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The term "backlash" can also be used to refer to the size of the gap, not just the phenomenon it causes; thus, one could speak of a pair of gears as having, for example, "0.1 mm of backlash." A pair of gears could be designed to have zero backlash, but this would presuppose perfection in manufacturing, uniform thermal expansion characteristics throughout the system, and no lubricant. Therefore, gear pairs are designed to have some backlash. It is usually provided by reducing the tooth thickness of each gear by half the desired gap distance. In the case of a large gear and a small pinion, however, the backlash is usually taken entirely off the gear and the pinion is given full sized teeth. Backlash can also be provided by moving the gears further apart. The backlash of a
1017:
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392:
133:
338:
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312:
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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
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1271:
612:
48:
1512:) axial force on each gear is zero when the gears are aligned correctly. If the gears become misaligned in the axial direction, the unstable arrangement generates a net force that may lead to disassembly of the gear train, while the stable arrangement generates a net corrective force. If the direction of rotation is reversed, the direction of the axial thrusts is also reversed, so a stable configuration becomes unstable, and vice versa.
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1572:
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
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1960:
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525:'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.
2011:
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free to rotate about the shaft, but with springs between the two-halves providing relative torque between them, so that one achieves, in effect, a single gear with expanding teeth. Another method involves tapering the teeth in the axial direction and letting the gear slide in the axial direction to take up slack.
1114:. 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.
2591:
of each gear tooth count equals 1, e.g. GCD(16,25)=1; if a 1:1 gear ratio is desired a relatively prime gear may be inserted in between the two gears; this maintains the 1:1 ratio but reverses the gear direction; a second relatively prime gear could also be inserted to restore the original rotational
1721:
Sometimes used in clocks, a 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
1717:
is one of those artisanal 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
1480:
Double helical gears overcome the problem of axial thrust presented by single helical gears by using a double set of teeth, slanted in opposite directions. A double helical gear can be thought of as two mirrored helical gears mounted closely together on a common axle. This arrangement cancels out the
1438:
Quite commonly, helical gears are used with the helix angle of one having the negative of the helix angle of the other; such a pair might also be referred to as having a right-handed helix and a left-handed helix of equal angles. The two equal but opposite angles add to zero: the angle between shafts
1848:
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
1278:
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
948:
tooth faces; each set will be effective only while the torque has one specific sense, and the two sets can be analyzed independently of the other. However, in this case the gear usually has also "flip over" symmetry, so that the two sets of tooth faces are congruent after the gear is flipped. This
690:
don't need lubrication. Plastic gears may even be intentionally designed to be the weakest part in a mechanism, so that in case of jamming they will fail first and thus avoid damage to more expensive parts. Such sacrificial gears may be a simpler alternative to other overload-protection devices such
4459:
is the error in motion that occurs when gears change direction. It exists because there is always some gap between the trailing face of the driving tooth and the leading face of the tooth behind it on the driven gear, and that gap must be closed before force can be transferred in the new direction.
1793:
Spiral bevel gears have the same advantages and disadvantages relative to their straight-cut cousins as helical gears do to spur gears, such as lower noise and vibration. Simplified calculated bevel gears on the basis of an equivalent cylindrical gear in normal section with an involute tooth form
1567:
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
1451:
at right angles, the helix angles are of the same hand because they must add to 90 degrees. (This is the case with the gears in the illustration above: they mesh correctly in the crossed configuration: for the parallel configuration, one of the helix angles should be reversed. The gears illustrated
1063:
If the two gears are sliced by an imaginary sphere whose center is the point where the two axes cross, each section will remain on the surface of that sphere as the gear rotates, and the section of one gear will interact only with the corresponding section of the other gear. In this way, a pair of
4528:
to avoid confusion with the metric module. Module is a direct dimension ("millimeters per tooth"), unlike diametrical pitch, which is an inverse dimension ("teeth per inch"). Thus, if the pitch diameter of a gear is 40 mm and the number of teeth 20, the module is 2, which means that there are
4467:
For situations that require precision, such as instrumentation and control, backlash can be minimized through one of several techniques. For instance, the gear can be split along a plane perpendicular to the axis, one half fixed to the shaft in the usual manner, the other half placed alongside it,
2757:
The complement of the angle between the direction that the teeth exert force on each other, and the line joining the centers of the two gears. For involute gears, the teeth always exert force along the line of action, which, for involute gears, is a straight line; and thus, for involute gears, the
1507:
For both possible rotational directions, there exist two possible arrangements for the oppositely-oriented helical gears or gear faces. One arrangement is called stable, and the other unstable. In a stable arrangement, the helical gear faces are oriented so that each axial force is directed toward
855:
One major advantage of gears is that their rigid body and the snug interlocking of the teeth ensure precise tracking of the rotation acros the gear train, limited only by backlash and other mechanical defects. For this reason they are favored in precision applications such as watches. Gear trains
2079:
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
2001:
Most gears are ideally rigid bodies which transmit torque and movement through the lever principle and contact forces between the teeth. Namely, the torque applied to one gear causes it to rotate as rigid body, so that its teeth push against those of the matched gear, which in turn rotates as a
1104:
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
4611:
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,
863:
than the equivalent pulleys. More importantly, the distance between the axes of matched gears is limited and cannot be changed once they are manufactured. There are also applications where slippage under overload or transients (as occurs with belts, hydraulics, and friction wheels) is not only
4157:
Linear pitch in an axial plane and in a pitch surface. In helical gears and worms, axial pitch has the same value at all diameters. In gearing of other types, axial pitch may be confined to the pitch surface and may be a circular measurement. The term axial pitch is preferred to the term linear
4028:
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
1617:
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
1181:
Gear teeth typically extend across the whole thickness of the gear. Another criterion for classifying gears is the general direction of the teeth across that dimension. This attribute is affected by the relative position and direction of the axes or rotation of the gears that are to be meshed
1757:
Cycloidal gears were 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
1007:
If the two gears are cut by an imaginary plane perpendicular to the axes, each section of one gear will interact only with the corresponding section of the other gear. Thus the three-dimensional gear train can be understood as a stack of gears that are flat and infinitesimally thin — that is,
2228:
A predefined diametral position on the gear where the circular tooth thickness, pressure angle and helix angles are defined. The standard pitch diameter is a design dimension and cannot be measured, but is a location where other measurements are made. Its value is based on the number of teeth
1571:
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
1312:
For a "crossed" or "skew" configuration, the gears must have the same pressure angle and normal pitch; however, the helix angle and handedness can be different. The relationship between the two shafts is actually defined by the helix angle(s) of the two shafts and the handedness, as defined:
983:
Actual gears deviate from this model in many ways: they are not perfectly rigid, their mounting does not ensure that the rotation axis will be perfectly fixed in space, the teeth may have slightly different shapes and spacing, the tooth faces are not perfectly smooth, and so on. Yet, these
3553:
The number of angular pitches through which a tooth surface rotates from the beginning to the end of contact. In a simple way, it can be defined as a measure of the average number of teeth in contact during the period during which a tooth comes and goes out of contact with the mating
1676:
The teeth of antique or artisanal gears that were cut by hand from sheet material, like those in the
Antikhytera mechanism, generally had simple profiles, such as triangles. The teeth of larger gears — such as used in windmills — were usually pegs with simple shapes like cylinders,
1481:
net axial thrust, since each half of the gear thrusts in the opposite direction, resulting in a net axial force of zero. This arrangement can also remove the need for thrust bearings. However, double helical gears are more difficult to manufacture due to their more complicated shape.
299:. In all those cases, terms like "first gear", "high gear", and "reverse gear" refer to the overall torque ratios of different meshing configurations, rather than to specific physical gears. These terms may be applied even when the vehicle does not actually contain gears, as in a
3977:
Measurement of the distance across several teeth in a normal plane. As long as the measuring device has parallel measuring surfaces that contact on an unmodified portion of the involute, the measurement wis along a line tangent to the base cylinder. It is used to determine tooth
3389:
4097:
4177:
An involute helical gear is the base pitch in the normal plane. It is the normal distance between parallel helical involute surfaces on the plane of action in the normal plane, or is the length of arc on the normal base helix. It is a constant distance in any helical involute
3879:
3831:
1758:
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 commonly used in mechanical clocks.
1904:
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direction while maintaining uniform wear with all 4 gears in this case. Mechanical engineers, at least in continental Europe, usually use the module instead of circular pitch. The module, just like the circular pitch, can be used for all types of cogs, not just
5105:
3377:
3804:
Diameter on a gear at which the line of action intersects the maximum (or minimum for internal pinion) addendum circle of the mating gear. This is also referred to as the start of active profile, the start of contact, the end of contact, or the end of active
4197:
In an involute gear, the pitch is on the base circle or along the line of action. Corresponding sides of involute gear teeth are parallel curves, and the base pitch is the constant and fundamental distance between them along a common normal in a transverse
290:
or "gearbox" containing a set of gears that can be meshed in multiple configurations. The gearbox lets the operator vary the torque that is applied to the wheels without changing the engine's speed. Gearboxes are used also in many other machines, such as
2200:, however, the tooth-to-tooth force is always directed along the same line—that is, the line of action is constant. This implies that for involute gears the path of contact is also a straight line, coincident with the line of action—as is indeed the case.
414:
Another early surviving example of geared mechanism is a complex calendrical device showing the phase of the Moon, the day of the month and the places of the Sun and the Moon in the Zodiac was invented in the
Byzantine empire in the early 6th century AD.
4548:
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.
1211:
The teeth can be either internal or external. Two spur gears mesh together correctly only if fitted to parallel shafts. No axial thrust is created by the tooth loads. Spur gears are excellent at moderate speeds but tend to be noisy at high speeds.
1109:
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
1778:
shapes. These include
Gleason types (circular arc with non-constant tooth depth), Oerlikon and Curvex types (circular arc with constant tooth depth), Klingelnberg Cyclo-Palloid (Epicycloid with constant tooth depth) or Klingelnberg Palloid.
1718:
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.
1257:
gear the tooth walls are not parallel to the axis of rotation, but are set at an angle. An imaginary pitch surface (cylinder, cone, or hyperboloid, depending on the relative axis positions) intersects each tooth face along an arc of an
1266:
or 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".
1128:
3475:
The locus of successive contact points between a pair of gear teeth, during the phase of engagement. For conjugate gear teeth, the path of action passes through the pitch point. It is the trace of the surface of action in the plane of
2195:
Line along which the force between two meshing gear teeth is directed. It has the same direction as the force vector. In general, the line of action changes from moment to moment during the period of engagement of a pair of teeth. For
1000:
In the most common configuration, the axes of rotation of the two gears are parallel, and usually their sizes are such that they contact near a point between the two axes. In this configuration, the two gears turn in opposite senses.
2113:
705:
In spite of the advantages of metal and plastic, wood continued to be used for large gears until a couple of centuries ago, because of cost, weight, tradition, or other considerations. In 1967 the
Thompson Manufacturing Company of
2080:
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
1487:
are a special type of helical gears. They do not have a groove in the middle like some other double helical gears do; the two mirrored helical gears are joined so that their teeth form a V shape. This can also be applied to
2705:
4278:
4049:
is the distance between a point on one tooth and the corresponding point on an adjacent tooth. It is a dimension measured along a line or curve in the transverse, normal, or axial directions. The use of the single word
964:
of one of its tooth faces. At that moment and at those points, the two faces must have the same perpendicular direction but opposite orientation. But since the two gears are rotating around different axes, the points
3646:
856:
also can have fewer separate parts (only two) and have minimal power loss, minimal wear, and long life. Gears are also often the most efficient and compact way of transmitting torque between two non-parallel axes.
3817:
Distance on a pitch circle through which a helical or spiral tooth moves from the position at which contact begins at one end of the tooth trace on the pitch surface to the position where contact ceases at the other
2716:
In cylindrical gears, cylinder formed by projecting a pitch circle in the axial direction. More generally, the surface formed by the sum of all the pitch circles as one moves along the axis. For bevel gears it is a
4496:
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
1595:. 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
3793:
2582:
to create an even contact between every cog of both wheels, and thereby avoid unnecessary wear and damage. An even uniform gear wear is achieved by ensuring the tooth counts of the two gears meshing together are
5964:
3033:
Ratio of the number of teeth to the pitch diameter. Could be measured in teeth per inch or teeth per centimeter, but conventionally has units of per inch of diameter. Where the module, m, is in metric units
3510:
The curve on either tooth surface along which theoretical single point contact occurs during the engagement of gears with crowned tooth surfaces or gears that normally engage with only single point contact.
1688:
Because of their sub-optimal profile, the effective gear ratio of such artisanal matching gears was not constant, but fluctuated over each tooth cycle, resulting in vibrations, noise, and accelerated wear.
1434:
is the helix angle for the gear. The crossed configuration is less mechanically sound because there is only a point contact between the gears, whereas in the parallel configuration there is a line contact.
4357:
3567:
The contact ratio in a transverse plane. It is the ratio of the angle of action to the angular pitch. For involute gears it is most directly obtained as the ratio of the length of action to the base pitch.
2218:
Circle centered on and perpendicular to the axis, and passing through the pitch point. A predefined diametral position on the gear where the circular tooth thickness, pressure angle and helix angles are
1733:
There is an infinite variety of tooth profiles that will achieve this goal. In fact, given a fairly arbitrary tooth shape, it is possible to develop a tooth profile for the mating gear that will do it.
2916:
140:
Gears are among the most common mechanical parts. They come in a great variety of shapes and materials, and are used for many different functions and applications. Diameters may range from a few
4529:
2 mm of pitch diameter for each tooth. 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.
824:; however, this alternative is typically used only for prototypes or very limited production quantities, because of its high cost, low accuracy, and relatively low strength of the resulting part.
4556:
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.
3939:
Length of the chord that subtends a circular thickness arc in the plane normal to the pitch helix. Any convenient measuring diameter may be selected, not necessarily the standard pitch diameter.
3706:
3027:
2375:
2324:
2049:
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.
6049:
2564:
656:. Steel is most commonly used because of its high strength-to-weight ratio and low cost. Aluminum is not as strong as steel for the same geometry, but is lighter and easier to machine.
2858:
929:
If the gear is meant to transmit or receive torque with a definite sense only (clockwise or counterclockwise with respect to some reference viewpoint), the action surface consists of
1408:
1360:
4405:
3945:
Height from the top of the tooth to the chord subtending the circular thickness arc. Any convenient measuring diameter may be selected, not necessarily the standard pitch diameter.
