Two meshing gears transmitting rotational motion. Note that the smaller gear is rotating faster. Although the larger gear is rotating less quickly, its torque is proportionally greater. One subtlety of this particular arrangement is that the linear speed at the rim is the same on both gears.

A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine. Geared devices can change the speed, torque, and direction of a power source. The most common situation is for a gear to mesh with another gear, however a gear can also mesh a non-rotating toothed part, called a rack, thereby producing translation instead of rotation.

The gears in a transmission are analogous to the wheels in a pulley. An advantage of gears is that the teeth of a gear prevent slipping.

When two gears of unequal number of teeth are combined a mechanical advantage is produced, with both the rotational speeds and the torques of the two gears differing in a simple relationship.

In transmissions which offer multiple gear ratios, such as bicycles and cars, the term gear, as in first gear, refers to a gear ratio rather than an actual physical gear. The term is used to describe similar devices even when gear ratio is continuous rather than discrete, or when the device does not actually contain any gears, as in a continuously variable transmission.^[1]

The earliest known reference to gears was circa A.D. 50 by Hero of Alexandria,^[2] but they can be traced back to the Greek mechanics of the Alexandrian school in the 3rd century B.C. and were greatly developed by the Greek polymath Archimedes (287–212 B.C.).^[3] The Antikythera mechanism is an example of a very early and intricate geared device, designed to calculate astronomical positions. Its time of construction is now estimated between 150 and 100 BC.^[4]

Definition of gear terminology.

Comparison with drive mechanisms[link]

The definite velocity ratio which results from having teeth gives gears an advantage over other drives (such as traction drives and V-belts) in precision machines such as watches that depend upon an exact velocity ratio. In cases where driver and follower are in close proximity gears also have an advantage over other drives in the reduced number of parts required; the downside is that gears are more expensive to manufacture and their lubrication requirements may impose a higher operating cost.

The automobile transmission allows selection between gears to give various mechanical advantages.

Types[link]

External vs internal gears[link]

Internal gear

An external gear is one with the teeth formed on the outer surface of a cylinder or cone. Conversely, an internal gear is one with the teeth formed on the inner surface of a cylinder or cone. For bevel gears, an internal gear is one with the pitch angle exceeding 90 degrees. Internal gears do not cause direction reversal.^[5]

Spur[link]

Spur gear

Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder or disk with the teeth projecting radially, and although they are not straight-sided in form, the edge of each tooth is straight and aligned parallel to the axis of rotation. These gears can be meshed together correctly only if they are fitted to parallel shafts.

Helical[link]

Helical gears
Top: parallel configuration
Bottom: crossed configuration

Helical or "dry fixed" gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling causes the tooth shape to be a segment of a helix. Helical gears can be meshed in a parallel or crossed orientations. The former refers to when the shafts are parallel to each other; this is the most common orientation. In the latter, the shafts are non-parallel, and in this configuration are sometimes known as "skew gears".

The angled teeth engage more gradually than do spur gear teeth causing them to run more smoothly and quietly.^[6] With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel; a moving curve of contact then grows gradually across the tooth face to a maximum then recedes until the teeth break contact at a single point on the opposite side. In spur gears teeth suddenly meet at a line contact across their entire width causing stress and noise. Spur gears make a characteristic whine at high speeds. Whereas spur gears are used for low speed applications and those situations where noise control is not a problem, the use of helical gears is indicated when the application involves high speeds, large power transmission, or where noise abatement is important. The speed is considered to be high when the pitch line velocity exceeds 25 m/s.^[7]

A disadvantage of helical gears is a resultant thrust along the axis of the gear, which needs to be accommodated by appropriate thrust bearings, and a greater degree of sliding friction between the meshing teeth, often addressed with additives in the lubricant.

Skew gears[link]

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:^[8]

Failed to parse (Missing texvc executable; please see math/README to configure.): E = \beta_1 + \beta_2

for gears of the same handedness

Failed to parse (Missing texvc executable; please see math/README to configure.): E = \beta_1 - \beta_2

for gears of opposite handedness

Where Failed to parse (Missing texvc executable; please see math/README to configure.): \beta

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.[8]

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 is zero – that is, the shafts are parallel. Where the sum or the difference (as described in the equations above) is not zero the shafts are crossed. For shafts crossed at right angles the helix angles are of the same hand because they must add to 90 degrees.

• 3D Animation of helical gears (parallel axis)
• 3D Animation of helical gears (crossed axis)

Double helical[link]

Double helical gears

Double helical gears, or herringbone gears, overcome the problem of axial thrust presented by "single" helical gears, by having two sets of teeth that are set in a V shape. A double helical gear can be thought of as two mirrored helical gears joined together. This arrangement cancels out the net axial thrust, since each half of the gear thrusts in the opposite direction. Double helical gears are more difficult to manufacture due to their more complicated shape.

