at which point it will engage. A LSD can use clutches like a posi when engaged, or may also be a solid mechanical connection like a locker or spool. It is called limited slip because it does just that; it limits the amount that one wheel can "slip" (spin).

• A locking differential
Locking differential
A locking differential, diff-lock or locker is a variation on the standard automotive differential. A locking differential may provide increased traction compared to a standard, or "open" differential by restricting each of the two wheels on an axle to the same rotational speed without regard to...

, such as ones using differential gears in normal use but using air or electrically controlled mechanical system, which when locked allow no difference in speed between the two wheels on the axle. They employ a mechanism for allowing the axles to be locked relative to each other, causing both wheels to turn at the same speed regardless of which has more traction; this is equivalent to effectively bypassing the differential gears entirely. Other locking systems may not even use differential gears but instead drive one wheel or both depending on torque value and direction. Automatic mechanical lockers do allow for some differentiation under certain load conditions, while a selectable locker typically couples both axles with a solid mechanical connection like a spool when engaged.

• A high-friction 'Automatic Torque Biasing' (ATB) differential, such as the Torsen
Torsen
Torsen is a type of differential used in automobiles. It was invented by American Vernon Gleasman and manufactured by the Gleason Corporation. Torsen is a contraction of Torque-Sensing...

differential, where the friction is between the gear teeth rather than at added clutches. This applies more torque to the driven roadwheel with highest resistance (grip or traction) than is available at the other driven roadwheel when the limit of friction is reached at that other wheel. When tested with the wheels off the ground, if one wheel is rotated with the differential case held, the other wheel will still rotate in the opposite direction as for an open differential but there with be some frictional losses and the torque will be distributed at other than 50/50. Although marketed as being "torque-sensing", it functions the same as a limited slip differential. 3D Animation of a Torsen Differential

• A very high-friction differential, such as the ZF "sliding pins and cams" type, so that there is locking from very high internal friction. When tested with the wheels off the ground with torque applied to one wheel it will lock, but it is still possible for the differential action to occur in use, albeit with considerable frictional losses, and with the road loads at each wheel in opposite directions rather than the same (acting with a "locking and releasing" action rather than a distributed torque).

• Electronic traction control system
Traction control system
A traction control system , also known as anti-slip regulation , is typically a secondary function of the anti-lock braking system on production motor vehicles, designed to prevent loss of traction of driven road wheels...

s usually use the anti-lock braking system
Anti-lock braking system
An anti-lock braking system is a safety system that allows the wheels on a motor vehicle to continue interacting tractively with the road surface as directed by driver steering inputs while braking, preventing the wheels from locking up and therefore avoiding skidding.An ABS generally offers...

(ABS) roadwheel speed sensors to detect a spinning roadwheel, and apply the brake
Brake
A brake is a mechanical device which inhibits motion. Its opposite component is a clutch. The rest of this article is dedicated to various types of vehicular brakes....

to that wheel. This progressively raises the reaction torque at that roadwheel, and the differential compensates by transmitting more torque through the other roadwheel—the one with better traction. In Volkswagen Group
Volkswagen Group
Volkswagen Group is a German multinational automobile manufacturing group. , Volkswagen was ranked as the world’s third largest motor vehicle manufacturer and Europe's largest....

vehicles, this specific function is called 'Electronic Differential Lock' (EDL).

• A Spool is just what it sounds like. It may replace the spider gears within the differential carrier, or the entire carrier. A spool locks both axle shafts together 100% for maximum traction. This is typically only used in drag racing
Drag racing
Drag racing is a competition in which specially prepared automobiles or motorcycles compete two at a time to be the first to cross a set finish line, from a standing start, in a straight line, over a measured distance, most commonly a ¼-mile straight track....

applications, where the vehicle is to be driven in a straight line while applying tremendous torque to both wheels.