1208:, the tooth faces are straight along the direction parallel to the axis of rotation. Any imaginary cylinder with the same axis will cut the teeth along parallel straight lines.
3268:
Distance from any point on a thread to the corresponding point on the adjacent thread, measured parallel to the axis. For a single-thread worm, lead and linear pitch are the same.
3070:
2495:
2435:
4437:
3245:
1606:, 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
880:
that is fixed in space, without sliding along it. Thus, each point of the gear can move only along a circle that is perpendicular to its axis and centered on it. At any moment
686:
have been replacing metals in many applications, especially those with moderate speed and torque. They are not as strong as steel, but are cheaper, can be mass-manufactured by
637:, were commonly made of wood rather than metal. They were cogwheels, made by inserting a series of wooden pegs or cogs around the rim of a wheel. The cogs were often made of
4524:. The term module is understood to mean the pitch diameter in millimetres divided by the number of teeth. When the module is based upon inch measurements, it is known as the
5319:
4054:
without qualification may be ambiguous, and for this reason it is preferable to use specific designations such as transverse circular pitch, normal base pitch, axial pitch.
1973:
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
6154:
1060:
Independently of the angle between the axes, the larger of two unequal matching bevel gears may be internal or external, depending the desired relative sense of rotation.
3289:
3500:
For involute, parallel-axis gears with either spur or helical teeth, is the rectangular area in the plane of action bounded by the length of action and the effective
2753:
5288:
3580:
The contact ratio in an axial plane, or the ratio of the face width to the axial pitch. For bevel and hypoid gears it is the ratio of face advance to circular pitch.
3158:
the Angle between a tangent to the helix and the gear axis. It is zero in the limiting case of a spur gear, albeit it can considered as the hypotenuse angle as well.
3082:
In involute gears, the tooth profile is generated by the involute of the base circle. The radius of the base circle is somewhat smaller than that of the pitch circle
1432:
3488:
The imaginary surface in which contact occurs between two engaging tooth surfaces. It is the summation of the paths of action in all sections of the engaging teeth.
3321:
3186:
3154:
3110:
2945:
2786:
2269:
4476:
Although gears can be made with any pitch, for convenience and interchangeability standard pitches are frequently used. Pitch is a property associated with linear
349:
mentions gears around 330 BC, as wheel drives in windlasses. He observed that the direction of rotation is reversed when one gear wheel drives another gear wheel.
3961:
Displacement of the tool datum line from the reference cylinder, made non-dimensional by dividing by the normal module. It is used to specify the tooth thickness.
3967:
Measurement of the distance taken over a pin positioned in a tooth space and a reference surface. The reference surface may be the reference axis of the gear, a
4983:
475:. It had seven faces and 107 moving parts; it showed the positions of the sun, the moon and the five planets then known, as well as religious feast days. The
5663:
468:
4585:
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
3293:
Angle between a tangent to the helix and a plane perpendicular to the axis. Note that the complement of the helix angle is usually given for helical gears.
1730:
In most modern gears, the tooth profile is usually not straight or circular, but of special form designed to achieve a constant angular velocity ratio.
1649:, the shape of the cross-section of a tooth face by an imaginary cut perpendicular to the pitch surface, such as the transverse, normal, or axial plane.
1508:
the center of the gear. In an unstable arrangement, both axial forces are directed away from the center of the gear. In either arrangement, the total (or
980:
On the other hand, at any given moment there is at least one such pair of contact points; usually more than one, even a whole line or surface of contact.
3955:
from the reference cylinder, made non-dimensional by dividing by the normal module. It is used to specify the tooth thickness, often for zero backlash.
4599:
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
2607:
6682:
5039:
4215:
3534:
The arc of the pitch circle through which a tooth profile moves from its beginning of contact until the point of contact arrives at the pitch point.
3114:
In involute gears, distance from one face of a tooth to the corresponding face of an adjacent tooth on the same gear, measured along the base circle
1837:: 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
1472:
766:
molding. Molded gearing is usually powder metallurgy, plastic injection, or metal die casting. Gears produced by powder metallurgy often require a
6231:
5366:
4850:
4821:
Shuailong Zhang, Mohamed
Elsayed, Ran Peng, Yujie Chen (2021): "Reconfigurable multi-component micromachines driven by optoelectronic tweezers".
2723:
Angle with vertex at the gear center, one leg on the point where mating teeth first make contact, the other leg on the point where they disengage.
1808:
1599:, 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.
2071:
pair there is no contact between the two members; the torque is instead transmitted through magnetic fields. The cogs of each gear are constant
117:
or other rotating parts and/or to change the axis of rotation and/or to invert the sense of rotation. A gear may also be used to transmit linear
3598:
3325:
Same as described earlier in this list. Note that for a worm it is still measured in a plane perpendicular to the gear axis, not a tilted plane.
992:
One criterion for classifying gears is the relative position and direction of the axes or rotation of the gears that are to be meshed together.
82:
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 cavities
4603:, each leg has a 400-micrometer strip of teeth, pitch radius 200 micrometers, with 10 to 12 fully interlocking spur-type gear teeth, including
1742:
However, two constant velocity tooth profiles are the most commonly used in modern times for gears with parallel or crossed axes, based on the
5578:
6243:
6208:
6185:
6164:
5792:
5496:
5423:
1588:. 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.
3971:
or either one or two pins positioned in the tooth space or spaces opposite the first. This measurement is used to determine tooth thickness.
3725:
1302:, which has no axial thrust - and also provides self-aligning of the gears. This results in less axial thrust than a comparable spur gear.
488:
However, the oldest functioning gears by far were created by Nature, and are seen in the hind legs of the nymphs of the planthopper insect
603:('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.
5385:
6074:
283:. Depending on the geometry of the pair, the sense of rotation may also be inverted (from clockwise to anti-clockwise , or vice-versa).
6029:
1016:
1004:
Occasionally the axes are parallel but one gear is nested inside the other. In this configuration, both gears turn in the same sense.
906:. All other parts of the surface are irrelevant (except that they cannot be crossed by any part of the matching gear). In a gear with
6528:
6059:
5834:
5741:
3250:
Several other helix parameters can be viewed either in the normal or transverse planes. The subscript n usually indicates the normal.
1990:
300:
6291:
4300:
2970:
Distance from one face of a tooth to the corresponding face of an adjacent tooth on the same gear, measured along the pitch circle.
1136:
3262:
Distance from any point on a thread to the corresponding point on the next turn of the same thread, measured parallel to the axis.
180:. Most gears are round and have equal teeth, designed to operate as smoothly as possible; but there are several applications for
6508:
4647:
4145:
Circular pitch in the normal plane, and also the length of the arc along the normal pitch helix between helical teeth or threads.
2578:
are the number of cogs (teeth) for each of the two wheels (gears). These numbers (or at least one of them) is often chosen among
1892:
1111:
671:
Still, because of cost or other considerations, some early metal gears had wooden cogs, each tooth forming a type of specialised
482:
408:
3482:
The path of action for involute gears. It is the straight line passing through the pitch point and tangent to both base circles.
2871:
1031:
arrangement, the axes of rotation of the two gears are not parallel but cross at an arbitrary angle except zero or 180 degrees.
6367:
3525:
The arc of the pitch circle through which a tooth profile moves from the beginning to the end of contact with a mating profile.
3494:
The surface of action for involute, parallel axis gears with either spur or helical teeth. It is tangent to the base cylinders.
472:
411:
connected to the wheels and to a pointer on top of the chariot kept the direction of latter unchanged as the chariot turned.
6054:
2949:
The distance from the top of the tooth to the root; it is equal to addendum plus dedendum or to working depth plus clearance.
6104:
5759:
3866:
859:
On the other hand, gears are more expensive to manufacture, may require periodic lubrication, and may have greater mass and
5289:"Plastic gears are more reliable when engineers account for material properties and manufacturing processes during design."
4607:
curves at the base of each tooth to reduce the risk of shearing. The joint rotates like mechanical gears, and synchronizes
6297:
5296:
3921:
Circular thickness in the normal plane. In a helical gear it may be considered as the length of arc along a normal helix.
3652:
2983:
902:
of the gear consists of all points of its surface that, in normal operation, may contact the matching gear with positive
210:
to decrease. The opposite effect is obtained when a large gear drives a small one. The changes are proportional to the
6675:
3842:
2394:, mechanical engineers usually use a scaling factor that replaces it with a regular value instead. This is known as the
400:
132:
1501:
1227:. Such gears are generally used only at speeds below 5 m/s (1000 ft/min), or, for small gears, 1000 r.p.m.
391:
4842:
1652:
The tooth profile is crucial for the smoothness and uniformity of the movement of matching gears, as well as for the
2329:
2276:
164:
in some mining equipment. Other types of parts that are somewhat similar in shape and function to gears include the
6263:
4987:
3933:
In involute teeth, length of arc on the base circle between the two involute curves forming the profile of a tooth.
3543:
The arc of the pitch circle through which a tooth profile moves from contact at the pitch point until contact ends.
3516:
The distance on the line of action through which the point of contact moves during the action of the tooth profile.
3388:
2507:
2046:
for its advantages over traditional gearing systems, including lack of backlash, compactness and high gear ratios.
5130:
4845:"MY GEAR is Bigger than YOUR GEAR: Industry Battles it Out for World’s Largest Gear Title"]. Online article from
4564:
3890:
2602:
Diameters determined from the number of teeth and the center distance at which gears operate. Example for pinion:
1515:
Stable double helical gears can be directly interchanged with spur gears without any need for different bearings.
6649:
2101:
667:
A cast gearwheel (above) meshing with a cogged mortise wheel (below). The wooden cogs are held in place by nails.
476:
5339:
1685:
inserted into a smooth wooden or metal wheel; or were holes with equally simple shapes cut into such a wheel.
710:
still had a very active business in supplying tens of thousands of maple gear teeth per year, mostly for use in
6279:
Kravchenko A.I., Bovda A.M. Gear with magnetic couple. Pat. of
Ukraine N. 56700 – Bul. N. 2, 2011 – F16H 49/00.
5709:
Kravchenko A.I., Bovda A.M. Gear with magnetic couple. Pat. of
Ukraine N. 56700 – Bul. N. 2, 2011 – F16H 49/00.
4025:
2808:
798:
791:
707:
287:
4735:
1367:
1319:
1105:
faces, the oil is normally designated HP (for hypoid) followed by a number denoting the viscosity. Also, the
6668:
6503:
4902:
4652:
4590:
4377:
3854:
2588:
2075:
with periodic alternation of opposite magnetic poles on mating surfaces. Gear components are mounted with a
1940:, but it also provided the advantage of increasing the flywheel speed so Watt could use a lighter flywheel.
751:
4919:
4114:
Arc distance along a specified pitch circle or pitch line between corresponding profiles of adjacent teeth.
1091:
In this case, the best shape for each pitch surface is neither cylindrical nor conical but a portion of a
4691:
4451:
4096:
3039:
2462:
2130:
2076:
1888:
950:
404:
6131:
5454:
2407:
5680:
Giorgio
Figliolini, Jorge Angeles (2005): "Algorithms for Involute and Octoidal Bevel-Gear Generation".
5327:(2nd ed.). Boca Raton, FL.: CRC Press, an imprint of Taylor & Francis Group. pp. 691, 702.
4864:"Levers - Moments, levers and gears - AQA - GCSE Physics (Single Science) Revision - AQA - BBC Bitesize"
4560:
4410:
4084:
3878:
3202:
1974:
1169:
is one whose teeth project at right angles to the plane. A crown gear is also sometimes meshed with an
832:
Besides gear trains, other alternative methods of transmitting torque between non-coaxial parts include
593:
377:
362:
337:
31:
5718:
ISO/DIS 21771:2007 : "Gears – Cylindrical Involute Gears and Gear Pairs – Concepts and Geometry",
5392:, Tennessee Tech University, Department of Mechanical Engineering, ME 362 lecture notes, archived from
4754:
4464:
equals the sum of the backlash of each pair of gears, so in long trains backlash can become a problem.
4035:
or fillet curve, the concave portion of the tooth profile where it joins the bottom of the tooth space.
3830:
3720:
For bevel gears, the square root of the sum of the squares of the transverse and face contact ratios.
1783:
6571:
6079:
5997:
5976:
5919:
5869:
5013:
4593:
characterized their functional significance in 2013 by doing high-speed photography of the nymphs of
3927:
In helical gears and worms, tooth thickness in an axial cross section at the standard pitch diameter.
2002:
rigid body transmitting the torque to its axle. Some specialized gear escape this pattern, however.
1921:
541:
196:
5488:
3412:
1794:
show a deviant tooth form with reduced tooth strength by 10-28% without offset and 45% with offset.
1664:
1443:. Where the sum or the difference (as described in the equations above) is not zero, the shafts are
984:
deviations from the ideal model can be ignored for a basic analysis of the operation of a gear set.
6415:
6410:
6360:
5827:
Innovation in Maxwell's Electromagnetic Theory: Molecular Vortices, Displacement Current, and Light
5667:
5584:
5411:
4541:
3424:
2030:
2019:
1917:
1912:
1880:
1826:
1629:
Worm gears can be right or left-handed, following the long-established practice for screw threads.
1611:
915:
787:
683:
679:
663:
585:
457:
39:
3376:
3340:
973:
are moving along different circles; therefore, the contact cannot last more than one instant, and
86:
on the part, or separate pegs inserted into it. In the latter case, the gear is usually called a
6777:
6639:
6010:
5885:
5859:
5273:
4707:
4629:
4604:
4595:
4029:
working profile. Without undercut the fillet curve and the working profile have a common tangent.
2442:
2143:
1215:
For arrangements with crossed non-parallel axes, the faces in a straight-cut gear are parts of a
860:
845:
739:
727:
548:
490:
354:
353:
was one of the first who used gears in water raising devices. Gears appear in works connected to
350:
6325:
5166:
5080:
5014:"World's first computer, the Antikythera Mechanism, 'started up' in 178 B.C., scientists claim"
4512:
When gear dimensions are in the metric system the pitch specification is generally in terms of
4072:
3448:
3436:
3364:
3352:
960:
of each tooth face will at some moment contact a tooth face of the matching gear at some point
322:
The earliest surviving gears date from the 4th century BC in China (Zhan Guo times – Late East
6715:
6629:
6456:
6425:
6405:
6287:
6239:
6204:
6181:
6160:
6034:
6002:
5904:
5830:
5788:
5737:
5492:
5419:
5393:
5154:
4158:
pitch. The axial pitch of a helical worm and the circular pitch of its worm gear are the same.