For both possible rotational directions, there exist two possible arrangements for the oppositely-oriented helical gears or gear faces. One arrangement is stable, and the other is unstable. In a stable orientation, the helical gear faces are oriented so that each axial force is directed toward the center of the gear. In an unstable orientation, both axial forces are directed away from the center of the gear. In both arrangements, the total (or net) 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 will generate 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.

Stable double helical gears can be directly interchanged with spur gears without any need for different bearings.

Bevel[link]

A bevel gear is shaped like a right circular cone with most of its tip cut off. When two bevel gears mesh, their imaginary vertices must occupy the same point. Their shaft axes also intersect at this point, forming an arbitrary non-straight angle between the shafts. The angle between the shafts can be anything except zero or 180 degrees. Bevel gears with equal numbers of teeth and shaft axes at 90 degrees are called miter gears.

• 3D Animation of two bevel gears

Spiral bevels[link]

Spiral bevel gears

The teeth of a bevel gear may be straight-cut as with spur gears, or they may be cut in a variety of other shapes. Spiral bevel gear teeth are curved along the tooth's length and set at an angle, analogously to the way helical gear teeth are set at an angle compared to spur gear teeth. Zerol bevel gears have teeth which are curved along their length, but not angled. Spiral bevel gears have the same advantages and disadvantages relative to their straight-cut cousins as helical gears do to spur gears. Straight bevel gears are generally used only at speeds below 5 m/s (1000 ft/min), or, for small gears, 1000 r.p.m.^[9]

Hypoid[link]

Hypoid gear

Hypoid gears resemble spiral bevel gears except the shaft axes do not intersect. The pitch surfaces appear conical but, to compensate for the offset shaft, are in fact hyperboloids of revolution.^[10][11] Hypoid gears are almost always designed to operate with shafts at 90 degrees. Depending on which side the shaft is offset to, relative to the angling of the teeth, contact between hypoid gear teeth may be even smoother and more gradual than with spiral bevel gear teeth. Also, the pinion can be designed with fewer teeth than a spiral bevel pinion, with the result that gear ratios of 60:1 and higher are feasible using a single set of hypoid gears.^[12] This style of gear is most commonly found driving mechanical differentials; which are normally straight cut bevel gears; in motor vehicle axles.

Crown[link]

Crown gear

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

Worm[link]

Worm gear

4-start worm and wheel

Worm gears resemble screws. A worm gear is usually meshed with a spur gear or a helical gear, which is called the gear, wheel, or worm wheel.

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.^[13] A disadvantage is the potential for considerable sliding action, leading to low efficiency.^[14]

Worm gears can be considered 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; and it is these attributes which give it screw like qualities. The distinction between a worm and a helical gear is made when at least one tooth persists for a full rotation around the helix. If this occurs, it is a 'worm'; if not, it is a 'helical gear'. A worm may have as few as one tooth. If that tooth persists for several turns around the helix, the worm will appear, superficially, to have more than one tooth, but what one in fact sees is the same tooth reappearing at intervals along the length of the worm. The usual screw nomenclature applies: a one-toothed worm is called single thread or single start; a worm with more than one tooth is called multiple thread or multiple start. The helix angle of a worm is not usually specified. Instead, the lead angle, which is equal to 90 degrees minus the helix angle, is given.

In a worm-and-gear set, the worm can always drive the gear. However, if the gear attempts to drive the worm, it may or may not succeed. Particularly if the lead angle is small, the gear's teeth may simply lock against the worm's teeth, because the force component circumferential to the worm is not sufficient to overcome friction. Worm-and-gear sets that do lock are called self locking, which can be used to advantage, as for instance when it is desired to set the position of a mechanism by turning the worm and then have the mechanism hold that position. An example is the machine head found on some types of stringed instruments.

If the gear in a worm-and-gear set is an ordinary helical gear only a single point of contact will be achieved.^[15] If medium to high power transmission is desired, the tooth shape of the gear is modified to achieve more intimate contact by making both gears partially envelop each other. This is done by making both concave and joining them at a saddle point; this is called a cone-drive.^[16] or "Double enveloping"

Worm gears can be right or left-handed following the long established practice for screw threads.^[5]

• 3D Animation of a worm-gear set

Non-circular[link]

Non-circular gears

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

Rack and pinion[link]

Rack and pinion gearing

A rack is a toothed bar or rod that can be thought of as a sector gear with an infinitely large radius of curvature. Torque can be converted to linear force by meshing a rack with a pinion: the pinion turns; the rack moves in a straight line. Such a mechanism is used in automobiles to convert the rotation of the steering wheel into the left-to-right motion of the tie rod(s). 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 then derived from that. The rack and pinion gear type is employed in a rack railway.