• In a four-wheel drive
Four-wheel drive
Four-wheel drive, 4WD, or 4×4 is a four-wheeled vehicle with a drivetrain that allows all four wheels to receive torque from the engine simultaneously...

vehicle, a viscous coupling unit
Viscous coupling unit
A viscous coupling is a mechanical device which transfers torque and rotation by the medium of a viscous fluid. It is made of a number of circular plates with tabs or perforations, fitted very close to each other in a sealed drum. Alternate plates are connected to a driving shaft at one end of the...

can replace a centre differential entirely, or be used to limit slip in a conventional 'open' differential. It works on the principle of allowing the two output shafts to counter-rotate relative to each other, by way of a system of slotted plates that operate within a viscous fluid, often silicone
Silicone
Silicones are inert, synthetic compounds with a variety of forms and uses. Typically heat-resistant and rubber-like, they are used in sealants, adhesives, lubricants, medical applications , cookware, and insulation....

. The fluid allows slow relative movements of the shafts, such as those caused by cornering, but will strongly resist high-speed movements, such as those caused by a single wheel spinning. This system is similar to a limited slip differential.

A four-wheel drive (4WD) vehicle will have at least two differentials (one in each axle
Axle
An axle 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 its surroundings, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle...

for each pair of driven roadwheels), and possibly a centre differential to apportion torque between the front and rear axles. In some cases (e.g. Lancia Delta Integrale, Porsche 964
Porsche 964
The Porsche 964 is the company's internal name for the version of the Porsche 911 model manufactured and sold between 1989 and 1994. It featured significant styling revisions over previous versions of the 911, most prominently the more integrated bumpers , although it was still obviously a 911...

Carrera 4 of 1989) the centre differential is an epicyclic
Epicyclic gearing
Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer gears, or planet gears, revolving about a central, or sun gear. Typically, the planet gears are mounted on a movable arm or carrier which itself may rotate relative to the sun gear...

differential (see below) to divide the torque asymmetrically, but at a fixed rate between the front and rear axle. Other methods utilise an 'Automatic Torque Biasing' (ATB) centre differential, such as a Torsen
Torsen
Torsen is a type of differential used in automobiles. It was invented by American Vernon Gleasman and manufactured by the Gleason Corporation. Torsen is a contraction of Torque-Sensing...

—which is what Audi
Audi
Audi AG is a German automobile manufacturer, from supermini to crossover SUVs in various body styles and price ranges that are marketed under the Audi brand , positioned as the premium brand within the Volkswagen Group....

use in their quattro cars (with longitudinal engine
Longitudinal engine
In automotive engineering, a longitudinal engine is an internal combustion engine in which the crankshaft is oriented along the long axis of the vehicle, front to back....

s).

4WD vehicles without a centre differential should not be driven on dry, paved roads in four-wheel drive mode, as small differences in rotational speed between the front and rear wheels cause a torque to be applied across the transmission
Transmission (mechanics)
A machine consists of a power source and a power transmission system, which provides controlled application of the power. Merriam-Webster defines transmission as: an assembly of parts including the speed-changing gears and the propeller shaft by which the power is transmitted from an engine to a...

. This phenomenon is known as "wind-up", and can cause considerable damage to the transmission or drive train. On loose surfaces these differences are absorbed by the tire slippage on the road surface.

A transfer case
Transfer case
A transfer case is a part of a four-wheel-drive system found in four-wheel-drive and all-wheel-drive vehicles. The transfer case is connected to the transmission and also to the front and rear axles by means of drive shafts...

may also incorporate a centre differential, allowing the drive shafts to spin at different speeds. This permits the four-wheel drive vehicle to drive on paved surfaces without experiencing "wind-up".

## Epicyclic differential

An epicyclic differential uses epicyclic gearing
Epicyclic gearing
Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer gears, or planet gears, revolving about a central, or sun gear. Typically, the planet gears are mounted on a movable arm or carrier which itself may rotate relative to the sun gear...

to split and apportion torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

asymmetrically between the front and rear axles. An epicyclic differential is at the heart of the Toyota Prius
Toyota Prius
The Toyota Prius is a full hybrid electric mid-size hatchback, formerly a compact sedan developed and manufactured by the Toyota Motor Corporation...

automotive drive train, where it interconnects the engine, motor-generators, and the drive wheels (which have a second differential for splitting torque as usual). It has the advantage of being relatively compact along the length of its axis (that is, the sun gear shaft).

Epicyclic gears are also called planetary gears because the axes of the planet gears revolve around the common axis of the sun and ring gears that they mesh with and roll between. In the image, the yellow shaft carries the sun gear which is almost hidden. The blue gears are called planet gears and the pink gear is the ring gear or annulus.