3274:
2391:
2136:
2089:
2081:
2058:
1968:
1937:
1870:
1775:
1497:
1270:
937:; which have the same shape and are positioned in the same way relative to the axis, spaced 1/
841:
747:
743:
687:
672:
657:
611:
578:
311:
181:
47:
5147:
3400:
3199:
Circular pitch in the plane of rotation of the gear. Sometimes just called "circular pitch".
2738:
1774:
For non-parallel axes with non-straight tooth cuts, the best tooth profile is one of several
1283:
is important. The speed is considered high when the pitch line velocity exceeds 25 m/s.
1151:
otherwise. In a pair of matching wheels, only one of them (the larger one) may be internal.
6466:
6326:
Short historical account on the application of analytical geometry to the form of gear teeth
5992:
5984:
5877:
5850:
MacKinnon, Angus (2002). "Quantum Gears: A Simple Mechanical System in the Quantum Regime".
5685:
5480:
4965:
4826:
4545:
2584:
1876:
1682:
1484:
1417:
1306:
1295:
567:
419:
204:
110:
6275:
Scientific and Technical Information Branch, NASA-RP-1152; AVSCOM Technical Report 84-C-15.
4906:
4863:
4805:
3299:
3164:
3139:
3088:
2923:
2764:
2254:
1943:
In the illustration, the sun is yellow, the planet red, the reciprocating arm is blue, the
1807:
6746:
6710:
6523:
6420:
6400:
5106:"The Portable Byzantine Sundial Calendar: The Second Oldest Geared Mechanism in Existence"
4789:
4657:
4612:
giving the insect more power as the gears rotate to their stopping point and then unlock.
4553:
4456:
3996:
Teeth in which the working depth is less than 2.000 divided by the normal diametral pitch.
1884:
1816:
1787:
1280:
1216:
944:
If the torque on each gear may have both senses, the action surface will have two sets of
806:
366:
145:
126:
71:
5481:
5267:
1825:
is a toothed bar or rod that can be thought of as a sector gear with an infinitely large
949:
arrangement ensures that the two gears are firmly locked together, at all times, with no
5980:
5923:
5873:
6772:
6705:
6691:
6533:
6353:
6330:
5808:
5063:
4537:
4492:
measurements, standard diametral pitch values with units of "per inch" are chosen; the
4481:
2732:
2035:
1838:
1782:
The tooth faces in these gear types are not involute cylinders or cones but patches of
1678:
1291:
1064:
meshed 3D gears can be understood as a stack of nested infinitely thin cup-like gears.
837:
778:
to shape the teeth to the necessary precision. The most common form of gear cutting is
626:, and the earliest surviving Chinese gears are made of iron, These metals, as well as
559:
533:
327:
157:
4623:
3968:
1861:
6766:
6513:
6482:
5881:
5407:
4969:
4485:
2197:
2085:
2062:
1986:
1925:
1750:
1544:
885:
802:
296:
6014:
5889:
4575:
3990:
Teeth in which the working depth equals 2.000 divided by the normal diametral pitch.
3906:
1903:
1523:
94:
may be one of those pegs or the whole gear. Two or more meshing gears are called a
6487:
1929:
1850:
1744:
1619:
1607:
1249:
1190:
814:
783:
771:
755:
735:
694:
381:
323:
185:
5272:(6th, illus. ed.). Lexington, MA; Philadelphia, PA: George B. Grant. p.
4843:
https://www.geartechnology.com/ext/resources/issues/0313x/worlds_largest_gears.pdf
4723:
4675:
1701:
Cage gear in Pantigo Windmill, Long Island (with the driving gearwheel disengaged)
977:
will then either slide across the other face, or stop contacting it altogether.
6175:
5766:
4770:
4060:
479:, built in 1386, it is the world's oldest still working geared mechanical clock.
6725:
6720:
6634:
6594:
6316:- antique and vintage gears, sprockets, ratchets and other gear-related objects.
6214:
6150:
5655:
5143:
4586:
3952:
2961:
Depth of engagement of two gears, that is, the sum of their operating addendums.
2446:
1982:
1959:
1766:
1493:
1097:
1092:
1049:
Bevel gears with equal numbers of teeth and shaft axes at 90 degrees are called
849:
821:
731:
715:
446:
358:
316:
177:
173:
122:
4830:
2955:
Distance between the root circle of a gear and the addendum circle of its mate.
2700:{\displaystyle d_{w}={\frac {2a}{u+1}}={\frac {2a}{{\frac {z_{2}}{z_{1}}}+1}}.}
2010:
6730:
6614:
6561:
6518:
6451:
6446:
6395:
6319:
4619:
4461:
4273:{\displaystyle P_{\rm {d}}={\frac {N}{d}}={\frac {25.4}{m}}={\frac {\pi }{p}}}
3501:
1948:
1933:
1833:
can be converted to linear force by meshing a rack with a round gear called a
1540:
1489:
1461:
1456:
1224:
1170:
1161:
1035:
919:
873:
833:
762:
As of 2014, an estimated 80% of all gearing produced worldwide is produced by
711:
634:
574:
461:
380:
an example of a very early and intricate geared device, designed to calculate
373:
169:
149:
141:
95:
27:
Rotating circular machine part with teeth that mesh with another toothed part
17:
6644:
6624:
6619:
6441:
6390:
6109:
5988:
5965:"Interacting Gears Synchronize Propulsive Leg Movements in a Jumping Insect"
4477:
2805:
Radial distance from the pitch surface to the outermost point of the tooth.
2171:. In the case of worms, it is the number of thread starts that the worm has.
2120:
2043:
1669:
1596:
1561:
1309:
between the meshing teeth, often addressed with additives in the lubricant.
1200:
1101:
for short. Hypoid gears are most commonly found with shafts at 90 degrees.
1085:
1021:
810:
775:
767:
763:
645:
616:
537:
507:
453:
430:
346:
83:
52:
6006:
1637:
1235:
5241:
3641:{\displaystyle \epsilon _{\gamma }=\epsilon _{\alpha }+\epsilon _{\beta }}
630:, have been generally used for clocks and similar mechanisms to this day.
6586:
6576:
6566:
5864:
5732:
Gunnar Dahlvig (1982), "Construction elements and machine construction",
4885:
4642:
4637:
4505:
in inch measurements, which mesh with linear rack, are actually (linear)
3984:
Teeth of engaging gears, one or both of which have non-standard addendum.
3469:
A line or curve along which two tooth surfaces are tangent to each other.
2868:
Radial distance from the depth of the tooth trough to the pitch surface.
2593:
2039:
1944:
1653:
903:
884:, all points of the gear will be rotating around that axis with the same
699:
653:
644:
Wooden gears have been gradually replaced by ones made or metal, such as
370:
165:
75:
68:
35:
6238:(ANSI/AGMA 1012-F90 ed.), American Gear Manufacturers Association,
6105:"The first-ever naturally occurring gears are found on an insect's legs"
4295:
Value of diametrical pitch in a normal plane of a helical gear or worm.
3120:
Contact between teeth other than at the intended parts of their surfaces
2212:
Point where the line of action crosses a line joining the two gear axes.
1127:
1072:
376:(287–212 BC). The earliest surviving gears in Europe were found in the
6322:- movies and photos of hundreds of working models at Cornell University
5191:
5040:"An Ancient Greek Astronomical Calculation Machine Reveals New Secrets"
4210:
Ratio of the number of teeth to the standard pitch diameter in inches.
2168:
2112:
1842:
1135:
1039:
872:
For basic analysis purposes, each gear can be idealized as a perfectly
779:
434:
385:
5689:
5373:(ANSI/AGMA 1012-G05 ed.), American Gear Manufacturers Association
4012:
3905:
Length of arc between the two sides of a gear tooth, on the specified
1697:
1531:
1290:
along the axis of the gear, which must be accommodated by appropriate
485:
gears were used by the British clock maker Joseph Williamson in 1720.
6556:
4984:"The Antikythera Mechanism Research Project: Why is it so important?"
4907:
On the Origin of Clockwork, Perpetual Motion Devices, and the Compass
4540:
adopted the gear model in different ways. In the nineteenth century,
4372:
Angle subtended by the circular pitch, usually expressed in radians.
3788:{\displaystyle m_{\rm {o}}={\sqrt {m_{\rm {p}}^{2}+m_{\rm {F}}^{2}}}}
2579:
2454:
2189:
Path followed by the point of contact between two meshing gear teeth.
2072:
1830:
1591:
In a worm-and-gear set, the worm can always drive the gear. However,
1287:
1147:
if its teeth are directed generally away from the rotation axis, and
1106:
623:
442:
388:. Its time of construction is now estimated between 150 and 100 BC.
106:
79:
3593:
The sum of the transverse contact ratio and the face contact ratio.
1936:
used it on his early steam engines to get around the patent on the
1305:
A second disadvantage of helical gears is also a greater degree of
4574:
4011:
2009:
1978:
1958:
1902:
1860:
1806:
1765:
1696:
1663:
1636:
1553:
1530:
1522:
1471:
1269:
1259:
1234:
1189:
1134:
1126:
1071:
1015:
662:
649:
638:
610:
423:
390:
336:
331:
310:
292:
192:
161:
153:
131:
118:
46:
6660:
4726:
in the Merriam-Webster dictionary online. Accessed on 2018-09-20.
1593:
if the gear attempts to drive the worm, it may or may not succeed
6340:
6282:
Sclater, Neil. (2011). "Gears: devices, drives and mechanisms."
6272:
6133:
Functioning 'mechanical gears' seen in nature for the first time
6075:"This Insect Has The Only Mechanical Gears Ever Found in Nature"
1043:
895:), in the same sense. The speed need not be constant over time.
660:
may be used with alloys that cannot be easily cast or machined.
438:
114:
6664:
6349:
5783:
Oberg, E.; Jones, F. D.; Horton, H. L.; Ryffell, H. H. (2000),
4008:
Teeth in which the addendums of two engaging gears are unequal.
1223:) go through the meeting point of the two axes, resulting in a
770:
step after they are removed from the mold. Cast gears require
6262:
Coy, John J.; Townsend, Dennis P.; Zaretsky, Erwin V. (1985),
4352:{\displaystyle P_{\rm {nd}}={\frac {P_{\rm {d}}}{\cos \psi }}}
797:
Metal gears intended for heavy duty operation, such as in the
627:
101:
The smaller member of a pair of meshing gears is often called
5937:
Sander, K. (1957), "Bau und Funktion des Sprungapparates von
105:. Most commonly, gears and gear trains can be used to trade
5000:
The Mechanism is thought to date from between 150 and 100 BC
3811:
Intersection of the limit diameter and the involute profile.
3329:
Subscript w denotes the worm, subscript g denotes the gear.
2034:
is a specialized gearing mechanism often used in industrial
361:
circa AD 50, but can be traced back to the mechanics of the
30:
This article is about mechanical gears. For other uses, see
2729:
Segment of a pitch circle subtended by the angle of action.
6203:
Industrial Press (2012), Machinery's Handbook (29th ed.),
5321:
Dudley's Handbook of Practical Gear Design and Manufacture
3126:
A set of gears, any of which mates properly with any other
2911:{\displaystyle b={\frac {1}{2}}(D-{\text{root diameter}})}
2790:
Diameter of the gear, measured from the tops of the teeth.
55:
rotating at different velocity due to differing gear ratio
2390:
Since it is impractical to calculate circular pitch with
2206:
Axis of revolution of the gear; center line of the shaft.
2177:
The larger of two interacting gears or a gear on its own.
6345:
6331:
Mathematical Tutorial for Gearing (Relating to Robotics)
5905:"Does the Three Wave Hypothesis Imply Hidden Structure?"
4956:
Lewis, M. J. T. (1993). "Gearing in the Ancient World".
2796:
Diameter of the gear, measured at the base of the tooth.
1985:
and more. Common applications include textile machines,
6313:
5963:
Burrows, Malcolm; Sutton, Gregory (13 September 2013).
4520:, which is effectively a length measurement across the
4002:
Teeth in which two engaging gears have equal addendums.
3463:
Any point at which two tooth profiles touch each other.
195:"machine". When a small gear drives a larger one, the
6335:
5545:
4480:
and so differs whether the standard values are in the
1786:. Manufacturing such tooth faces may require a 5-axis
5546:"Minimizing gearbox noise inside and outside the box"
4413:
4380:
4303:
4218:
3728:
3655:
3601:
3302:
3277:
3205:
3167:
3142:
3091:
3042:
2986:
2926:
2874:
2811:
2767:
2741:
2610:
2510:
2465:
2457:. When the diametral pitch, DP, is in English units,
2410:
2332:
2279:
2257:
1420:
1370:
1322:
1294:. However, this issue can be circumvented by using a
384:
positions of the sun, moon, and planets, and predict
6320:
Kinematic Models for Design Digital Library (KMODDL)
6236:
Gear Nomenclature: Definitions of Terms with Symbols
5371:
Gear Nomenclature, Definitions of Terms with Symbols
2441:
where m is the module and p the circular pitch. The
6739:
6698:
6607:
6585:
6549:
6542:
6496:
6475:
6434:
6383:
5068:
Science and Civilization in China: Volume 4, Part 2
3701:{\displaystyle m_{\rm {t}}=m_{\rm {p}}+m_{\rm {F}}}
3022:{\displaystyle DP={\frac {N}{d}}={\frac {\pi }{p}}}
691:as clutches and torque- or current-limited motors.
622:The gears of the Antikythera mechanism are made of
129:, a straight bar with a row of compatible teeth.
6341:Gear Technology, the Journal of Gear Manufacturing
6156:McGraw-Hill Encyclopedia of Science and Technology
4431:
4399:
4351:
4272:
3787:
3700:
3640:
3315:
3283:
3239:
3180:
3148:
3104:
3064:
3021:
2939:
2910:
2852:
2780:
2747:
2699:
2558:
2489:
2429:
2369:
2318:
2263:
1668:Wooden cogs set in bevel mortise wheels driving a
1426:
1402:
1354:
6286:5th ed. New York: McGraw Hill. pp. 131–174.
5787:(26th ed.), Industrial Press, p. 2649,
5216:
1046:whose apex is the meeting point of the two axes.
6234:; American National Standards Institute (2005),
6216:Engineers Edge, Gear Design and Engineering Data
5654:Freeth, Tony; Jones, Alexander (February 2012).
