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Rotating circular machine part with teeth that mesh with another toothed part
mechanical gears

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 rotational power. While doing so, they can change the torque and rotational speed being transmitted (in inverse proportion) and also change the rotational axis of the power being transmitted. The teeth on the two meshing gears all have the same shape. The basic principle behind the operation of gears is analogous to the basic principle of levers. Meshing gears of different diameters produce three changes — (i) a change in torque, creating a mechanical advantage, (ii) an inverse change in rotational speed and (iii) a change in the sense of the rotation, a clockwise rotation becoming an anti clockwise one and vice versa. The ratio of the output torque to the input torque is equal to the ratio of the diameter of the output gear to that of the input gear This is called the gear ratio. The ratio of the output rotational speed to the input rotational speed is equal to the inverse of the ratio of the diameter of the output gear to that of the input gear The diameters of the gears are measured at a point between the root and tips of the gear teeth called the pitch circle. A gear may also be known informally as a cog. Two or more meshing gears, working in a sequence, are called a gear train or a transmission. The gears in a transmission are analogous to the wheels in a crossed, belt pulley system. An advantage of gears is that the teeth of a gear prevent slippage. In transmissions with multiple gear ratios—such as bicycles, motorcycles, and cars—the term "gear" (e. g.,e "first gear") refers to a gear ratio rather than an actual physical gear. The term describes similar devices, even when the gear ratio is continuous rather than discrete, or when the device does not actually contain gears, as in a continuously variable transmission (CVT). Sometimes a CVT is referred to as an "infinitely variable transmission". Furthermore, a gear can mesh with a linear toothed part, called a rack, producing movement in a straight line instead of rotation (movement in a circle). See Rack and Pinion for an example.

The word gear is probably from Old Norse gørvi (plural gørvar) 'apparel, gear,' related to gøra, gørva 'to make, construct, build; set in order, prepare,' a common verb in Old Norse, "used in a wide range of situations from writing a book to dressing meat". In this context, the meaning of 'toothed wheel in machinery' first attested 1520s; specific mechanical sense of 'parts by which a motor communicates motion' is from 1814; specifically of a vehicle (bicycle, automobile, etc.) by 1888. A cog is a tooth on a wheel. From Middle English cogge, from Old Norse (compare Norwegian kugg ('cog'), Swedish kugg, kugge ('cog, tooth')), from Proto Germanic *kuggō (compare Dutch kogge ('cogboat'), German Kock), from Proto Indo European *gugā ('hump, ball') (compare Lithuanian gugà ('pommel, hump, hill'), from PIE *gēw ('to bend, arch'). First used c. 1300 in the sense of 'a wheel having teeth or cogs; late 14c., 'tooth on a wheel'; cog wheel, early 15c. Historically, cogs were teeth made of wood rather than metal, and a cogwheel technically consisted of a series of wooden gear teeth located around a mortise wheel, each tooth forming a type of specialised 'through' mortise and tenon joint. The wheel can be made of wood, cast iron, or other material. Wooden cogs were formerly used when large metal gears could not be cut, when the cast tooth was not even approximately of the proper shape, or the size of the wheel made manufacture impractical. The cogs were often made of maple wood. In 1967 the Thompson Manufacturing Company of Lancaster, New Hampshire still had a very active business in supplying tens of thousands of maple gear teeth per year, mostly for use in paper mills and grist mills, some dating back over 100 years. Since a wooden cog performs exactly the same function as a cast or machined metal tooth, the word was applied by extension to both, and the distinction has been generally lost.

The definite ratio that teeth give gears provides an advantage over other drives (such as traction drives and V belts) in precision machines such as watches that depend upon an exact velocity ratio. In cases where driver and follower are proximal, gears also have an advantage over other drives in the reduced number of parts required. The downside is that gears are more expensive to manufacture and their lubrication requirements may impose a higher operating cost per hour.

An external gear is one with the teeth formed on the outer surface of a cylinder or cone. Conversely, an internal gear is one with the teeth formed on the inner surface of a cylinder or cone. For bevel gears, an internal gear is one with the pitch angle exceeding 90 degrees. Internal gears do not cause output shaft direction reversal. No axial thrust is created by the tooth loads. Spur gears are excellent at moderate speeds but tend to be noisy at high speeds.