Epicyclic[link]

Epicyclic gearing

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

Sun and planet[link]

Sun (yellow) and planet (red) gearing

Sun and planet gearing was a method of converting reciprocating motion into rotary motion in steam engines. It was famously used by James Watt on his early steam engines in order to get around the patent on the crank.

In the illustration, the sun is yellow, the planet red, the reciprocating arm is blue, the flywheel is green and the driveshaft is grey.

Harmonic drive[link]

Harmonic drive gearing

A harmonic drive is a specialized gearing mechanism often used in industrial motion control, robotics and aerospace for its advantages over traditional gearing systems, including lack of backlash, compactness and high gear ratios.

Cage gear[link]

Cage gear in Pantigo Windmill, Long Island

A cage gear, also called a lantern gear or lantern pinion has cylindrical rods for teeth, parallel to the axle and arranged in a circle around it, much as the bars on a round bird cage or lantern. The assembly is held together by disks at either end into which the tooth rods and axle are set. Lantern gears are more efficient than solid pinions, and dirt can fall through the rods rather than becoming trapped and increasing wear.

Sometimes used in clocks, the lantern pinion should always be driven by a gearwheel, not used as the driver. The lantern pinion was not initially favoured by conservative clock makers. It became popular in turret clocks where dirty working conditions were most commonplace. Domestic American clock movements often used them.

Magnetic gear[link]

All cogs of each gear component of such gear are performed as a constant magnet with periodic alternation of opposite magnetic poles on mating surfaces and nearest poles of cogs of different gear components are similar. And gear components are mounted with a backlash with capability of mechanical gearing.

At not too big load such gear works without touch of motive details and has a raised reliability without noise.

(Literature: Kravchenko A.I., Bovda A.M. Gear with magnetic couple. Pat. of Ukraine N. 56700 – Bul. N. 2, 2011 – F16H 49/00.)

Nomenclature[link]

General nomenclature[link]

Rotational frequency, n 

Measured in rotation over time, such as RPM.

Angular frequency, ω 

Measured in radians per second. Failed to parse (Missing texvc executable; please see math/README to configure.): 1 \mathrm{RPM} = \pi/30

rad/second

Number of teeth, N 

How many teeth a gear has, an integer. In the case of worms, it is the number of thread starts that the worm has.

Gear, wheel 

The larger of two interacting gears or a gear on its own.

Pinion 

The smaller of two interacting gears.

Path of contact 

Path followed by the point of contact between two meshing gear teeth.

Line of action, pressure line 

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 involute gears, 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.

Axis 

Axis of revolution of the gear; center line of the shaft.

Pitch point, p 

Point where the line of action crosses a line joining the two gear axes.

Pitch circle, pitch line 

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 defined.

Pitch diameter, d 

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 basic dimension and cannot be measured, but is a location where other measurements are made. Its value is based on the number of teeth, the normal module (or normal diametral pitch), and the helix angle. It is calculated as:

Failed to parse (Missing texvc executable; please see math/README to configure.): d= \frac{N m_n}{\cos \psi}

in metric units or Failed to parse (Missing texvc executable; please see math/README to configure.): d= \frac{N}{P_d \cos \psi}
in imperial units.[17]

Module, m 

A scaling factor used in metric gears with units in millimeters whose effect is to enlarge the gear tooth size as the module increases and reduce the size as the module decreases. Module can be defined in the normal (m_n), the transverse (m_t), or the axial planes (m_a) depending on the design approach employed and the type of gear being designed.^[17] Module is typically an input value into the gear design and is seldom calculated.

Operating pitch diameters 

Diameters determined from the number of teeth and the center distance at which gears operate.^[5] Example for pinion:

Failed to parse (Missing texvc executable; please see math/README to configure.): d_w = \frac{2a}{u+1} = \frac{2a}{\frac{z_2}{z_1}+1}.

Pitch surface 

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 cone.

Angle of action 

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.

Arc of action 

Segment of a pitch circle subtended by the angle of action.

Pressure angle, Failed to parse (Missing texvc executable; please see math/README to configure.): \theta

: 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 pressure angle is constant.

Outside diameter, Failed to parse (Missing texvc executable; please see math/README to configure.): D_o

: Diameter of the gear, measured from the tops of the teeth.

Root diameter 

Diameter of the gear, measured at the base of the tooth.

Addendum, a 

Radial distance from the pitch surface to the outermost point of the tooth. Failed to parse (Missing texvc executable; please see math/README to configure.): a=(D_o-D)/2

Dedendum, b 

Radial distance from the depth of the tooth trough to the pitch surface. Failed to parse (Missing texvc executable; please see math/README to configure.): b=(D-{root diameter})/2

Whole depth, Failed to parse (Missing texvc executable; please see math/README to configure.): h_t

: The distance from the top of the tooth to the root; it is equal to addendum plus dedendum or to working depth plus clearance.