5629:
5617:
5605:
5562:
5512:
5510:
5508:
5418:(2nd ed.), New York: Chelsea, p. 287,
5131:"Astrolabe By Muhammad Ibn Abi Bakr Al Isfahani"
3190:Circular pitch in the plane normal to the teeth.
1977:, a non-circular gear's main objective might be
1286:A disadvantage of helical gears is a resultant
6195:Vallance, Alex; Doughtie, Venton Levy (1964),
5720:International Organization for Standardization
5437:
5435:
2370:{\displaystyle d={\frac {N}{P_{d}\cos \psi }}}
2319:{\displaystyle d={\frac {Nm_{n}}{\cos \psi }}}
1875:In epicyclic gearing, one or more of the gear
1034:For best operation, each wheel then must be a
188:has an extremely uneven operation, by design.
6676:
6361:
6314:Geararium. Museum of gears and toothed wheels
6284:Mechanisms and Mechanical Devices Sourcebook.
5487:. New York: Industrial Press. 2012. pp.
5149:Economic History of Medieval India, 1200-1500
2559:{\displaystyle a={\frac {m}{2}}(z_{1}+z_{2})}
1457:3D animation of helical gears (parallel axis)
191:Gears can be seen are instances of the basic
8:
5664:Institute for the Study of the Ancient World
5167:"Giovanni Dondi's Astrarium, 1364 | cabinet"
4920:"Gears from Archimedes, Heron and Dionysius"
4682:online, sense (6a). Accessed on 2018-09-20.
1580:; a worm with more than one tooth is called
1462:3D animation of helical gears (crossed axis)
1080:The gears in a matching pair are said to be
813:. For large gears that are prone to warp, a
615:Wooden cogwheel driving a lantern pinion or
464:, some time during the 13th–14th centuries.
6294:. Drawings and designs of various gearings.
6159:(10th ed.), McGraw-Hill Professional,
5641:
5516:
5441:
5361:
5359:
5357:
5355:
5353:
3915:Circular thickness in the transverse plane.
2502:The distance between the two axis becomes:
1845:(s) that are attached to the front wheels.
1672:. Note wooden spur gears in the background.
1645:Another criterion to classify gears is the
1602:Worm-and-gear sets that do lock are called
1500:. Another type of double helical gear is a
633:Historically, large gears, such as used in
6683:
6669:
6661:
6546:
6368:
6354:
6346:
6180:(3rd ed.), McGraw-Hill Professional,
5958:
5956:
5573:
5571:
1618:making both concave and joining them at a
1274:An external contact helical gear in action
876:that, in normal operation, turns around a
369:, and were greatly developed by the Greek
217:, the ratio of the tooth counts. namely,
5998:1983/69cf1502-217a-4dca-a0d3-f8b247794e92
5996:
5863:
5656:"The Cosmos in the Antikythera Mechanism"
5369:; American National Standards Institute,
4785:
4783:
4750:
4748:
4414:
4412:
4387:
4379:
4329:
4328:
4322:
4309:
4308:
4302:
4260:
4247:
4234:
4224:
4223:
4217:
3777:
3771:
3770:
3757:
3751:
3750:
3744:
3734:
3733:
3727:
3691:
3690:
3676:
3675:
3661:
3660:
3654:
3632:
3619:
3606:
3600:
3307:
3301:
3276:
3210:
3204:
3172:
3166:
3141:
3096:
3090:
3052:
3041:
3009:
2996:
2985:
2931:
2925:
2900:
2881:
2873:
2853:{\displaystyle a={\frac {1}{2}}(D_{o}-D)}
2835:
2818:
2810:
2772:
2766:
2740:
2677:
2667:
2661:
2650:
2624:
2615:
2609:
2547:
2534:
2517:
2509:
2472:
2464:
2417:
2409:
2349:
2339:
2331:
2296:
2286:
2278:
2256:
1419:
1394:
1381:
1369:
1346:
1333:
1321:
467:A complex astronomical clock, called the
449:, and the number of days since new moon.
6098:
6096:
6050:"Insects Use Gears in Hind Legs to Jump"
6028:Herkewitz, William (12 September 2013),
2129:Measured in rotation over time, such as
693:
395:Modern model of a south-pointing chariot
6336:American Gear Manufacturers Association
6232:American Gear Manufacturers Association
6073:Stromberg, Joseph (12 September 2013),
5754:
5752:
5367:American Gear Manufacturers Association
4668:
4126:Circular pitch in the transverse plane.
4056:
3826:
3336:
2402:of the wheel and is simply defined as:
1452:cannot mesh with the shafts parallel.)
1403:{\displaystyle E=\beta _{1}-\beta _{2}}
1355:{\displaystyle E=\beta _{1}+\beta _{2}}
1038:, whose overall shape is like a slice (
922:with itself when the gear rotates by 1/
5734:Konstruktionselement och maskinbyggnad
4943:
4472:Standard pitches and the module system
4400:{\displaystyle \tau ={\frac {360}{z}}}
1088:-- neither parallel nor intersecting.
828:Comparison with other drive mechanisms
199:of this ideal lever causes the torque
6030:"The First Gear Discovered in Nature"
5070:, page 298. Taipei: Caves Books, Ltd.
3872:Tooth thickness measurement over pins
2183:The smaller of two interacting gears.
1907:Sun (yellow) and planet (red) gearing
1841:into the left-to-right motion of the
1095:of revolution. Such gears are called
471:, was built between 1348 and 1364 by
7:
6103:Robertson, Adi (12 September 2013).
5809:"Elements of metric gear technology"
3065:{\displaystyle DP={\frac {25.4}{m}}}
2587:to each other; this occurs when the
2490:{\displaystyle m={\frac {25.4}{DP}}}
2453:is sometimes used with the units of
1173:such as found in mechanical clocks.
718:, some dating back over 100 years.
326:), which have been preserved at the
2430:{\displaystyle m={\frac {p}{\pi }}}
1991:continuously variable transmissions
918:about the axis, meaning that it is
6529:Continuously variable transmission
6303:, February 1945, pp. 120–125.
6048:Lee, Jane J. (12 September 2013),
5941:WALKER (Homoptera - Fulgoridae)",
4432:{\displaystyle {\frac {2\pi }{z}}}
4330:
4313:
4310:
4225:
3772:
3752:
3735:
3692:
3677:
3662:
3240:{\displaystyle p_{n}=p\cos(\psi )}
801:of cars and trucks, the teeth are
599:('pommel, hump, hill'), from PIE *
301:continuously variable transmission
168:, which is meant to engage with a
25:
5760:"W. M. Berg Gear Reference Guide"
3942:Chordal addendum (chordal height)
1410:for gears of opposite handedness,
1362:for gears of the same handedness,
1262:. Helical gears can be meshed in
172:instead of another gear, and the
6136:, PHYS.ORG, Cambridge University
5081:"vertical dial | British Museum"
4622:
4095:
4083:
4071:
4059:
3889:
3877:
3865:
3853:
3841:
3829:
3447:
3435:
3423:
3411:
3399:
3387:
3375:
3363:
3351:
3339:
2111:
1439:is zero—that is, the shafts are
809:while leaving the core soft but
5829:. University of Chicago Press.
4812:online. Accessed on 2024-07-29.
4796:online. Accessed on 2024-07-29.
4777:online. Accessed on 2024-07-29.
4761:online. Accessed on 2024-07-29.
4742:online. Accessed on 2024-07-27.
4714:online. Accessed on 2024-07-27.
4698:online. Accessed on 2024-07-27.
4571:Gear mechanism in natural world
3951:Displacement of the basic rack
3394:Lines of contact (helical gear)
2570:where a is the axis distance, z
910:teeth, the working surface has
726:The most common techniques for
5318:Radzevich, Stephen P. (2012).
4509:values with units of "inches"
4201:Diametral pitch (transverse),
3234:
3228:
2905:
2891:
2847:
2828:
2553:
2527:
2167:How many teeth a gear has, an
1981:variations, axle displacement
1084:if their axes of rotation are
517:) 'apparel, gear,' related to
1:
6406:Epicyclic (planetary) gearing
6255:Analytical Mechanics of Gears
4005:Long and short-addendum teeth
3912:Transverse circular thickness
3896:Long and short addendum teeth
3808:Start of active profile (SAP)
3497:Zone of action (contact zone)
2589:greatest common divisor (GCD)
2497:in conventional metric units.
2244:; or normal diametral pitch,
2192:Line of action, pressure line
1243:Bottom: crossed configuration
1008:essentially two-dimensional.
956:During operation, each point
532:is a tooth on a wheel. From
6461:
6199:(4th ed.), McGraw-Hill.
5682:Journal of Mechanical Design
5630:Vallance & Doughtie 1964
5618:Vallance & Doughtie 1964
5606:Vallance & Doughtie 1964
5563:Vallance & Doughtie 1964
5416:Geometry and the Imagination
5012:Owen Jarus (14 April 2022).
4970:10.1016/0160-9327(93)90099-O
4533:Gear model in modern physics
473:Giovanni Dondi dell'Orologio
437:showing the position of the
403:(c. 200–265 AD) described a
5338:Fred Eberle (August 2014).
4866:. Bbc.co.uk. 1 January 1970
4759:Oxford Learner's Dictionary
4740:Oxford Learner's Dictionary
4696:Oxford Learner's Dictionary
4117:Transverse circular pitch,
3557:Transverse contact ratio, m
3193:Transverse circular pitch,
2758:pressure angle is constant.
1560:, which looks similar to a
1241:Top: parallel configuration
805:to make them hard and more
698:Wooden gears of a historic
673:'through' mortise and tenon
74:typically used to transmit
6794:
6253:Buckingham, Earle (1949),
6174:Norton, Robert L. (2004),
5882:10.1088/0957-4484/13/5/328
5825:Siegel, Daniel M. (1991).
5384:Canfield, Stephen (1997),
4831:10.1038/s41467-021-25582-8
4810:Collins English Dictionary
4775:Merriam-Webster Dictionary
4712:Collins English Dictionary
4680:Merriam-Webster Dictionary
4449:
4286:Normal diametrical pitch,
4036:
3085:Base pitch, normal pitch,
2445:of module are customarily
2099:
2088:enclosure without using a
2084:can transmit force into a
2056:
2017:
1966:
1920:is a method of converting
1910:
1868:
1814:
1556:. A worm is meshed with a
1538:
864:acceptable but desirable.
29:
6650:Spur gear corrected tooth
6298:"Wheels That Can't Slip."
6197:Design of machine members
5700:Diss. Hünecke, TU Dresden
5269:A Treatise on Gear Wheels
5266:Grant, George B. (1893).
5217:"Etymology 1: Cog (noun)"
4794:Cambridge Dictionary Plus
4736:Definition of "gearwheel"
4724:Definition of "gearwheel"
4708:Definition of "gearwheel"
3918:Normal circular thickness
3714:Modified contact ratio, m
2599:Operating pitch diameters
2102:List of gear nomenclature
1738:Parallel and crossed axes
477:Salisbury Cathedral clock
429:Around 1221 AD, a geared
341:The Antikythera mechanism
5110:www.thearchaeologist.org
4841:Matthew Jaster (2013): [
4589:and scientists from the
4090:Base pitch relationships
3936:Normal chordal thickness
3284:{\displaystyle \lambda }
2251:), and the helix angle (
2215:Pitch circle, pitch line
1893:mechanical differentials
1626:or "Double enveloping".
1219:whose generating lines (
708:Lancaster, New Hampshire
592:('hump, ball') (compare
6257:, McGraw-Hill Book Co..
5989:10.1126/science.1240284
5684:, volume 127, issue 4.
4903:Derek J. de Solla Price
4653:Superposition principle
4591:University of Cambridge
4181:Transverse base pitch,
4129:Normal circular pitch,
3981:Modified addendum teeth
3930:Base circular thickness
3848:Thickness relationships
3161:Normal circular pitch,
2748:{\displaystyle \theta }
1889:automatic transmissions
1811:Rack and pinion gearing
1610:found on some types of
1217:general conical surface
1020:Bevel gear operating a
420:mechanical water clocks
5943:Zool. Jb. Jena (Anat.)
5903:Sanduk, M. I. (2007).
4924:www.hellenicaworld.com
4851:Archived on 2024-07-30
4825:, volume 12, issue 1.
4582:
4452:Backlash (engineering)
4433:
4401:
4353:
4274:
4017:
3789:
3702:
3642:
3583:Total contact ratio, m
3317:
3285:
3241:
3182:
3150:
3106:
3066:
3023:
2941:
2912:
2854:
2782:
2749:
2701:
2560:
2491:
2431:
2371:
2320:
2265:
2131:revolutions per minute
2015:
1964:
1918:Sun and planet gearing
1908:
1881:sun and planet gearing
1866:
1812:
1771:
1702:
1673:
1642:
1641:Profile of a spur gear
1536:
1535:4-start worm and wheel
1528:
1477:
1428:
1427:{\displaystyle \beta }
1404:
1356:
1275:
1244:
1195:
1140:
1132:
1077:
1024:
988:Relative axis position
933:separate patches, the
794:may be used instead.
702:
668:
619:
558:('cog, tooth')), from
405:south-pointing chariot
396:
342:
319:
137:
56:
5390:Dynamics of Machinery
4886:"Transmission Basics"
4823:Nature Communications
4578:
4565:wave–particle duality
4561:three wave hypothesis
4544:developed a model of
4434:
4402:
4354:
4275:
4015:
3964:Measurement over pins
3790:
3703:
3643:
3570:Face contact ratio, m
3318:
3316:{\displaystyle d_{w}}
3286:
3242:
3183:
3181:{\displaystyle p_{n}}
3151:
3149:{\displaystyle \psi }
3107:
3105:{\displaystyle p_{b}}
3067:
3024:
2942:
2940:{\displaystyle h_{t}}
2913:
2855:
2783:
2781:{\displaystyle D_{o}}
2750:
2702:
2561:
2492:
2432:
2372:
2321:
2266:
2264:{\displaystyle \psi }
2013:
1962:
1906:
1864:
1810:
1769:
1700:
1667:
1640:
1534:
1526:
1475:
1429:
1405:
1357:
1273:
1238:
1193:
1143:A gear is said to be
1138:
1130:
1123:Internal and external
1075:
1019:
836:driven by sprockets,
820:Gears can be made by
697:
666:
614:
399:The Chinese engineer
394:
378:Antikythera mechanism
363:Library of Alexandria
340:
314:
286:Most vehicles have a
135:
50:
32:Gear (disambiguation)
6572:Shaft-driven bicycle
6080:Smithsonian Magazine
6062:on 13 September 2013
5785:Machinery's Handbook
5550:Motion System Design
5483:Machinery's Handbook
5412:Cohn-Vossen, Stephan
5293:Motion System Design
5171:www.cabinet.ox.ac.uk
4692:Definition of "gear"
4676:Definition of "gear"
4411:
4378:
4301:
4216:
3999:Equal addendum teeth
3726:
3653:
3599:
3300:
3275:
3203:
3165:
3140:
3089:
3040:
2984:
2924:
2872:
2809:
2765:
2739:
2608:
2596:based straight cogs.