Helical or "dry fixed" gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling makes the tooth shape a segment of a helix. Helical gears can be meshed in parallel or crossed orientations. The former refers to when the shafts are parallel to each other; this is the most common orientation. In the latter, the shafts are non parallel, and in this configuration the gears are sometimes known as "skew gears". The angled teeth engage more gradually than do spur gear teeth, causing them to run more smoothly and quietly. With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel; a moving curve of contact then grows gradually across the tooth face to a maximum, then recedes until the teeth break contact at a single point on the opposite side. In spur gears, teeth suddenly meet at a line contact across their entire width, causing stress and noise. Spur gears make a characteristic whine at high speeds. For this reason spur gears are used in low speed applications and in situations where noise control is not a problem, and helical gears are used in high speed applications, large power transmission, or where noise abatement is important. The speed is considered high when the pitch line velocity exceeds 25 m/s. A disadvantage of helical gears is a resultant thrust along the axis of the gear, which must be accommodated by appropriate thrust bearings. However, this issue can be circumvented by using a herringbone gear or double helical gear, which has no axial thrust and also provides self aligning of the gears. This results in less axial thrust than a comparable spur gear. A second disadvantage of helical gears is also a greater degree of sliding friction between the meshing teeth, often addressed with additives in the lubricant.

Hypoid gears resemble spiral bevel gears except the shaft axes do not intersect. The pitch surfaces appear conical but, to compensate for the offset shaft, are in fact hyperboloids of revolution. Hypoid gears are almost always designed to operate with shafts at 90 degrees. Depending on which side the shaft is offset to, relative to the angling of the teeth, contact between hypoid gear teeth may be even smoother and more gradual than with spiral bevel gear teeth, but also have a sliding action along the meshing teeth as it rotates and therefore usually require some of the most viscous types of gear oil to avoid it being extruded from the mating tooth faces, the oil is normally designated HP (for hypoid) followed by a number denoting the viscosity. Also, the pinion can be designed with fewer teeth than a spiral bevel pinion, with the result that gear ratios of 60:1 and higher are feasible using a single set of hypoid gears. This style of gear is most common in motor vehicle drive trains, in concert with a differential. Whereas a regular (nonhypoid) ring and pinion gear set is suitable for many applications, it is not ideal for vehicle drive trains because it generates more noise and vibration than a hypoid does. Bringing hypoid gears to market for mass production applications was an engineering improvement of the 1920s.

Crown gears or contrate gears are a particular form of bevel gear whose teeth project at right angles to the plane of the wheel; in their orientation the teeth resemble the points on a crown. A crown gear can only mesh accurately with another bevel gear, although crown gears are sometimes seen meshing with spur gears. A crown gear is also sometimes meshed with an escapement such as found in mechanical clocks.

Worms resemble screws. A worm is meshed with a worm wheel, which looks similar to a spur gear. Worm and gear sets are a simple and compact way to achieve a high torque, low speed gear ratio. For example, helical gears are normally limited to gear ratios of less than 10:1 while worm and gear sets vary from 10:1 to 500:1. A disadvantage is the potential for considerable sliding action, leading to low efficiency. A worm gear is a species of helical gear, but its helix angle is usually somewhat large (close to 90 degrees) and its body is usually fairly long in the axial direction. These attributes give it screw like qualities. The distinction between a worm and a helical gear is that at least one tooth persists for a full rotation around the helix. If this occurs, it is a 'worm'; if not, it is a 'helical gear'. A worm may have as few as one tooth. If that tooth persists for several turns around the helix, the worm appears, superficially, to have more than one tooth, but what one in fact sees is the same tooth reappearing at intervals along the length of the worm. The usual screw nomenclature applies: a one toothed worm is called single thread or single start; a worm with more than one tooth is called multiple thread or multiple start. The helix angle of a worm is not usually specified. Instead, the lead angle, which is equal to 90 degrees minus the helix angle, is given. In a worm and gear set, the worm can always drive the gear. However, if the gear attempts to drive the worm, it may or may not succeed. Particularly if the lead angle is small, the gear's teeth may simply lock against the worm's teeth, because the force component circumferential to the worm is not sufficient to overcome friction. In traditional music boxes, however, the gear drives the worm, which has a large helix angle. This mesh drives the speed limiter vanes which are mounted on the worm shaft. Worm and gear sets that do lock are called self locking, which can be used to advantage, as when it is desired to set the position of a mechanism by turning the worm and then have the mechanism hold that position. An example is the machine head found on some types of stringed instruments. If the gear in a worm and gear set is an ordinary helical gear only a single point of contact is achieved. If medium to high power transmission is desired, the tooth shape of the gear is modified to achieve more intimate contact by making both gears partially envelop each other. This is done by making both concave and joining them at a saddle point; this is called a cone drive or "Double enveloping". Worm gears can be right or left handed, following the long established practice for screw threads.