Clearance 

Distance between the root circle of a gear and the addendum circle of its mate.

Working depth 

Depth of engagement of two gears, that is, the sum of their operating addendums.

Circular pitch, p 

Distance from one face of a tooth to the corresponding face of an adjacent tooth on the same gear, measured along the pitch circle.

Diametral pitch, Failed to parse (Missing texvc executable; please see math/README to configure.): p_d

: Ratio of the number of teeth to the pitch diameter. Could be measured in teeth per inch or teeth per centimeter.

Base circle 

In involute gears, where the tooth profile is the involute of the base circle. The radius of the base circle is somewhat smaller than that of the pitch circle.

Base pitch, normal pitch, Failed to parse (Missing texvc executable; please see math/README to configure.): p_b

: 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.

Interference 

Contact between teeth other than at the intended parts of their surfaces.

Interchangeable set 

A set of gears, any of which will mate properly with any other.

Helical gear nomenclature[link]

Helix angle, Failed to parse (Missing texvc executable; please see math/README to configure.): \psi

: 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.

Normal circular pitch, Failed to parse (Missing texvc executable; please see math/README to configure.): p_n

: Circular pitch in the plane normal to the teeth.

Transverse circular pitch, p 

Circular pitch in the plane of rotation of the gear. Sometimes just called "circular pitch". Failed to parse (Missing texvc executable; please see math/README to configure.): p_n=p\cos(\psi)

Several other helix parameters can be viewed either in the normal or transverse planes. The subscript n usually indicates the normal.

Worm gear nomenclature[link]

Lead 

Distance from any point on a thread to the corresponding point on the next turn of the same thread, measured parallel to the axis.

Linear pitch, p 

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.

Lead angle, Failed to parse (Missing texvc executable; please see math/README to configure.): \lambda

: Angle between a tangent to the helix and a plane perpendicular to the axis. Note that it is the complement of the helix angle which is usually given for helical gears.

Pitch diameter, Failed to parse (Missing texvc executable; please see math/README to configure.): d_w

: 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.

Subscript w denotes the worm, subscript g denotes the gear.

Tooth contact nomenclature[link]

• 

  Line of contact

• 

  Path of action

• 

  Line of action

• 

  Plane of action

• 

  Lines of contact (helical gear)

• 

  Arc of action

• 

  Length of action

• 

  Limit diameter

• 

  Face advance

• 

  Zone of action

Point of contact 

Any point at which two tooth profiles touch each other.

Line of contact

A line or curve along which two tooth surfaces are tangent to each other.

Path of action 

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 rotation.

Line of action 

The path of action for involute gears. It is the straight line passing through the pitch point and tangent to both base circles.

Surface of action 

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.

Plane of action

The surface of action for involute, parallel axis gears with either spur or helical teeth. It is tangent to the base cylinders.

Zone of action (contact zone) 

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 face width.

Path of contact

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.

Length of action

The distance on the line of action through which the point of contact moves during the action of the tooth profile.

Arc of action, Q_t 

The arc of the pitch circle through which a tooth profile moves from the beginning to the end of contact with a mating profile.

Arc of approach, Q_a 

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.

Arc of recess, Q_r 

The arc of the pitch circle through which a tooth profile moves from contact at the pitch point until contact ends.

Contact ratio, m_c, ε 

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 in which a tooth comes and goes out of contact with the mating gear.

Transverse contact ratio, m_p, ε_α 

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.

Face contact ratio, m_F, ε_β 

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.

Total contact ratio, m_t, ε_γ 

The sum of the transverse contact ratio and the face contact ratio.

Failed to parse (Missing texvc executable; please see math/README to configure.): \epsilon_\gamma = \epsilon_\alpha + \epsilon_\beta

Failed to parse (Missing texvc executable; please see math/README to configure.): m_{\rm t} = m_{\rm p} + m_{\rm F}

Modified contact ratio, m_o 

For bevel gears, the square root of the sum of the squares of the transverse and face contact ratios.

Failed to parse (Missing texvc executable; please see math/README to configure.): m_{\rm o} = (m_{\rm p}^2 + m_{\rm F}^2)^{0.5}

Limit diameter 

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 profile.

Start of active profile (SAP) 

Intersection of the limit diameter and the involute profile.

Face advance 

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 end.

Tooth thickness nomeclature[link]

• 

  Tooth thickness

• 

  Thickness relationships

• 

  Chordal thickness

• 

  Tooth thickness measurement over pins

• 

  Span measurement

• 

  Long and short addendum teeth

Circular thickness 

Length of arc between the two sides of a gear tooth, on the specified datum circle.