2508:
2463:
2408:
2330:
2277:
2255:
1922:reciprocating motion
1879:moves. Examples are
1857:Epicyclic gear train
1612:stringed instruments
1418:
1368:
1320:
680:engineering plastics
460:, for use in roller
456:was invented in the
203:to increase but the
197:mechanical advantage
176:, meant to engage a
6411:Sun and planet gear
6177:Design of Machinery
6055:National Geographic
5981:2013Sci...341.1254B
5975:(6151): 1254–1256.
5924:2007Apei...14..113S
5874:2002Nanot..13..678M
5668:New York University
5620:, pp. 280, 296
5287:Smith, Zan (2000),
5044:Scientific American
4806:Definition of "cog"
4790:Definition of "cog"
4771:Definition of "cog"
4755:Definition of "cog"
4542:James Clerk Maxwell
4161:Normal base pitch,
3782:
3762:
3123:Interchangeable set
2384:Module or modulus,
2326:in metric units or
2086:hermetically sealed
2020:strain wave gearing
1913:Sun and planet gear
1827:radius of curvature
1798:Special gear trains
1622:; this is called a
1568:to low efficiency.
1300:double helical gear
1177:Tooth cut direction
916:rotational symmetry
846:hydraulic couplings
684:composite materials
586:Proto-Indo-European
458:Indian subcontinent
351:Philon of Byzantium
330:of Henan Province,
40:Geared (video game)
6640:Gear manufacturing
6476:Geartooth profiles
5939:Pyrilla perpusilla
5544:Schunck, Richard,
5531:Theory of Machines
5461:. 16 November 2000
5396:on 29 August 2008.
5340:"Materials Matter"
5085:The British Museum
4630:Engineering portal
4596:Issus coleoptratus
4583:
4580:Issus coleoptratus
4429:
4397:
4349:
4270:
4018:
3902:Circular thickness
3785:
3766:
3746:
3698:
3638:
3528:Arc of approach, Q
3313:
3281:
3237:
3178:
3146:
3102:
3062:
3019:
2937:
2908:
2850:
2778:
2761:Outside diameter,
2745:
2697:
2556:
2487:
2427:
2392:irrational numbers
2377:in imperial units.
2367:
2316:
2261:
2092:, which may leak.
2016:
1965:
1963:Non-circular gears
1955:Non-circular gears
1909:
1867:
1813:
1772:
1770:Spiral bevel gears
1703:
1674:
1643:
1537:
1529:
1478:
1424:
1400:
1352:
1276:
1245:
1196:
1141:
1133:
1078:
1025:
861:rotational inertia
740:investment casting
728:gear manufacturing
703:
669:
620:
491:Issus coleoptratus
409:differential gears
397:
365:in 3rd-century BC
355:Hero of Alexandria
343:
320:
182:non-circular gears
138:
57:
6760:
6759:
6658:
6657:
6603:
6602:
6426:Non-circular gear
6391:Spur gear systems
6245:978-1-55589-846-5
6209:978-0-8311-2900-2
6187:978-0-07-121496-4
6166:978-0-07-144143-8
6035:Popular Mechanics
5794:978-0-8311-2666-7
5772:on 21 April 2015.
5736:(in Swedish), 7,
5690:10.1115/1.1900147
5498:978-0-8311-2900-2
5459:howstuffworks.com
5425:978-0-8284-1087-8
5155:Pearson Education
4567:to a bevel gear.
4494:diametrical pitch
4427:
4395:
4347:
4268:
4255:
4242:
4102:Principal pitches
3860:Chordal thickness
3783:
3485:Surface of action
3060:
3017:
3004:
2973:Diametral pitch,
2903:
2889:
2826:
2692:
2683:
2645:
2525:
2485:
2425:
2365:
2314:
2161:Number of teeth,
2154:rad/minute = π/30
2137:Angular frequency
2090:radial shaft seal
2082:magnetic coupling
2059:Magnetic coupling
1969:Non-circular gear
1947:is green and the
1928:that was used in
1871:Epicyclic gearing
1865:Epicyclic gearing
1784:octoidal surfaces
1776:spiral bevel gear
1485:Herringbone gears
1476:Herringbone gears
1206:straight-cut gear
1198:In a cylindrical
1118:Tooth orientation
842:belts and pulleys
748:powder metallurgy
744:injection molding
688:injection molding
658:powder metallurgy
506:is probably from
76:rotational motion
51:Two intermeshing
16:(Redirected from
6785:
6731:Spherical (ball)
6685:
6678:
6671:
6662:
6547:
6370:
6363:
6356:
6347:
6276:
6270:
6258:
6249:
6220:
6200:
6191:
6170:
6138:
6137:
6128:
6122:
6121:
6119:
6117:
6100:
6091:
6090:
6089:
6087:
6070:
6064:
6063:
6058:, archived from
6045:
6039:
6038:
6025:
6019:
6018:
6000:
5960:
5951:
5950:
5934:
5928:
5927:
5909:
5900:
5894:
5893:
5867:
5865:cond-mat/0205647
5847:
5841:
5840:
5822:
5816:
5815:
5813:
5805:
5799:
5798:
5780:
5774:
5773:
5771:
5765:. Archived from
5764:
5756:
5747:
5746:
5729:
5723:
5716:
5710:
5707:
5701:
5698:
5692:
5678:
5672:
5671:
5651:
5645:
5642:McGraw-Hill 2007
5639:
5633:
5627:
5621:
5615:
5609:
5603:
5597:
5596:
5594:
5592:
5583:, archived from
5575:
5566:
5560:
5554:
5553:
5541:
5535:
5534:
5526:
5520:
5517:McGraw-Hill 2007
5514:
5503:
5502:
5486:
5477:
5471:
5470:
5468:
5466:
5455:"How Gears Work"
5451:
5445:
5442:McGraw-Hill 2007
5439:
5430:
5429:
5404:
5398:
5397:
5381:
5375:
5374:
5363:
5348:
5347:
5335:
5329:
5328:
5326:
5315:
5309:
5308:
5306:
5304:
5295:, archived from
5284:
5278:
5277:
5263:
5257:
5256:
5254:
5252:
5238:
5232:
5231:
5229:
5227:
5213:
5207:
5206:
5204:
5202:
5188:
5182:
5181:
5179:
5177:
5163:
5157:
5141:
5135:
5134:
5127:
5121:
5120:
5118:
5116:
5102:
5096:
5095:
5093:
5091:
5077:
5071:
5061:
5055:
5054:
5052:
5050:
5035:
5029:
5028:
5026:
5024:
5009:
5003:
5002:
4997:
4995:
4986:. Archived from
4980:
4974:
4973:
4953:
4947:
4941:
4935:
4934:
4932:
4930:
4916:
4910:
4900:
4894:
4893:
4892:. 27 April 2005.
4882:
4876:
4875:
4873:
4871:
4860:
4854:
4839:
4833:
4819:
4813:
4803:
4797:
4787:
4778:
4768:
4762:
4752:
4743:
4733:
4727:
4721:
4715:
4705:
4699:
4689:
4683:
4673:
4632:
4627:
4626:
4546:electromagnetism
4438:
4436:
4435:
4430:
4428:
4423:
4415:
4406:
4404:
4403:
4398:
4396:
4388:
4365:Angular pitch, θ
4358:
4356:
4355:
4350:
4348:
4346:
4335:
4334:
4333:
4323:
4318:
4317:
4316:
4279:
4277:
4276:
4271:
4269:
4261:
4256:
4248:
4243:
4235:
4230:
4229:
4228:
4108:Circular pitch,
4099:
4087:
4075:
4063:
3987:Full-depth teeth
3974:Span measurement
3893:
3884:Span measurement
3881:
3869:
3857:
3845:
3833:
3794:
3792:
3791:
3786:
3784:
3781:
3776:
3775:
3761:
3756:
3755:
3745:
3740:
3739:
3738:
3707:
3705:
3704:
3699:
3697:
3696:
3695:
3682:
3681:
3680:
3667:
3666:
3665:
3647:
3645:
3644:
3639:
3637:
3636:
3624:
3623:
3611:
3610:
3546:Contact ratio, m
3537:Arc of recess, Q
3519:Arc of action, Q
3513:Length of action
3460:Point of contact
3451:
3439:
3427:
3418:Length of action
3415:
3403:
3391:
3379:
3367:
3355:
3343:
3322:
3320:
3319:
3314:
3312:
3311:
3296:Pitch diameter,
3290:
3288:
3287:
3282:
3246:
3244:
3243:
3238:
3215:
3214:
3187:
3185:
3184:
3179:
3177:
3176:
3155:
3153:
3152:
3147:
3111:
3109:
3108:
3103:
3101:
3100:
3072:in English units
3071:
3069:
3068:
3063:
3061:
3053:
3028:
3026:
3025:
3020:
3018:
3010:
3005:
2997:
2964:Circular pitch,
2946:
2944:
2943:
2938:
2936:
2935:
2917:
2915:
2914:
2909:
2904:
2901:
2890:
2882:
2859:
2857:
2856:
2851:
2840:
2839:
2827:
2819:
2787:
2785:
2784:
2779:
2777:
2776:
2754:
2752:
2751:
2746:
2706:
2704:
2703:
2698:
2693:
2691:
2684:
2682:
2681:
2672:
2671:
2662:
2659:
2651:
2646:
2644:
2633:
2625:
2620:
2619:
2585:relatively prime
2565:
2563:
2562:
2557:
2552:
2551:
2539:
2538:
2526:
2518:
2496:
2494:
2493:
2488:
2486:
2484:
2473:
2436:
2434:
2433:
2428:
2426:
2418:
2376:
2374:
2373:
2368:
2366:
2364:
2354:
2353:
2340:
2325:
2323:
2322:
2317:
2315:
2313:
2302:
2301:
2300:
2287:
2270:
2268:
2267:
2262:
2222:Pitch diameter,
2157:
2153:
2149:
2115:
2031:strain wave gear
2014:Harmonic gearing
1709:, also called a
1681:, or triangular
1433:
1431:
1430:
1425:
1409:
1407:
1406:
1401:
1399:
1398:
1386:
1385:
1361:
1359:
1358:
1353:
1351:
1350:
1338:
1337:
1307:sliding friction
1296:herringbone gear
868:Ideal gear model
205:rotational speed
111:rotational speed
21:
6793:
6792:
6788:
6787:
6786:
6784:
6783:
6782:
6763:
6762:
6761:
6756:
6735:
6694:
6689:
6659:
6654:
6599:
6581:
6538:
6524:Bicycle gearing
6492:
6471:
6430:
6421:Cycloidal drive
6401:Rack and pinion
6379:
6374:
6310:
6301:Popular Science
6268:
6261:
6252:
6246:
6230:
6227:
6225:Further reading
6213:
6194:
6188:
6173:
6167:
6149:
6141:
6130:
6129:
6125:
6115:
6113:
6102:
6101:
6094:
6085:
6083:
6072:
6071:
6067:
6047:
6046:
6042:
6027:
6026:
6022:
5962:
5961:
5954:
5936:
5935:
5931:
5907:
5902:
5901:
5897:
5849:
5848:
5844:
5837:
5824:
5823:
5819:
5811:
5807:
5806:
5802:
5795:
5782:
5781:
5777:
5769:
5762:
5758:
5757:
5750:
5744:
5731:
5730:
5726:
5717:
5713:
5708:
5704:
5699:
5695:
5679:
5675:
5653:
5652:
5648:
5640:
5636:
5628:
5624:
5616:
5612:
5604:
5600:
5590:
5588:
5587:on 26 June 2009
5577:
5576:
5569:
5561:
5557:
5543:
5542:
5538:
5529:Khurmi, R. S.,
5528:
5527:
5523:
5515:
5506:
5499:
5479:
5478:
5474:
5464:
5462:
5453:
5452:
5448:
5440:
5433:
5426:
5406:
5405:
5401:
5383:
5382:
5378:
5365:
5364:
5351:
5337:
5336:
5332:
5324:
5317:
5316:
5312:
5302:
5300:
5299:on 14 July 2011
5286:
5285:
5281:
5265:
5264:
5260:
5250:
5248:
5240:
5239:
5235:
5225:
5223:
5215:
5214:
5210:
5200:
5198:
5190:
5189:
5185:
5175:
5173:
5165:
5164:
5160:
5142:
5138:
5129:
5128:
5124:
5114:
5112:
5104:
5103:
5099:
5089:
5087:
5079:
5078:
5074:
5062:
5058:
5048:
5046:
5037:
5036:
5032:
5022:
5020:
5018:livescience.com
5011:
5010:
5006:
4993:
4991:
4982:
4981:
4977:
4955:
4954:
4950:
4942:
4938:
4928:
4926:
4918:
4917:
4913:
4901:
4897:
4884:
4883:
4879:
4869:
4867:
4862:
4861:
4857:
4847:Gear Technology
4840:
4836:
4820:
4816:
4804:
4800:
4788:
4781:
4769:
4765:
4753:
4746:
4734:
4730:
4722:
4718:
4706:
4702:
4690:
4686:
4674:
4670:
4666:
4658:Kinematic chain
4628:
4621:
4618:
4601:I. coleoptratus
4573:
4554:quantum physics
4552:More recently,
4535:
4488:systems. Using
4474:
4454:
4448:
4416:
4409:
4408:
4376:
4375:
4368:
4336:
4324:
4304:
4299:
4298:
4292:
4219:
4214:
4213:
4207:
4194:
4187:
4174:
4167:
4154:
4142:
4135:
4123:
4103:
4100:
4091:
4088:
4079:
4076:
4067:
4064:
4044:
3924:Axial thickness
3897:
3894:
3885:
3882:
3873:
3870:
3861:
3858:
3849:
3846:
3837:
3836:Tooth thickness
3834:
3825:
3823:Tooth thickness
3729:
3724:
3723:
3717:
3686:
3671:
3656:
3651:
3650:
3628:
3615:
3602:
3597:
3596:
3590:
3586:
3577:
3573:
3564:
3560:
3549:
3540:
3531:
3522:
3507:Path of contact
3491:Plane of action
3466:Line of contact
3455:
3452:
3443:
3440:
3431:
3428:
3419:
3416:
3407:
3404:
3395:
3392:
3383:
3382:Plane of action
3380:
3371:
3368:
3359:
3356:
3347:
3346:Line of contact
3344:
3335:
3303:
3298:
3297:
3273:
3272:
3265:Linear pitch, p
3256:
3206:
3201:
3200:
3168:
3163:
3162:
3138:
3137:
3133:
3092:
3087:
3086:
3038:
3037:
2982:
2981:
2927:
2922:
2921:
2870:
2869:
2831:
2807:
2806:
2768:
2763:
2762:
2737:
2736:
2720:Angle of action
2673:
2663:
2660:
2652:
2634:
2626:
2611:
2606:
2605:
2577:
2573:
2543:
2530:
2506:
2505:
2477:
2461:
2460:
2406:
2405:
2345:
2344:
2328:
2327:
2303:
2292:
2288:
2275:
2274:
2253:
2252:
2249:
2242:
2186:Path of contact
2155:
2151:
2147:
2109:
2104:
2098:
2065:
2057:Main articles:
2055:
2022:
2008:
1999:
1997:Non-rigid gears
1971:
1957:
1915:
1901:
1885:cycloidal drive
1873:
1859:
1819:
1817:Rack and pinion
1805:
1803:Rack and pinion
1800:
1788:milling machine
1764:
1740:
1728:
1695:
1679:parallelepipeds
1662:
1635:
1582:multiple thread
1547:
1539:Main articles:
1521:
1470:
1416:
1415:
1390:
1377:
1366:
1365:
1342:
1329:
1318:
1317:
1292:thrust bearings
1281:noise abatement
1242:
1240:
1233:
1188:
1179:
1157:
1125:
1120:
1070:
1014:
998:
990:
870:
838:friction drives
830:
761:
724:
648:at first, then
609:
500:
367:Ptolemaic Egypt
309:
281:
274:
263:
256:
248:
241:
230:
223:
43:
28:
23:
22:
15:
12:
11:
5:
6791:
6789:
6781:
6780:
6775:
6765:
6764:
6758:
6757:
6755:
6754:
6749:
6743:
6741:
6737:
6736:
6734:
6733:
6728:
6723:
6718:
6713:
6708:
6702:
6700:
6696:
6695:
6692:Kinematic pair
6690:
6688:
6687:
6680:
6673:
6665:
6656:
6655:
6653:
6652:
6647:
6642:
6637:
6632:
6627:
6622:
6617:
6611:
6609:
6605:
6604:
6601:
6600:
6598:
6597:
6591:
6589:
6583:
6582:
6580:
6579:
6574:
6569:
6564:
6559:
6553:
6551:
6544:
6540:
6539:
6537:
6536:
6531:
6526:
6521:
6516:
6511:
6506:
6500:
6498:
6494:
6493:
6491:
6490:
6485:
6479:
6477:
6473:
6472:
6470:
6469:
6464:
6459:
6454:
6449:
6444:
6438:
6436:
6432:
6431:
6429:
6428:
6423:
6418:
6416:Harmonic drive
6413:
6408:
6403:
6398:
6393:
6387:
6385:
6381:
6380:
6375:
6373:
6372:
6365:
6358:
6350:
6344:
6343:
6338:
6333:
6328:
6323:
6317:
6309:
6308:External links
6306:
6305:
6304:
6295:
6280:
6277:
6259:
6250:
6244:
6226:
6223:
6222:
6221:
6211:
6201:
6192:
6186:
6171:
6165:
6140:
6139:
6123:
6092:
6065:
6040:
6020:
5952:
5929:
5918:(2): 113–125.