Non circular gears are designed for special purposes. While a regular gear is optimized to transmit torque to another engaged member with minimum noise and wear and maximum efficiency, a non circular gear's main objective might be ratio variations, axle displacement oscillations and more. Common applications include textile machines, potentiometers and continuously variable transmissions.

A rack is a toothed bar or rod that can be thought of as a sector gear with an infinitely large radius of curvature. Torque can be converted to linear force by meshing a rack with a round gear called a pinion: the pinion turns, while the rack moves in a straight line. Such a mechanism is used in the steering of automobiles to convert the rotation of the steering wheel into the left to right motion of the tie rod(s) that are attached to the front wheels. Racks also feature in the theory of gear geometry, where, for instance, the tooth shape of an interchangeable set of gears may be specified for the rack (infinite radius), and the tooth shapes for gears of particular actual radii are then derived from that. The rack and pinion gear type is also used in a rack railway.

In epicyclic gearing, one or more of the gear axes moves. Examples are sun and planet gearing (see below), cycloidal drive, automatic transmissions, and mechanical differentials.

Sun and planet gearing is a method of converting reciprocating motion into rotary motion that was used in steam engines. James Watt used it on his early steam engines to get around the patent on the crank, but it also provided the advantage of increasing the flywheel speed so Watt could use a lighter flywheel. In the illustration, the sun is yellow, the planet red, the reciprocating arm is blue, the flywheel is green and the driveshaft is gray.

A harmonic gear or strain wave gear is a specialized gearing mechanism often used in industrial motion control, robotics and aerospace for its advantages over traditional gearing systems, including lack of backlash, compactness and high gear ratios. Though the diagram does not demonstrate the correct configuration, it is a "timing gear," conventionally with far more teeth than a traditional gear to ensure a higher degree of precision.

A cage gear, also called a lantern gear or lantern pinion, has cylindrical rods for teeth, parallel to the axle and arranged in a circle around it, much as the bars on a round bird cage or lantern. The assembly is held together by disks at each end, into which the tooth rods and axle are set. Cage gears are more efficient than solid pinions, and dirt can fall through the rods rather than becoming trapped and increasing wear. They can be constructed with very simple tools as the teeth are not formed by cutting or milling, but rather by drilling holes and inserting rods. Sometimes used in clocks, the cage gear should always be driven by a gearwheel, not used as the driver. The cage gear was not initially favoured by conservative clock makers. It became popular in turret clocks where dirty working conditions were most commonplace. Domestic American clock movements often used them.

All cogs of each gear component of magnetic gears act as a constant magnet with periodic alternation of opposite magnetic poles on mating surfaces. Gear components are mounted with a backlash capability similar to other mechanical gearings. Although they cannot exert as much force as a traditional gear due to limits on magnetic field strength, such gears work without touching and so are immune to wear, have very low noise, minimal power losses from friction and can slip without damage making them very reliable. They can be used in configurations that are not possible for gears that must be physically touching and can operate with a non metallic barrier completely separating the driving force from the load. The magnetic coupling can transmit force into a hermetically sealed enclosure without using a radial shaft seal, which may leak.

A profile is one side of a tooth in a cross section between the outside circle and the root circle. Usually a profile is the curve of intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane. The fillet curve (root fillet) is the concave portion of the tooth profile where it joins the bottom of the tooth space.2

As mentioned near the beginning of the article, the attainment of a nonfluctuating velocity ratio is dependent on the profile of the teeth. Friction and wear between two gears is also dependent on the tooth profile. There are a great many tooth profiles that provide constant velocity ratios. In many cases, given an arbitrary tooth shape, it is possible to develop a tooth profile for the mating gear that provides a constant velocity ratio. However, two constant velocity tooth profiles are the most commonly used in modern times: the cycloid and the involute. The cycloid was more common until the late 1800s. Since then, the involute has largely superseded it, particularly in drive train applications. The cycloid is in some ways the more interesting and flexible shape; however the involute has two advantages: it is easier to manufacture, and it permits the center to center spacing of the gears to vary over some range without ruining the constancy of the velocity ratio. Cycloidal gears only work properly if the center spacing is exactly right. Cycloidal gears are still used in mechanical clocks. An undercut is a condition in generated gear teeth when any part of the fillet curve lies inside of a line drawn tangent to the working profile at its point of juncture with the fillet. Undercut may be deliberately introduced to facilitate finishing operations. With undercut the fillet curve intersects the working profile. Without undercut the fillet curve and the working profile have a common tangent.