Transverse circular thickness 

Circular thickness in the transverse plane.

Normal circular thickness 

Circular thickness in the normal plane. In a helical gear it may be considered as the length of arc along a normal helix.

Axial thickness

In helical gears and worms, tooth thickness in an axial cross section at the standard pitch diameter.

Base circular thickness

In involute teeth, length of arc on the base circle between the two involute curves forming the profile of a tooth.

Normal chordal thickness

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.

Chordal addendum (chordal height) 

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.

Profile shift 

Displacement of the basic rack datum line 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.

Rack shift 

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.

Measurement over pins 

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 datum surface or either one or two pins positioned in the tooth space or spaces opposite the first. This measurement is used to determine tooth thickness.

Span measurement 

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 will be along a line tangent to the base cylinder. It is used to determine tooth thickness.

Modified addendum teeth 

Teeth of engaging gears, one or both of which have non-standard addendum.

Full-depth teeth 

Teeth in which the working depth equals 2.000 divided by the normal diametral pitch.

Stub teeth 

Teeth in which the working depth is less than 2.000 divided by the normal diametral pitch.

Equal addendum teeth 

Teeth in which two engaging gears have equal addendums.

Long and short-addendum teeth 

Teeth in which the addendums of two engaging gears are unequal.

Pitch nomenclature[link]

Pitch is the distance between a point on one tooth and the corresponding point on an adjacent tooth.^[5] It is a dimension measured along a line or curve in the transverse, normal, or axial directions. The use of the single word pitch 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.

• 

  Pitch

• 

  Tooth pitch

• 

  Base pitch relationships

• 

  Principal pitches

Circular pitch, p 

Arc distance along a specified pitch circle or pitch line between corresponding profiles of adjacent teeth.

Transverse circular pitch, p_t 

Circular pitch in the transverse plane.

Normal circular pitch, p_n, p_e 

Circular pitch in the normal plane, and also the length of the arc along the normal pitch helix between helical teeth or threads.

Axial pitch, p_x 

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 pitch. The axial pitch of a helical worm and the circular pitch of its worm gear are the same.

Normal base pitch, p_N, p_bn 

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 gear.

Transverse base pitch, p_b, p_bt 

In an involute gear, the pitch 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 plane.

Diametral pitch (transverse), P_d 

Ratio of the number of teeth to the standard pitch diameter in inches.

Failed to parse (Missing texvc executable; please see math/README to configure.): P_{\rm d} = \frac{N}{d} = \frac{25.4}{m} = \frac{\pi}{p}

Normal diametral pitch, P_nd 

Value of diametral pitch in a normal plane of a helical gear or worm.

Failed to parse (Missing texvc executable; please see math/README to configure.): P_{\rm nd} = \frac{P_{\rm d}}{\cos\psi}

Angular pitch, θ_N, τ 

Angle subtended by the circular pitch, usually expressed in radians.

Failed to parse (Missing texvc executable; please see math/README to configure.): \tau = \frac{360}{z}

degrees or Failed to parse (Missing texvc executable; please see math/README to configure.):  \frac{2\pi}{z} 
radians

Backlash[link]

Backlash 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. 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 gear train equals the sum of the backlash of each pair of gears, so in long trains backlash can become a problem.

For situations in which precision is important, such as instrumentation and control, backlash can be minimised 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, 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 providing for the gear to be slid in the axial direction to take up slack.

Shifting of gears[link]

In some machines (e.g., automobiles) it is necessary to alter the gear ratio to suit the task, a process known as gear shifting or changing gear. There are several ways of shifting gears, for example:

• Manual transmission
• Automatic transmission
• Derailleur gears which are actually sprockets in combination with a roller chain
• Hub gears (also called epicyclic gearing or sun-and-planet gears)

There are several outcomes of gear shifting in motor vehicles. In the case of vehicle noise emissions, there are higher sound levels emitted when the vehicle is engaged in lower gears. The design life of the lower ratio gears is shorter, so cheaper gears may be used (i.e. spur for 1st and reverse) which tends to generate more noise due to smaller overlap ratio and a lower mesh stiffness etc. than the helical gears used for the high ratios. This fact has been utilized in analyzing vehicle generated sound since the late 1960s, and has been incorporated into the simulation of urban roadway noise and corresponding design of urban noise barriers along roadways.^[18]

Tooth profile[link]

• 

  Profile of a spur gear

• 

  Undercut

A profile is one side of a tooth in a cross section between the outside circle and the root circle. Usually a profile is the curve of intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane.