## Spur-gear differential

This is another type of differential that was used in some early automobiles, more recently the Oldsmobile Toronado
The original Toronado began as a design painting by Oldsmobile stylist David North in 1962. His design, dubbed the "Flame Red Car," was for a compact sports/personal car never intended for production...

, as well as other non-automotive applications. It consists of spur gears only.

A spur-gear differential has two equal-sized spur gears, one for each half-shaft, with a space between them. Instead of the Bevel gear
Bevel gear
Bevel gears are gears where the axes of the two shafts intersect and the tooth-bearing faces of the gears themselves are conically shaped.Bevel gears are most often mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well...

, also known as a miter gear, assembly (the "spider") at the centre of the differential, there is a rotating carrier on the same axis as the two shafts. Torque from a prime mover or transmission
Transmission (mechanics)
A machine consists of a power source and a power transmission system, which provides controlled application of the power. Merriam-Webster defines transmission as: an assembly of parts including the speed-changing gears and the propeller shaft by which the power is transmitted from an engine to a...

, such as the drive shaft of a car, rotates this carrier.

Mounted in this carrier are one or more pairs of identical pinions, generally longer than their diameters, and typically smaller than the spur gears on the individual half-shafts. Each pinion pair rotates freely on pins supported by the carrier. Furthermore, the pinions pairs are displaced axially, such that they mesh only for the part of their length between the two spur gears, and rotate in opposite directions. The remaining length of a given pinion meshes with the nearer spur gear on its axle. Therefore, each pinion couples that spur gear to the other pinion, and in turn, the other spur gear, so that when the drive shaft rotates the carrier, its relationship to the gears for the individual wheel axles is the same as that in a bevel-gear differential.

## Non-automotive applications

The oldest known example of a differential was once thought to be in the Antikythera mechanism
Antikythera mechanism
The Antikythera mechanism is an ancient mechanical computer designed to calculate astronomical positions. It was recovered in 1900–1901 from the Antikythera wreck. Its significance and complexity were not understood until decades later. Its time of construction is now estimated between 150 and 100...

. It was supposed to have used such a train to produce the difference between two inputs, one input related to the position of the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

on the zodiac
Zodiac
In astronomy, the zodiac is a circle of twelve 30° divisions of celestial longitude which are centred upon the ecliptic: the apparent path of the Sun across the celestial sphere over the course of the year...

, and the other input related to the position of the moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

on the zodiac; the output of the differential gave a quantity related to the moon's phase
Lunar phase
A lunar phase or phase of the moon is the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases change cyclically as the Moon orbits the Earth, according to the changing relative positions of the Earth, Moon, and Sun...

. It has now been proven that the assumption of the existence of a differential gearing arrangement was incorrect.

Chinese south-pointing chariots may also have been very early applications of differentials. The chariot had a pointer which constantly pointed to the south, no matter how the chariot turned as it travelled. It could therefore be used as a type of compass
Compass
A compass is a navigational instrument that shows directions in a frame of reference that is stationary relative to the surface of the earth. The frame of reference defines the four cardinal directions – north, south, east, and west. Intermediate directions are also defined...

. It is widely thought that a differential mechanism responded to any difference between the speeds of rotation of the two wheels of the chariot, and turned the pointer appropriately. However, there is considerable uncertainty about this.

The earliest definitely verified use of a differential was in a clock made by Joseph Williamson in 1720. It employed a differential to add the Equation of Time
Equation of time
The equation of time is the difference between apparent solar time and mean solar time. At any given instant, this difference will be the same for every observer...

to local mean time
Local mean time
Local mean time is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude...

, as determined by the clock mechanism, to produce solar time
Solar time
Solar time is a reckoning of the passage of time based on the Sun's position in the sky. The fundamental unit of solar time is the day. Two types of solar time are apparent solar time and mean solar time .-Introduction:...

, which would have been the same as the reading of a sundial
Sundial
A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style onto a surface marked with lines indicating the hours of the day. The style is the time-telling edge of the gnomon, often a thin rod or a...

. During the 18th Century, sundials were considered to show the "correct" time, so an ordinary clock would frequently have to be readjusted, even if it worked perfectly, because of seasonal variations in the Equation of Time. Williamson's clock showed sundial time without needing readjustment. Nowadays, we consider clocks to be "correct" and sundials usually incorrect, so many sundials carry instructions about how to use their readings to obtain clock time.