Numerous nonferrous alloys, cast irons, powder metallurgy and plastics can be used in the manufacture of gears. However, steels are most commonly used because of their high strength to weight ratio and low cost. Plastic is commonly used where cost or weight is a concern. A properly designed plastic gear can replace steel in many cases because it has many desirable properties, including dirt tolerance, low speed meshing, the ability to "skip" quite well and the ability to be made with materials that don't need additional lubrication. Manufacturers have used plastic gears to reduce costs in consumer items including copy machines, optical storage devices, cheap dynamos, consumer audio equipment, servo motors, and printers. Another advantage of the use of plastics, formerly (such as in the 1980s), was the reduction of repair costs for certain expensive machines. In cases of severe jamming (as of the paper in a printer), the plastic gear teeth would be torn free of their substrate, allowing the drive mechanism to then spin freely (instead of damaging itself by straining against the jam). This use of "sacrificial" gear teeth avoided destroying the much more expensive motor and related parts. This method has been superseded, in more recent designs, by the use of clutches and torque or current limited motors.

Although gears can be made with any pitch, for convenience and interchangeability standard pitches are frequently used. Pitch is a property associated with linear dimensions and so differs whether the standard values are in the imperial (inch) or metric systems. Using inch measurements, standard diametral pitch values with units of "per inch" are chosen; the diametrical pitch is the number of teeth on a gear of one inch pitch diameter. Common standard values for spur gears are 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 48, 64, 72, 80, 96, 100, 120, and 200. Certain standard pitches such as 1/10 and 1/20 in inch measurements, which mesh with linear rack, are actually (linear) circular pitch values with units of "inches" The preferred standard module values are 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 1.25, 1.5, 2.0, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40 and 50.

As of 2014, an estimated 80% of all gearing produced worldwide is produced by net shape molding. Molded gearing is usually either powder metallurgy or plastic. Many gears are done when they leave the mold (including injection molded plastic and die cast metal gears), but powdered metal gears require sintering, and sand castings or investment castings require gear cutting or other machining to finish them. The most common form of gear cutting is hobbing, but gear shaping, milling, and broaching also exist. 3D printing as a production method is expanding rapidly. For metal gears in the transmissions of cars and trucks, the teeth are heat treated to make them hard and more wear resistant while leaving the core soft and tough. For large gears that are prone to warp, a quench press is used.

Modern physics adopted the gear model in different ways. In the nineteenth century, James Clerk Maxwell developed a model of electromagnetism in which magnetic field lines were rotating tubes of incompressible fluid. Maxwell used a gear wheel and called it an "idle wheel" to explain the electric current as a rotation of particles in opposite directions to that of the rotating field lines. More recently, quantum physics uses "quantum gears" in their model. A group of gears can serve as a model for several different systems, such as an artificially constructed nanomechanical device or a group of ring molecules. The three wave hypothesis compares the wave–particle duality to a bevel gear.

The gear mechanism was previously considered exclusively artificial, but as early as 1957, gears had been recognized in the hind legs of various species of planthoppers and scientists from the University of Cambridge characterized their functional significance in 2013 by doing high speed photography of the nymphs of Issus coleoptratus at Cambridge University. These gears are found only in the nymph forms of all planthoppers, and are lost during the final molt to the adult stage. In I. coleoptratus, each leg has a 400 micrometer strip of teeth, pitch radius 200 micrometers, with 10 to 12 fully interlocking spur type gear teeth, including filleted curves at the base of each tooth to reduce the risk of shearing. The joint rotates like mechanical gears, and synchronizes Issus's hind legs when it jumps to within 30 microseconds, preventing yaw rotation. The gears are not connected all the time. One is located on each of the juvenile insect's hind legs, and when it prepares to jump, the two sets of teeth lock together. As a result, the legs move in almost perfect unison, giving the insect more power as the gears rotate to their stopping point and then unlock.