The fillet curve (root fillet) is the concave portion of the tooth profile where it joins the bottom of the tooth space.²

As mentioned near the beginning of the article, the attainment of a non fluctuating velocity ratio is dependent on the profile of the teeth. Friction and wear between two gears is also dependent on the tooth profile. There are a great many tooth profiles that will give a constant velocity ratio, and in many cases, given an arbitrary tooth shape, it is possible to develop a tooth profile for the mating gear that will give a constant velocity ratio. However, two constant velocity tooth profiles have been by far the most commonly used in modern times. They are the cycloid and the involute. The cycloid was more common until the late 1800s; since then the involute has largely superseded it, particularly in drive train applications. The cycloid is in some ways the more interesting and flexible shape; however the involute has two advantages: it is easier to manufacture, and it permits the center to center spacing of the gears to vary over some range without ruining the constancy of the velocity ratio. Cycloidal gears only work properly if the center spacing is exactly right. Cycloidal gears are still used in mechanical clocks.

An undercut is a condition in generated gear teeth when any part of the fillet curve lies inside of a line drawn tangent to the working profile at its point of juncture with the fillet. Undercut may be deliberately introduced to facilitate finishing operations. With undercut the fillet curve intersects the working profile. Without undercut the fillet curve and the working profile have a common tangent.

Gear materials[link]

Wooden gears of a historic windmill

Numerous nonferrous alloys, cast irons, powder-metallurgy and plastics are used in the manufacture of gears. However, steels are most commonly used because of their high strength-to-weight ratio and low cost. Plastic is commonly used where cost or weight is a concern. A properly designed plastic gear can replace steel in many cases because it has many desirable properties, including dirt tolerance, low speed meshing, the ability to "skip" quite well^[19], and the ability to be made with materials not needing additional lubrication. Manufacturers have employed plastic gears to reduce costs in consumer items including copy machines, optical storage devices, VCRs, cheap dynamos, consumer audio equipment, servo motors, and printers.

The module system[link]

Countries which have adopted the metric system generally use the module system. As a result, the term module is usually understood to mean the pitch diameter in millimeters divided by the number of teeth. When the module is based upon inch measurements, it is known as the English module to avoid confusion with the metric module. Module is a direct dimension, whereas diametral pitch is an inverse dimension (like "threads 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 2 mm of pitch diameter for each tooth.^[20]

Manufacture[link]

Gear Cutting simulation (length 1m35s) faster, high bitrate version.

This section requires expansion.

Gears are most commonly produced via hobbing, but they are also shaped, broached, and cast. Plastic gears can also be injection molded; for prototypes, 3D printing in a suitable material can be used. For metal gears the teeth are usually heat treated to make them hard and more wear resistant while leaving the core soft and tough. For large gears that are prone to warp, a quench press is used.

Inspection[link]

Gear geometry can be inspected and verified using various methods such as industrial CT scanning, coordinate-measuring machines, white light scanner or laser scanning. Particularly useful for plastic gears, industrial CT scanning can inspect internal geometry and imperfections such as porosity.

Gear model in modern physics[link]

Modern physics adopted the gear model in different ways. In the nineteenth century, James Clerk Maxwell developed a model of electromagnetism in which magnetic field lines were rotating tubes of incompressible fluid. Maxwell used a gear wheel and called it an "idle wheel" to explain the electrical current as a rotation of particles in opposite directions to that of the rotating field lines.^[21]

More recently, quantum physics uses "quantum gears" in their model. A group of gears can serve as a model for several different systems, such as an artificially constructed nanomechanical device or a group of ring molecules.^[22]

The Three Wave Hypothesis compares the wave–particle duality to a bevel gear.^[23]

See also[link]

• Gear box
• List of gear nomenclature
• Rack and pinion
• Sprocket

References[link]

Bibliography[link]

• American Gear Manufacturers Association; American National Standards Institute (2005), Gear Nomenclature, Definitions of Terms with Symbols (ANSI/AGMA 1012-F90 ed.), American Gear Manufacturers Association, ISBN 978-1-55589-846-5. 
• McGraw-Hill (2007), McGraw-Hill Encyclopedia of Science and Technology (10th ed.), McGraw-Hill Professional, ISBN 978-0-07-144143-8. 
• Norton, Robert L. (2004), Design of Machinery (3rd ed.), McGraw-Hill Professional, ISBN 978-0-07-121496-4, http://books.google.com/?id=iepqRRbTxrgC. 
• Vallance, Alex; Doughtie, Venton Levy (1964), Design of machine members (4th ed.), McGraw-Hill. 