In the first half of the twentieth century, mechanical analog computer
Analog computer
An analog computer is a form of computer that uses the continuously-changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved...

s, called differential analyzers, were constructed that used differential gear trains to perform addition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....

and subtraction
Subtraction
In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...

. The U.S. Navy Mk.1 gun fire control computer used about 160 differentials of the bevel-gear type.

A differential gear train can be used to allow a difference between two input axles. Mill
Gristmill
The terms gristmill or grist mill can refer either to a building in which grain is ground into flour, or to the grinding mechanism itself.- Early history :...

s often used such gears to apply torque in the required axis. Differentials are also used in this way in watchmaking to link two separate regulating systems with the aim of averaging out errors. Greubel Forsey
Greubel Forsey
Greubel Forsey is a watchmaking company specializing in very high-end complicated timepieces. It was launched in 2004 by Robert Greubel and Stephen Forsey and is based in La Chaux-de-Fonds, Switzerland....

use a differential to link two double tourbillon systems in their Quadruple Differential Tourbillon.

## Active differentials

A relatively new technology is the electronically-controlled 'active differential'. An electronic control unit
Electronic control unit
In automotive electronics, electronic control unit is a generic term for any embedded system that controls one or more of the electrical systems or subsystems in a motor vehicle....

(ECU) uses inputs from multiple sensors, including yaw rate, steering input angle, and lateral acceleration—and adjusts the distribution of torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

to compensate for undesirable handling behaviours like understeer
Understeer
Understeer and oversteer are vehicle dynamics terms used to describe the sensitivity of a vehicle to steering. Simply put, oversteer is what occurs when a car turns by more than the amount commanded by the driver...

. Active differentials used to play a large role in the World Rally Championship
World Rally Championship
The World Rally Championship is a rallying series organised by the FIA, culminating with a champion driver and manufacturer. The driver's world championship and manufacturer's world championship are separate championships, but based on the same point system. The series currently consists of 13...

, but in the 2006 season the FIA
Fédération Internationale de l'Automobile
The Fédération Internationale de l'Automobile is a non-profit association established as the Association Internationale des Automobile Clubs Reconnus on 20 June 1904 to represent the interests of motoring organisations and motor car users...

has limited the use of active differentials only to those drivers who have not competed in the World Rally Championship
World Rally Championship
The World Rally Championship is a rallying series organised by the FIA, culminating with a champion driver and manufacturer. The driver's world championship and manufacturer's world championship are separate championships, but based on the same point system. The series currently consists of 13...

in the last five years.

Fully integrated active differentials are used on the Ferrari F430
Ferrari F430
The Ferrari F430 is a sports car that was produced by the Italian automaker Ferrari from 2004 to 2009, as a successor to the 360. It debuted at the 2004 Paris Motor Show...

, Mitsubishi Lancer Evolution
Mitsubishi Lancer Evolution
The Mitsubishi Lancer Evolution, colloquially known as the Lancer Evo or Evo, is a high-performance sedan manufactured by Mitsubishi Motors. There have been ten official versions to date, and the designation of each model is most commonly a roman numeral...

, and on the rear wheels in the Acura RL
Acura RL
The Acura RL is the flagship car for North American luxury brand Acura — marketed in Japan as the Honda Legend and manufactured in Saitama, Japan...

. A version manufactured by ZF
ZF Friedrichshafen
ZF Friedrichshafen AG, also known as ZF Group, and commonly abbreviated to ZF, is a German public company headquartered in Friedrichshafen, in the south-west German region of Baden-Württemberg....

is also being offered on the latest Audi S4 and Audi A4
Audi A4
The first generation Audi A4 debuted in 1994, with production starting November 1994. It was built on the Volkswagen Group B5 platform, which it shared with the fourth generation Volkswagen Passat . It had a front-mounted longitudinal engine and front-wheel drive...

.

The second constraint of the differential is passive—it is actuated by the friction kinematics chain through the ground. The difference in torque on the roadwheels and tires (caused by turns or bumpy ground) drives the second degree of freedom
Degrees of freedom (engineering)
In mechanics, degrees of freedom are the set of independent displacements and/or rotations that specify completely the displaced or deformed position and orientation of the body or system...