5895:
5858:(5): 678–681.
5852:Nanotechnology
5842:
5836:978-0521353656
5835:
5817:
5800:
5793:
5775:
5748:
5743:978-9140115546
5742:
5724:
5711:
5702:
5693:
5673:
5646:
5634:
5632:, p. 290.
5622:
5610:
5608:, p. 287.
5598:
5567:
5555:
5536:
5521:
5519:, p. 742.
5504:
5497:
5472:
5446:
5444:, p. 743.
5431:
5424:
5408:Hilbert, David
5399:
5376:
5349:
5344:Gear Solutions
5330:
5310:
5279:
5258:
5233:
5208:
5183:
5158:
5136:
5122:
5097:
5072:
5064:Joseph Needham
5056:
5038:Freeth, Tony.
5030:
5004:
4975:
4964:(3): 110–115.
4948:
4936:
4911:
4895:
4877:
4855:
4834:
4814:
4798:
4779:
4763:
4744:
4728:
4716:
4700:
4684:
4667:
4665:
4662:
4661:
4660:
4655:
4650:
4645:
4640:
4634:
4633:
4617:
4614:
4572:
4569:
4538:Modern physics
4534:
4531:
4526:English module
4522:pitch diameter
4507:circular pitch
4473:
4470:
4450:Main article:
4447:
4444:
4443:
4442:
4441:
4440:
4426:
4422:
4419:
4394:
4391:
4386:
4383:
4370:
4366:
4362:
4361:
4360:
4359:
4345:
4342:
4339:
4332:
4327:
4321:
4315:
4312:
4307:
4293:
4290:
4283:
4282:
4281:
4280:
4267:
4264:
4259:
4254:
4251:
4246:
4241:
4238:
4233:
4227:
4222:
4208:
4205:
4199:
4195:
4192:
4185:
4179:
4175:
4172:
4165:
4159:
4155:
4152:
4146:
4143:
4140:
4133:
4127:
4124:
4121:
4115:
4112:
4105:
4104:
4101:
4094:
4092:
4089:
4082:
4080:
4077:
4070:
4068:
4065:
4058:
4043:
4040:
4039:
4038:
4033:
4030:
4022:
4010:
4009:
4006:
4003:
4000:
3997:
3994:
3991:
3988:
3985:
3982:
3979:
3975:
3972:
3965:
3962:
3959:
3956:
3949:
3946:
3943:
3940:
3937:
3934:
3931:
3928:
3925:
3922:
3919:
3916:
3913:
3910:
3903:
3899:
3898:
3895:
3888:
3886:
3883:
3876:
3874:
3871:
3864:
3862:
3859:
3852:
3850:
3847:
3840:
3838:
3835:
3828:
3824:
3821:
3820:
3819:
3815:
3812:
3809:
3806:
3802:
3801:Limit diameter
3798:
3797:
3796:
3795:
3780:
3774:
3769:
3765:
3760:
3754:
3749:
3743:
3737:
3732:
3718:
3715:
3711:
3710:
3709:
3708:
3694:
3689:
3685:
3679:
3674:
3670:
3664:
3659:
3648:
3635:
3631:
3627:
3622:
3618:
3614:
3609:
3605:
3591:
3588:
3584:
3581:
3578:
3575:
3571:
3568:
3565:
3562:
3558:
3555:
3551:
3547:
3544:
3541:
3538:
3535:
3532:
3529:
3526:
3523:
3520:
3517:
3514:
3511:
3508:
3505:
3498:
3495:
3492:
3489:
3486:
3483:
3480:
3479:Line of action
3477:
3473:
3472:Path of action
3470:
3467:
3464:
3461:
3457:
3456:
3454:Zone of action
3453:
3446:
3444:
3441:
3434:
3432:
3430:Limit diameter
3429:
3422:
3420:
3417:
3410:
3408:
3405:
3398:
3396:
3393:
3386:
3384:
3381:
3374:
3372:
3370:Line of action
3369:
3362:
3360:
3358:Path of action
3357:
3350:
3348:
3345:
3338:
3334:
3331:
3327:
3326:
3323:
3310:
3306:
3294:
3291:
3280:
3269:
3266:
3263:
3260:
3255:
3252:
3248:
3247:
3236:
3233:
3230:
3227:
3224:
3221:
3218:
3213:
3209:
3197:
3191:
3188:
3175:
3171:
3159:
3156:
3145:
3132:
3129:
3128:
3127:
3124:
3121:
3118:
3115:
3112:
3099:
3095:
3083:
3080:
3076:
3075:
3074:
3073:
3059:
3056:
3051:
3048:
3045:
3031:
3030:
3029:
3016:
3013:
3008:
3003:
3000:
2995:
2992:
2989:
2977:
2971:
2968:
2962:
2959:
2956:
2953:
2950:
2947:
2934:
2930:
2918:
2907:
2899:
2896:
2893:
2888:
2885:
2880:
2877:
2866:
2860:
2849:
2846:
2843:
2838:
2834:
2830:
2825:
2822:
2817:
2814:
2803:
2797:
2794:
2791:
2788:
2775:
2771:
2759:
2755:
2744:
2733:Pressure angle
2730:
2727:
2724:
2721:
2718:
2714:
2710:
2709:
2708:
2707:
2696:
2690:
2687:
2680:
2676:
2670:
2666:
2658:
2655:
2649:
2643:
2640:
2637:
2632:
2629:
2623:
2618:
2614:
2600:
2597:
2575:
2571:
2568:
2567:
2566:
2555:
2550:
2546:
2542:
2537:
2533:
2529:
2524:
2521:
2516:
2513:
2500:
2499:
2498:
2483:
2480:
2476:
2471:
2468:
2451:English Module
2439:
2438:
2437:
2424:
2421:
2416:
2413:
2388:
2381:
2380:
2379:
2378:
2363:
2360:
2357:
2352:
2348:
2343:
2338:
2335:
2312:
2309:
2306:
2299:
2295:
2291:
2285:
2282:
2260:
2247:
2240:
2233:), the normal
2226:
2220:
2216:
2213:
2210:
2207:
2204:
2201:
2198:involute gears
2193:
2190:
2187:
2184:
2181:
2178:
2175:
2172:
2165:
2159:
2144:radians/second
2140:
2134:
2127:
2108:
2105:
2100:Main article:
2097:
2094:
2054:
2051:
2036:motion control
2018:Main article:
2007:
2004:
1998:
1995:
1987:potentiometers
1967:Main article:
1956:
1953:
1911:Main article:
1900:
1899:Sun and planet
1897:
1869:Main article:
1858:
1855:
1839:steering wheel
1815:Main article:
1804:
1801:
1799:
1796:
1763:
1760:
1739:
1736:
1727:
1724:
1715:lantern pinion
1694:
1691:
1661:
1658:
1634:
1631:
1586:multiple start
1520:
1517:
1498:Citroën Type A
1469:
1468:Double helical
1466:
1465:
1464:
1459:
1423:
1412:
1411:
1397:
1393:
1389:
1384:
1380:
1376:
1373:
1363:
1349:
1345:
1341:
1336:
1332:
1328:
1325:
1232:
1229:
1187:
1184:
1178:
1175:
1156:
1153:
1124:
1121:
1119:
1116:
1069:
1066:
1013:
1010:
997:
994:
989:
986:
941:turn apart.