Further reading[link]

• Buckingham, Earle (1949), Analytical Mechanics of Gears, McGraw-Hill Book Co.. 
• Coy, John J.; Townsend, Dennis P.; Zaretsky, Erwin V. (1985), Gearing, NASA Scientific and Technical Information Branch, NASA-RP-1152; AVSCOM Technical Report 84-C-15, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20020070912_2002115489.pdf. 
• Kravchenko A.I., Bovda A.M. Gear with magnetic couple. Pat. of Ukraine N. 56700 – Bul. N. 2, 2011 – F16H 49/00.

External links[link]

Wikimedia Commons has media related to: Gears

• Geararium. Museum of gears and toothed wheels Antique, vintage, contemporary gears, sprockets, gear-related objects and interesting connections.
• Kinematic Models for Design Digital Library (KMODDL) Movies and photos of hundreds of working models at Cornell University
• Mathematical Tutorial for Gearing (Relating to Robotics)
• Animation of an Involute Rack and Pinion
• Explanation Of Various Gears & Their Applications
• "Gearology" – A short introductory course on gears and related components
• American Gear Manufacturers Association website
• Gear Solutions Magazine, Your Resource for Machines Services and Tooling for the Gear Industry
• The Four Basic Styles of Gears
• Gear Technology, the Journal of Gear Manufacturing
• "Wheels That Can't Slip." Popular Science, February 1945, pp. 120–125.

Ken Block
Ken Block in 2008.
Nationality	American
Born	(1967-11-21) 21 November 1967 (age 44) Long Beach, California
2012 Rally America
Debut season	2005
Current team	Monster World Rally Team
Best finish	2nd Overall in Rally America in 2006 and 2008
Awards
2004[1] 2005[1] 2009	• One of the most influential people (#17) in Sports Business Journal • Ad Age's Marketing 50 • One of the Fast 50 in Fast Company Magazine • 40 Under 40 Awards, Sports Business Journal • Rally America's Rookie of the Year • Gymkhana 2 was 2009's #4 most viewed viral video

Ken Block (born November 21, 1967, in Long Beach, California)^[2] is a professional rally driver with the Monster World Rally Team. Block is also one of the co-founders and recently appointed Chief Brand Officer of DC Shoes.^[1] Block has also competed in many action sports events including skateboarding, snowboarding, and motocross.

Rallying[link]

2005[link]

In 2005, Ken Block began his national rallying career with the Vermont SportsCar team.^[3] Vermont SportsCar prepared a 2005 Subaru WRX STi for Block to compete. His first event of the rallying season was Sno*Drift, where he ended up finishing seventh overall and fifth in the Group N class.^[4] During the 2005 season, Block had five top five finishes and placed third overall in the Group N class and fourth overall in the Rally America National Championship.^[3] At the end of his first rallying year, Ken Block had won the Rally America Rookie of the Year award.^[5]

2006[link]

In 2006, Ken Block along with his DC rally teammate Travis Pastrana signed a new sponsorship deal with Subaru.^[3] Through this deal with Subaru, the teammates became known as "Subaru Rally Team USA."^[3] With the new rally season, Block also got a brand new Vermont SportsCar prepped 2006 Subaru WRX STi.^[3] He competed in the first ever X Games rally event at X Games XII.^[3] In the competition, Block ended up finishing third to take the bronze.^[3] He went on to compete in the 2006 Rally America National Championship, where he finished second overall.^[3]

2007[link]

In 2007, Ken Block competed in the X Games XIII rally event, where he placed second overall and won a silver medal.^[5] In the 2007 Rally America National Championship, Block finished third overall.^[5] During this season, Block also entered in a few rounds of the World Rally Championship; Rally Mexico and Rally New Zealand.^[4] In Rally New Zealand, Block recorded two top-five stage times in the Group N class.^[4] At the end of 2007, Block had achieved 19 podiums and 8 overall victories in rally events.^[1]

2008[link]

In 2008, Block was provided with a brand new rally prepped 2008 Subaru WRX STi to compete. Block decided to compete in the Rallye Baie-des Chaleurs of the Canadian Rally Championship to gain some experience with his new 2008 rally car and prepare for the World Rally Championships later this year.^[6] Block gained his first Canadian rally win at the event.^[6] This was only the second event for the new car.^[6] Block and his co-driver were unable to get any championship points at the event due to not having a Canadian competition license.^[6] Block competed in the Rally New York USA competition and finished in first place.^[7] In the X Games XIV rally competition, Block finished tied for third place with Dave Mirra.^[8] This occurrence was due to both competitors having issues with their car. Block, who made it to the semi-finals of the event, had a radiator problem after landing the car awkwardly on a jump. With both bronze place competitors in damaged cars unable to compete, the medals were awarded to both of them.^[8]