, (overcoming the torque of inner friction) to equalise the driving torque on the tires. The sensitivity of the differential depends on the inner friction through the second degree of freedom. All of the differentials (so called “active” and “passive”) use clutches and brakes for restricting the second degree of freedom, so all suffer from the same disadvantage—decreased sensitivity to a dynamically changing environment. The sensitivity of the ECU controlled differential is also limited by the time delay caused by sensors and the response time of the actuators.

## Automobiles without differentials

Although the vast majority of automobiles in the developed world use differentials, there are a few that do not. Several different types exist:
• Vehicles with a single driving wheel. Besides motorcycles, which are generally not classified as automobiles, this group includes most three-wheeled cars. These were quite common in Europe in the mid-20th Century, but have now become rare there. They are still common in some areas of the developing world, such as India. Some early four-wheeled cars also had only one driving wheel to avoid the need for a differential. However, this arrangement led to many problems. The system was unbalanced, the driving wheel would easily spin, etc.. Because of these problems, few such vehicles were made.

• Vehicles using two freewheel
Freewheel
thumb|Freewheel mechanismIn mechanical or automotive engineering, a freewheel or overrunning clutch is a device in a transmission that disengages the driveshaft from the driven shaft when the driven shaft rotates faster than the driveshaft...

s. A freewheel, as used on a pedal bicycle for example, allows a road wheel to rotate faster than the mechanism that drives it, allowing a cyclist to stop pedalling while going downhill. Some early automobiles had the engine driving two freewheels, one for each driving road wheel. When the vehicle turned, the engine would continue to drive the wheel on the inside of the curve, but the wheel on the outside was permitted to rotate faster by its freewheel. Thus, while turning, the vehicle had only one driving wheel.

• Vehicles with continuously variable transmission
Continuously variable transmission
A continuously variable transmission is a transmission that can change steplessly through an infinite number of effective gear ratios between maximum and minimum values. This contrasts with other mechanical transmissions that offer a fixed number of gear ratios...

s, such as the DAF Daffodil
DAF Daffodil
The DAF 750 is a small family car that was manufactured by DAF from 1961 until 1963. It replaced the DAF 600. At the same time as launching the 750, DAF launched the DAF Daffodil which was essentially the same car but with more luxurious fittings and a lot more chrome trim on the outside...

. The Daffodil, and other similar vehicles which were made until the 1970s by the Dutch company DAF, had a type of transmission that used an arrangement of belts and pulleys to provide an infinite number of gear ratios. The engine drove two separate transmissions which ran the two driving wheels. When the vehicle turned, the two wheels could rotate at different speeds, making the two transmissions shift to different gear ratios, thus functionally substituting for a differential. The slower moving wheel received more driving torque than the faster one, so the system had limited-slip characteristics. The duplication also provided redundancy. If one belt broke, the vehicle could still be driven.

• Vehicles with separate motors for the driving wheels. Electric cars can have a separate motor for each driving wheel, eliminating the need for a transmission and differential. Hybrid vehicles in which the final drive is electric can be configured similarly.

• Ball differential
Ball differential
A ball differential is a type of differential typically used on radio-controlled cars. It differs from a geared differential by using several small ball bearings rotating between two plates, instead of bevel gears.- History :...

• Limited slip differential
Limited slip differential
A limited slip differential is a type of differential gear arrangement that allows for some difference in angular velocity of the output shafts, but imposes a mechanical bound on the disparity...

• Locking differential
Locking differential
A locking differential, diff-lock or locker is a variation on the standard automotive differential. A locking differential may provide increased traction compared to a standard, or "open" differential by restricting each of the two wheels on an axle to the same rotational speed without regard to...

• Whippletree (mechanism)
Whippletree (mechanism)
A whippletree or whiffletree is a mechanism to distribute force evenly through linkages. The mechanism may also be referred to as an equalizer, leader bar or double tree. It consists of a bar pivoted at or near the centre, with force applied from one direction to the pivot, and from the other...

, which evenly divides linear force as a differential divides torque.
• Aron's electricity meter, an early electricity meter
Electricity meter
An electricity meter or energy meter is a device that measures the amount of electric energy consumed by a residence, business, or an electrically powered device....

, relying on the use of a mechanical differential.