900:action surface
869:
866:
829:
826:
807:wear resistant
723:
720:
678:More recently
608:
605:
560:Proto-Germanic
534:Middle English
499:
496:
422:were built in
328:Luoyang Museum
308:
305:
297:conveyor belts
279:
272:
261:
254:
246:
239:
228:
221:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6790:
6779:
6776:
6774:
6771:
6770:
6768:
6753:
6750:
6748:
6745:
6744:
6742:
6738:
6732:
6729:
6727:
6724:
6722:
6719:
6717:
6714:
6712:
6709:
6707:
6704:
6703:
6701:
6697:
6693:
6686:
6681:
6679:
6674:
6672:
6667:
6666:
6663:
6651:
6648:
6646:
6643:
6641:
6638:
6636:
6633:
6631:
6628:
6626:
6623:
6621:
6618:
6616:
6613:
6612:
6610:
6606:
6596:
6593:
6592:
6590:
6588:
6584:
6578:
6575:
6573:
6570:
6568:
6565:
6563:
6560:
6558:
6555:
6554:
6552:
6548:
6545:
6541:
6535:
6532:
6530:
6527:
6525:
6522:
6520:
6517:
6515:
6512:
6510:
6507:
6505:
6502:
6501:
6499:
6495:
6489:
6486:
6484:
6481:
6480:
6478:
6474:
6468:
6465:
6463:
6460:
6458:
6455:
6453:
6450:
6448:
6445:
6443:
6440:
6439:
6437:
6433:
6427:
6424:
6422:
6419:
6417:
6414:
6412:
6409:
6407:
6404:
6402:
6399:
6397:
6394:
6392:
6389:
6388:
6386:
6382:
6378:
6371:
6366:
6364:
6359:
6357:
6352:
6351:
6348:
6342:
6339:
6337:
6334:
6332:
6329:
6327:
6324:
6321:
6318:
6315:
6312:
6311:
6307:
6302:
6299:
6296:
6293:
6292:9780071704427
6289:
6285:
6281:
6278:
6274:
6267:
6266:
6260:
6256:
6251:
6247:
6241:
6237:
6233:
6229:
6228:
6224:
6218:
6217:
6212:
6210:
6206:
6202:
6198:
6193:
6189:
6183:
6179:
6178:
6172:
6168:
6162:
6158:
6157:
6152:
6148:
6147:
6146:
6145:
6135:
6134:
6127:
6124:
6112:
6111:
6106:
6099:
6097:
6093:
6082:
6081:
6076:
6069:
6066:
6061:
6057:
6056:
6051:
6044:
6041:
6037:
6036:
6031:
6024:
6021:
6016:
6012:
6008:
6004:
5999:
5994:
5990:
5986:
5982:
5978:
5974:
5970:
5966:
5959:
5957:
5953:
5948:
5945:(in German),
5944:
5940:
5933:
5930:
5925:
5921:
5917:
5913:
5906:
5899:
5896:
5891:
5887:
5883:
5879:
5875:
5871:
5866:
5861:
5857:
5853:
5846:
5843:
5838:
5832:
5828:
5821:
5818:
5810:
5804:
5801:
5796:
5790:
5786:
5779:
5776:
5768:
5761:
5755:
5753:
5749:
5745:
5739:
5735:
5728:
5725:
5721:
5715:
5712:
5706:
5703:
5697:
5694:
5691:
5687:
5683:
5677:
5674:
5669:
5665:
5661:
5657:
5650:
5647:
5644:, p. 744
5643:
5638:
5635:
5631:
5626:
5623:
5619:
5614:
5611:
5607:
5602:
5599:
5586:
5582:
5581:
5580:Helical gears
5574:
5572:
5568:
5565:, p. 281
5564:
5559:
5556:
5551:
5547:
5540:
5537:
5532:
5525:
5522:
5518:
5513:
5511:
5509:
5505:
5500:
5494:
5490:
5485:
5484:
5476:
5473:
5460:
5456:
5450:
5447:
5443:
5438:
5436:
5432:
5427:
5421:
5417:
5413:
5409:
5403:
5400:
5395:
5391:
5387:
5380:
5377:
5372:
5368:
5362:
5360:
5358:
5356:
5354:
5350:
5345:
5341:
5334:
5331:
5323:
5322:
5314:
5311:
5298:
5294:
5290:
5283:
5280:
5275:
5271:
5270:
5262:
5259:
5247:
5243:
5237:
5234:
5222:
5218:
5212:
5209:
5197:
5193:
5187:
5184:
5172:
5168:
5162:
5159:
5156:
5152:
5150:
5145:
5140:
5137:
5132:
5126:
5123:
5111:
5107:
5101:
5098:
5086:
5082:
5076:
5073:
5069:
5065:
5060:
5057:
5045:
5041:
5034:
5031:
5019:
5015:
5008:
5005:
5001:
4990:on 4 May 2012
4989:
4985:
4979:
4976:
4971:
4967:
4963:
4959:
4952:
4949:
4946:, p. 462
4945:
4940:
4937:
4925:
4921:
4915:
4912:
4908:
4904:
4899:
4896:
4891:
4890:HowStuffWorks
4887:
4881:
4878:
4865:
4859:
4856:
4852:
4848:
4844:
4838:
4835:
4832:
4828:
4824:
4818:
4815:
4811:
4807:
4802:
4799:
4795:
4791:
4786:
4784:
4780:
4776:
4772:
4767:
4764:
4760:
4756:
4751:
4749:
4745:
4741:
4737:
4732:
4729:
4725:
4720:
4717:
4713:
4709:
4704:
4701:
4697:
4693:
4688:
4685:
4681:
4677:
4672:
4669:
4663:
4659:
4656:
4654:
4651:
4649:
4646:
4644:
4641:
4639:
4636:
4635:
4631:
4625:
4620:
4615:
4613:
4610:
4606:
4602:
4598:
4597:
4592:
4588:
4581:
4577:
4570:
4568:
4566:
4563:compares the
4562:
4557:
4555:
4550:
4547:
4543:
4539:
4532:
4530:
4527:
4523:
4519:
4515:
4510:
4508:
4504:
4500:
4495:
4491:
4487:
4483:
4479:
4471:
4469:
4465:
4463:
4458:
4453:
4445:
4424:
4420:
4417:
4392:
4389:
4384:
4381:
4374:
4373:
4371:
4364:
4363:
4343:
4340:
4337:
4325:
4319:
4305:
4297:
4296:
4294:
4289:
4285:
4284:
4265:
4262:
4257:
4252:
4249:
4244:
4239:
4236:
4231:
4220:
4212:
4211:
4209:
4204:
4200:
4196:
4191:
4184:
4180:
4176:
4171:
4164:
4160:
4156:
4151:
4148:Axial pitch,
4147:
4144:
4139:
4132:
4128:
4125:
4120:
4116:
4113:
4111:
4107:
4106:
4098:
4093:
4086:
4081:
4074:
4069:
4062:
4057:
4055:
4053:
4048:
4041:
4037:
4034:
4031:
4027:
4023:
4020:
4019:
4014:
4007:
4004:
4001:
3998:
3995:
3992:
3989:
3986:
3983:
3980:
3976:
3973:
3970:
3969:datum surface
3966:
3963:
3960:
3957:
3954:
3950:
3948:Profile shift
3947:
3944:
3941:
3938:
3935:
3932:
3929:
3926:
3923:
3920:
3917:
3914:
3911:
3908:
3904:
3901:
3900:
3892:
3887:
3880:
3875:
3868:
3863:
3856:
3851:
3844:
3839:
3832:
3827:
3822:
3816:
3813:
3810:
3807:
3803:
3800:
3799:
3778:
3767:
3763:
3758:
3747:
3741:
3730:
3722:
3721:
3719:
3713:
3712:
3687:
3683:
3672:
3668:
3657:
3649:
3633:
3629:
3625:
3620:
3616:
3612:
3607:
3603:
3595:
3594:
3592:
3582:
3579:
3569:
3566:
3556:
3552:
3545:
3542:
3536:
3533:
3527:
3524:
3518:
3515:
3512:
3509:
3506:
3503:
3499:
3496:
3493:
3490:
3487:
3484:
3481:
3478:
3474:
3471:
3468:
3465:
3462:
3459:
3458:
3450:
3445:
3438:
3433:
3426:
3421:
3414:
3409:
3406:Arc of action
3402:
3397:
3390:
3385:
3378:
3373:
3366:
3361:
3354:
3349:
3342:
3337:
3333:Tooth contact
3332:
3330:
3324:
3308:
3304:
3295:
3292:
3278:
3270:
3267:
3264:
3261:
3258:
3257:
3253:
3251:
3231:
3225:
3222:
3219:
3216:
3211:
3207:
3198:
3196:
3192:
3189:
3173:
3169:
3160:
3157:
3143:
3136:Helix angle,
3135:
3134:
3130:
3125:
3122:
3119:
3116:
3113:
3097:
3093:
3084:
3081:
3078:
3077:
3057:
3054:
3049:
3046:
3043:
3036:
3035:
3032:
3014:
3011:
3006:
3001:
2998:
2993:
2990:
2987:
2980:
2979:
2978:
2976:
2972:
2969:
2967:
2963:
2960:
2958:Working depth
2957:
2954:
2951:
2948:
2932:
2928:
2920:Whole depth,
2919:
2902:root diameter
2897:
2894:
2886:
2883:
2878:
2875:
2867:
2865:
2861:
2844:
2841:
2836:
2832:
2823:
2820:
2815:
2812:
2804:
2802:
2798:
2795:
2793:Root diameter
2792:
2789:
2773:
2769:
2760:
2756:
2742:
2734:
2731:
2728:
2726:Arc of action
2725:
2722:
2719:
2715:
2713:Pitch surface
2712:
2711:
2694:
2688:
2685:
2678:
2674:
2668:
2664:
2656:
2653:
2647:
2641:
2638:
2635:
2630:
2627:
2621:
2616:
2612:
2604:
2603:
2601:
2598:
2595:
2590:
2586:
2581:
2569:
2548:
2544:
2540:
2535:
2531:
2522:
2519:
2514:
2511:
2504:
2503:
2501:
2481:
2478:
2474:
2469:
2466:
2459:
2458:
2456:
2452:
2448:
2444:
2440:
2422:
2419:
2414:
2411:
2404:
2403:
2401:
2397:
2393:
2389:
2387:
2383:
2382:
2361:
2358:
2355:
2350:
2346:
2341:
2336:
2333:
2310:
2307:
2304:
2297:
2293:
2289:
2283:
2280:
2273:
2272:
2258:
2250:
2243:
2236:
2232:
2227:
2225:
2221:
2217:
2214:
2211:
2208:
2205:
2202:
2199:
2194:
2191:
2188:
2185:
2182:
2179:
2176:
2173:
2170:
2166:
2164:
2160:
2145:
2141:
2138:
2135:
2133:(RPM or rpm).
2132:
2128:
2126:
2122:
2118:
2117:
2116:
2114:
2106:
2103:
2095:
2093:
2091:
2087:
2083:
2078:
2074:
2070:
2069:magnetic gear
2064:
2063:magnetic gear
2060:
2053:Magnetic gear
2052:
2050:
2047:
2045:
2041:
2037:
2033:
2032:
2027:
2026:harmonic gear
2021:
2012:
2006:Harmonic gear
2005:
2003:
1996:
1994:
1992:
1988:
1984:
1980:
1976:
1970:
1961:
1954:
1952:
1950:
1946:
1941:
1939:
1935:
1931:
1930:steam engines
1927:
1926:rotary motion
1923:
1919:
1914:
1905:
1898:
1896:
1894:
1890:
1886:
1883:(see below),
1882:
1878:
1872:
1863:
1856:
1854:
1852:
1846:
1844:
1840:
1836:
1832:
1828:
1824:
1818:
1809:
1802:
1797:
1795:
1791:
1789:
1785:
1780:
1777:
1768:
1761:
1759:
1755:
1753:
1752:
1747:
1746:
1737:
1735:
1731:
1725:
1723:
1719:
1716:
1712:
1708:
1699:
1692:
1690:
1686:
1684:
1680:
1671:
1666:
1659:
1657:
1655:
1650:
1648:
1647:tooth profile
1639:
1633:Tooth profile
1632:
1630:
1627:
1625:
1621:
1615:
1613:
1609:
1605:
1600:
1598:
1594:
1589:
1587:
1583:
1579:
1575:
1574:single thread
1569:
1565:
1563:
1559:
1555:
1551:
1546:
1545:Slewing drive
1542:
1533:
1525:
1518:
1516:
1513:
1511:
1505:
1503:
1499:
1495:
1491:
1486:
1482:
1474:
1467:
1463:
1460:
1458:
1455:
1454:
1453:
1450:
1447:. For shafts
1446:
1442:
1436:
1421:
1395:
1391:
1387:
1382:
1378:
1374:
1371:
1364:
1347:
1343:
1339:
1334:
1330:
1326:
1323:
1316:
1315:
1314:
1310:
1308:
1303:
1301:
1297:
1293:
1289:
1284:
1282:
1272:
1268:
1265:
1261:
1256:
1252:
1251:
1239:Helical gears
1237:
1230:
1228:
1226:
1222:
1218:
1213:
1209:
1207:
1203:
1202:
1192:
1185:
1183:
1176:
1174:
1172:
1168:
1167:contrate gear
1164:
1163:
1154:
1152:
1150:
1146:
1137:
1131:Internal gear
1129:
1122:
1117:
1115:
1113:
1108:
1102:
1100:
1099:
1094:
1089:
1087:
1083:
1074:
1067:
1065:
1061:
1058:
1056:
1052:
1047:
1045:
1041:
1037:
1032:
1030:
1023:
1018:
1011:
1009:
1005:
1002:
995:
993:
987:
985:
981:
978:
976:
972:
968:
963:
959:
954:
952:
947:
942:
940:
936:
932:
927:
926:of a turn.
925:
921:
917:
913:
909:
905:
901:
896:
894:
890:
887:
886:angular speed
883:
879:
878:rotation axis
875:
867:
865:
862:
857:
853:
851:
847:
843:
839:
835:
827:
825:
823:
818:
816:
812:
808:
804:
800:
799:transmissions
795:
793:
789:
785:
781:
777:
773:
769:
765:
759:
757:
753:
749:
745:
741:
737:
733:
729:
721:
719:
717:
713:
709:
701:
696:
692:
689:
685:
681:
676:
674:
665:
661:
659:
655:
651:
647:
642:
640:
636:
631:
629:
625:
618:
613:
606:
604:
602:
598:
595:
591:
587:
583:
580:
576:
572:
569:
565:
561:
557:
553:
550:
546:
543:
539:
535:
531:
526:
524:
520:
516:
512:
509:
505:
497:
495:
493:
492:
486:
484:
480:
478:
474:
470:
465:
463:
459:
455:
450:
448:
444:
440:
436:
433:was built in
432:
427:
425:
421:
416:
412:
410:
406:
402:
393:
389:
387:
383:
379:
375:
372:
368:
364:
360:
356:
352:
348:
339:
335:
333:
329:
325:
318:
313:
306:
304:
302:
298:
294:
289:
284:
282:
276:
269:
265:
258:
251:
245:
238:
234:
227:
220:
216:
213:
209:
206:
202:
198:
194:
189:
187:
183:
179:
175:
174:timing pulley
171:
167:
163:
159:
155:
151:
147:
146:micromachines
143:
134:
130:
128:
124:
123:linear motion
120:
116:
112:
108:
104:
99:
97:
93:
89:
85:
81:
77:
73:
70:
66:
62:
54:
49:
45:
41:
37:
33:
19:
18:Internal gear
6751:
6740:Higher pairs
6509:Differential
6504:Transmission
6457:Spiral bevel
6376:
6300:
6283:
6264:
6254:
6235:
6215:
6196:
6176:
6155:
6144:Bibliography
6143:
6142:
6132:
6126:
6116:14 September
6114:. Retrieved
6108:
6084:, retrieved
6078:
6068:
6060:the original
6053:
6043:
6033:
6023:
5972:
5968:
5946:
5942:
5938:
5932:
5915:
5911:
5898:
5855:
5851:
5845:
5826:
5820:
5803:
5784:
5778:
5767:the original
5733:
5727:
5719:
5714:
5705:
5696:
5681:
5676:
5666:– via
5659:
5649:
5637:
5625:
5613:
5601:
5589:, retrieved
5585:the original
5579:
5558:
5549:
5539:
5530:
5524:
5482:
5475:
5465:20 September
5463:. Retrieved
5458:
5449:
5415:
5402:
5394:the original
5389:
5386:"Gear Types"
5379:
5370:
5343:
5333:
5320:
5313:
5301:, retrieved
5297:the original
5292:
5282:
5268:
5261:
5249:. Retrieved
5245:
5236:
5224:. Retrieved
5220:
5211:
5199:. Retrieved
5195:
5186:
5174:. Retrieved
5170:
5161:
5148:
5139:
5125:
5113:. Retrieved
5109:
5100:
5088:. Retrieved
5084:
5075:
5067:
5059:
5047:. Retrieved
5043:
5033:
5021:. Retrieved
5017:
5007:
4999:
4992:. Retrieved
4988:the original
4978:
4961:
4957:
4951:
4939:
4927:. Retrieved
4923:
4914:
4898:
4889:
4880:
4868:. Retrieved
4858:
4846:
4837:
4822:
4817:
4809:
4801:
4793:
4774:
4766:
4758:
4739:
4731:
4719:
4711:
4703:
4695:
4687:
4679:
4671:
4648:Differential
4608:
4600:
4594:
4587:planthoppers
4584:
4579:
4558:
4551:
4536:
4525:
4521:
4517:
4513:
4511:
4506:
4502:
4498:
4493:
4489:
4475:
4466:
4455:
4287:
4202:
4189:
4182:
4169:
4162:
4149:
4137:
4130:
4118:
4109:
4051:
4046:
4045:
3907:datum circle
3814:Face advance
3442:Face advance
3328:
3271:Lead angle,
3249:
3194:
3131:Helical gear
3117:Interference
2974:
2965:
2863:
2800:
2450:
2399:
2395:
2385:
2245:
2238:
2234:
2230:
2223:
2162:
2142:Measured in
2124:
2110:
2096:Nomenclature
2068:
2066:
2048:
2029:
2025:
2023:
2000:
1983:oscillations
1972:
1942:
1916:
1874:
1851:rack railway
1847:
1834:
1822:
1820:
1792:
1781:
1773:
1756:
1749:
1743:
1741:
1732:
1729:
1726:Mathematical
1722:used them.