Block competed in the 2008 Rally America National championship, which concluded on October 17, 2008. In the event, he finished second overall with a strong victory in the last event. In the Lake Superior Performance Rally stage, Block finished over one minute ahead of his next closest competitor and secured the second overall position.^[9] Next up for Block this rally season is three World Rally Championship events.^[4]

2009[link]

Block appeared in a segment of motoring show Top Gear.^[10]

2010[link]

Ken Block testing Ford Fiesta for the 2010 Rally America season

Block driving a Ford Focus RS WRC at the 2010 Rallye de France

On January 6, 2010 the Monster World Rally Team announced Ken as their driver for selected rounds of the World Rally Championship, in which he will be campaigning the Monster/Ford Racing Focus RS WRC 08. His car will be prepared and run by the North of England based M-Sport, who also prepare the official Ford WRC cars. He will be simultaneously running in his sixth season of the Rally America Championship in an open class Ford Fiesta, as well as his fifth X-games. Ken will also be the first ever American driver to campaign for the World Rally Championship. On February 27, Block won the Rally in the 100 Acre Wood (Rally America) for the 5th consecutive time. This broke the record held by John Buffum.^[11] Ken is currently being trained by former Ford factory driver Markko Märtin. At the Spain rally, he won his first 2 points in World Rally Championship.

2011[link]

On March 23, Block and his co-driver Alex Gelsomino were taken to hospital, having rolled their Ford Fiesta RS WRC during the shakedown stage of the 2011 Rally de Portugal in Faro, Portugal.^[12] A representative of the Monster World Rally team later stated that both men were fine.^[13]

Complete Rally America results[link]

(key)

Complete WRC results[link]

* Season in progress.

PWRC results[link]

Other motorsport activities[link]

On October 15, 2009, it was reported that Block was close to a deal to join the World Rally Championship in a new Ford team. Long time co-driver Alex Gelsomino is also reportedly involved in the deal. Former Subaru WRC driver Chris Atkinson has been reported to be lined up as Block's team-mate in the all-new Monster Energy Drink Ford World Rally Team.^[14]

In 2005, Ken Block along with his DC Shoes associates participated in the Gumball 3000 Rally. For the event they sent out three modified 2004 Subaru WRX STi's sponsored by DC Shoes.^[15][16]

In 2006, Ken Block competed in the One Lap of America competition along with Brian Scotto. They were teamed up in a 2006 Subaru WRX STi and finished forty-fifth overall.^[17]

In 2006, for the Discovery Channel show Stunt Junkies, Ken Block jumped his Subaru WRX STi rally car 171 feet (52 m) and a max height of 25 feet (7.6 m).^[3] The whole episode was dedicated to Ken Block attempting this stunt.

In 2007, Ken Block joined the DC Shoes Snowboarding team at New Zealand's Snow Park.^[3] Block did massive jumps and assisted in snowboarding tricks while driving his rally car on the mountain alongside the snowboarders. The session made the cover of the December 2007 issue of Snowboarder Magazine and closed out the MTN.LAB 1.5 DVD.^[3]

In 2009, for the BBC show Top Gear, Ken took James May out for Gymkhana-style driving at Block's stunt course at Inyokern Airport, an operational California airport, also starring Ricky Carmichael, whom Ken describes as 'a good friend'.

In 2010, for the BBC show Top Gear, Ken took the feature car from the previous episode (a Reliant Robin) for a lap of the Top Gear test track. He rolled the car and was unable to complete a lap but was unhurt.

On January 6, 2010, the announcement is made as Ken joins up with Ford and begins his WRC career driving both a Ford Fiesta and Focus RS WRC.

On August 24, 2010, Block released the first of a three part Gymkhana 3 video release featuring his new Ford Fiesta.^[18]

Ken Block also holds the world record for the world's fastest snow cat, a modified Subaru STI called a Trax STI.^{[citation needed]}

On September 14, 2010, Block's third Gymkhana video, featuring a Ford Fiesta, was released on YouTube.^[19] The video got more than seven million views in its first week.

On August 16, 2011, the fourth Gymkhana video, The Hollywood Megamercial was released on YouTube, featuring Block driving around the Universal Studios backlot.^[20]

Involvement In Colin McRae: Dirt 2 and Dirt 3[link]

Ken Block is featured as a driver in Codemasters Colin McRae: Dirt 2, along with his Subaru Rally Team USA Impreza.
In Dirt 3 he is seen as a driver and Gymkhana teacher, his Monster World Rally Team vehicles are available in the game.

References[link]

External links[link]

Wikimedia Commons has media related to: Ken Block

• Ken Block's Official site
• Monster World Rally Team
• Rally Results and News
• Subaru Rally Team USA
• Rally America Website
• Ken Block Official Merchandise Store
• Ken Block Interview
• Gymkhana racing improved by Ken Block, Video, ~4min
• dirt2game.com