1720:
1714:
1711:lantern gear
1710:
1706:
1704:
1687:
1675:
1651:
1646:
1644:
1628:
1623:
1620:saddle point
1616:
1608:machine head
1604:self locking
1603:
1601:
1592:
1590:
1585:
1581:
1578:single start
1577:
1573:
1570:
1566:
1557:
1549:
1548:
1514:
1509:
1506:
1492:, as in the
1483:
1479:
1448:
1444:
1440:
1437:
1413:
1311:
1304:
1299:
1285:
1277:
1263:
1254:
1248:
1246:
1221:generatrices
1220:
1214:
1210:
1205:
1199:
1197:
1180:
1166:
1160:
1158:
1148:
1144:
1142:
1112:differential
1103:
1096:
1090:
1081:
1079:
1062:
1059:
1057:(UK) gears.
1054:
1050:
1048:
1033:
1028:
1026:
1006:
1003:
999:
991:
982:
979:
974:
970:
966:
961:
957:
955:
945:
943:
938:
934:
930:
928:
923:
911:
907:
899:
897:
892:
888:
881:
877:
871:
858:
854:
850:timing belts
831:
819:
815:quench press
803:heat treated
796:
784:gear shaping
772:gear cutting
760:
756:gear cutting
725:
704:
677:
670:
643:
632:
621:
600:
596:
589:
581:
570:
563:
555:
551:
544:
536:cogge, from
529:
527:
522:
518:
514:
510:
503:
501:
489:
487:
483:Differential
481:
466:
451:
428:
417:
413:
407:. A set of
398:
382:astronomical
344:
324:Zhou dynasty
321:
315:Iron gears,
288:transmission
285:
278:
271:
267:
260:
253:
249:
243:
236:
232:
225:
218:
214:
211:
207:
200:
190:
186:Geneva drive
139:
136:Geneva drive
113:between two
102:
100:
91:
87:
72:machine part
64:
60:
58:
44:
6716:Cylindrical
6699:Lower pairs
6635:Chain drive
6595:Wheel train
6467:Herringbone
6151:McGraw-Hill
6086:18 November
5660:ISAW Papers
5251:13 February
5201:13 February
5192:"gear (n.)"
5144:Irfan Habib
4944:Norton 2004
4929:21 November
4407:degrees or
4078:Tooth pitch
4032:Root fillet
3079:Base circle
2447:millimeters
2209:Pitch point
2174:Gear, wheel
2158:rad/second.
2119:Rotational
1597:music boxes
1494:final drive
1490:bevel gears
1093:hyperboloid
1076:Hypoid gear
935:tooth faces
834:link chains
822:3D printing
722:Manufacture
716:grist mills
712:paper mills
635:flour mills
462:cotton gins
426:by 725 AD.
359:Roman Egypt
345:In Europe,
317:Han dynasty
178:timing belt
160:to over 10
148:, to a few
6767:Categories
6630:Belt drive
6615:Ball screw
6562:Derailleur
6396:Worm drive
5246:Etymonline
5242:"cog (n.)"
5221:Wiktionary
5196:Etymonline
4994:10 January
4849:magazine.
4664:References
4484:(inch) or
4478:dimensions
4462:gear train
3993:Stub teeth
3978:thickness.
3958:Rack shift
3953:datum line
3502:face width
2862:Dedendum,
2799:Addendum,
1975:efficiency
1949:driveshaft
1934:James Watt
1656:and wear.
1624:cone-drive
1558:worm wheel
1541:Worm drive
1225:bevel gear
1182:together.
1171:escapement
1162:crown gear
1139:Crown gear
1086:skew lines
1036:bevel gear
874:rigid body
594:Lithuanian
374:Archimedes
212:gear ratio
184:, and the
170:link chain
96:gear train
53:spur gears
6778:Tribology
6711:Prismatic
6645:Freewheel
6625:Jackscrew
6620:Leadscrew
6497:Mechanics
6110:The Verge
5949:: 383–388
5533:, S.CHAND
5303:7 January
5151:, page 53
4958:Endeavour
4421:π
4382:τ
4344:ψ
4341:
4263:π
3634:β
3630:ϵ
3621:α
3617:ϵ
3608:γ
3604:ϵ
3476:rotation.
3279:λ
3254:Worm gear
3232:ψ
3226:
3144:ψ
3012:π
2952:Clearance
2898:−
2842:−
2743:θ
2423:π
2362:ψ
2359:
2311:ψ
2308:
2259:ψ
2121:frequency
2044:aerospace
1951:is gray.
1762:Skew axes
1754:curves.
1707:cage gear
1670:millstone
1660:Artisanal
1562:spur gear
1552:resemble
1527:Worm gear
1422:β
1392:β
1388:−
1379:β
1344:β
1331:β
1255:dry fixed
1201:spur gear
1194:Spur gear
1022:lock gate
920:congruent
817:is used.
792:broaching
776:machining
774:or other
768:sintering
764:net shape
646:cast iron
617:cage gear
607:Materials
566:(compare
547:('cog'),
542:Norwegian
540:(compare
538:Old Norse
508:Old Norse
502:The word
498:Etymology
469:Astrarium
454:worm gear
431:astrolabe
347:Aristotle
65:gearwheel
6706:Revolute
6608:See also
6587:Horology
6577:Sprocket
6567:Hub gear
6550:Bicycles
6543:Examples
6514:Coupling
6483:Involute
6153:(2007),
6015:24640726
6007:24031019
5890:14994774
5722:, (2007)
5414:(1952),
5066:(1986).
4870:16 March
4643:Sprocket
4638:Gear box
4616:See also
4605:filleted
4482:imperial
4457:Backlash
4446:Backlash
4026:undercut
4021:Undercut
4016:Undercut
3805:profile.
2594:evolvent
2219:defined.
2150:RPM = 2π
2077:backlash
2040:robotics
1945:flywheel
1751:involute
1654:friction
1441:parallel
1264:parallel
1186:Straight
1149:internal
1145:external
1053:(US) or
996:Parallel
951:backlash
904:pressure
752:blanking
700:windmill
654:aluminum
584:), from
513:(plural
445:and its
386:eclipses
371:polymath
166:sprocket
88:cogwheel
84:machined
69:rotating
36:Sprocket
6488:Cycloid
6462:Helical
6384:Systems
6265:Gearing
5977:Bibcode
5969:Science
5920:Bibcode
5912:Apeiron
5870:Bibcode
5591:15 June
5226:29 July
4808:in the
4792:in the
4773:in the
4757:in the
4738:in the
4710:in the
4694:in the
4678:in the
4609:Issus's
4518:modulus
4439:radians
2400:modulus
2169:integer
2107:General
2073:magnets
1843:tie rod
1745:cycloid
1496:of the
1449:crossed
1445:crossed
1250:helical
1231:Helical
1042:) of a
1040:frustum
1029:crossed
1012:Crossed
788:milling
780:hobbing
675:joint
641:wood.
575:cogboat
549:Swedish
441:in the
435:Isfahan
418:Geared
307:History
250:, and
154:watches
121:and/or
78:and/or
6726:Planar
6557:Cogset
6534:Offset
6435:Shapes
6290:
6242:
6207:
6184:
6163:
6013:
6005:
5888:
5833:
5791:
5740:
5495:
5422:
5176:5 June
5115:5 June
5090:5 June
5049:5 June
5023:5 June
4909:, p.84
4514:module
4486:metric
4198:plane.
2580:primes
2455:inches
2396:module
2235:module
2180:Pinion
2156:
2152:
2148:
1891:, and
1835:pinion
1831:Torque
1683:prisms
1554:screws
1504:gear.
1414:where
1288:thrust
1107:pinion
1098:hypoid
914:-fold
848:, and
790:, and
782:, but
754:; and
738:, and
624:bronze
579:German
515:gørvar
443:zodiac
401:Ma Jun
293:lathes
162:metres
107:torque
103:pinion
80:torque
38:, and
6773:Gears
6752:Gears
6721:Screw
6519:Train
6452:Crown
6447:Bevel
6377:Gears
6269:(PDF)
6011:S2CID
5908:(PDF)
5886:S2CID
5860:arXiv
5812:(PDF)
5770:(PDF)
5763:(PDF)
5662:(4).
5346:: 22.
5325:(PDF)
4178:gear.
4066:Pitch
4052:pitch
4047:Pitch
4042:Pitch
3554:gear.
2717:cone.
2574:and z
2449:; an
2443:units
2067:In a
1979:ratio
1938:crank
1924:into
1849:in a
1550:Worms
1260:helix
1247:In a
1155:Crown
1055:mitre
1051:miter
1027:In a
811:tough
650:steel
639:maple
571:kogge
568:Dutch
564:kuggō
556:kugge
523:gørva
511:gørvi
447:phase
424:China
357:, in
332:China
193:lever
125:to a
119:force
115:axles
90:. A
67:is a
6442:Spur
6288:ISBN
6273:NASA
6240:ISBN
6205:ISBN
6182:ISBN
6161:ISBN
6118:2013
6088:2020
6003:PMID
5831:ISBN
5789:ISBN
5738:ISBN
5593:2009
5493:ISBN
5489:2125
5467:2018
5420:ISBN
5305:2011
5253:2020
5228:2019
5203:2020
5178:2022
5117:2022
5092:2022
5051:2022
5025:2022
4996:2011
4931:2023
4872:2022
4559:The
4503:1/20
4501:and
4499:1/10
4490:inch
4250:25.4
3818:end.
3259:Lead
3055:25.4
2475:25.4
2203:Axis
2061:and
2042:and
1989:and
1877:axes
1823:rack
1748:and
1693:Cage
1543:and
1519:Worm
1502:Wüst
1082:skew
1068:Skew
1044:cone
969:and
898:The
736:sand
732:dies
730:are
714:and
682:and
652:and
601:gēw-
597:gugà
590:gugā
582:Kock
577:'),
552:kugg
545:kugg
519:gøra
504:gear
452:The
439:moon
295:and
264:= 1/
158:toys
156:and
127:rack
109:for
61:gear
6747:Cam
5993:hdl
5985:doi
5973:341
5878:doi
5686:doi
4966:doi
4827:doi
4516:or
4390:360
4369:, τ
4338:cos
4024:An
3587:, ε
3574:, ε
3561:, ε
3550:, ε
3223:cos
2398:or
2356:cos
2305:cos
2271:):
2146:. 1
2139:, ω
2028:or
1713:or
1584:or
1576:or
1510:net
1298:or
1253:or
1204:or
1165:or
852:.
628:tin
530:cog
152:in
144:in
98:.
92:cog
63:or
6769::
6271:,
6107:.
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6077:,
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6001:.
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5971:.
5967:.
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5914:.
5910:.
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5876:.
5868:.
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4782:^
4747:^
4291:nd
4193:bt
4188:,
4173:bn
4168:,
4136:,
2975:DP
2735:,
2123:,
2038:,
2024:A
1993:.
1932:.
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1821:A
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750:;
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528:A
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494:.
334:.
303:.
268:=
235:=
231:=
150:mm
142:μm
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6684:e
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6670:v
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6219:.
6190:.
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4425:z
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4367:N
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4320:=
4314:d
4311:n
4306:P
4288:P
4266:p
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4253:m
4245:=
4240:d
4237:N
4232:=
4226:d
4221:P
4206:d
4203:P
4190:p
4186:b
4183:p
4170:p
4166:N
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4153:x
4150:p
4141:e
4138:p
4134:n
4131:p
4122:t
4119:p
4110:p
3909:.
3779:2
3773:F
3768:m
3764:+
3759:2
3753:p
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3736:o
3731:m
3716:o
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3688:m
3684:+
3678:p
3673:m
3669:=
3663:t
3658:m
3626:+
3613:=
3589:γ
3585:t
3576:β
3572:F
3563:α
3559:p
3548:c
3539:r
3530:a
3521:t
3504:.
3309:w
3305:d
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3229:(
3220:p
3217:=
3212:n
3208:p
3195:p
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3170:p
3098:b
3094:p
3058:m
3050:=
3047:P
3044:D
3015:p
3007:=
3002:d
2999:N
2994:=
2991:P
2988:D
2966:p
2933:t
2929:h
2906:)
2895:D
2892:(
2887:2
2884:1
2879:=
2876:b
2864:b
2848:)
2845:D
2837:o
2833:D
2829:(
2824:2
2821:1
2816:=
2813:a
2801:a
2774:o
2770:D
2695:.
2689:1
2686:+
2679:1
2675:z
2669:2
2665:z
2657:a
2654:2
2648:=
2642:1
2639:+
2636:u
2631:a
2628:2
2622:=
2617:w
2613:d
2576:2
2572:1
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2549:2
2545:z
2541:+
2536:1
2532:z
2528:(
2523:2
2520:m
2515:=
2512:a
2482:P
2479:D
2470:=
2467:m
2420:p
2415:=
2412:m
2386:m
2351:d
2347:P
2342:N
2337:=
2334:d
2298:n
2294:m
2290:N
2284:=
2281:d
2248:d
2246:P
2241:n
2239:m
2237:(
2231:N
2229:(
2224:d
2163:N
2125:n
1396:2
1383:1
1375:=
1372:E
1348:2
1340:+
1335:1
1327:=
1324:E
975:p
971:q
967:p
962:q
958:p
946:N
939:N
931:N
924:N
912:N
908:N
893:t
891:(
889:ω
882:t
588:*
562:*
280:2
277:N
275:/
273:1
270:N
266:r
262:1
259:ω
257:/
255:2
252:ω
247:1
244:N
242:/
240:2
237:N
233:r
229:1
226:T
224:/
222:2
219:T
215:r
208:ω
201:T
42:.
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