Editing Gear (section)

==Nomenclature==
{{Main|List of gear nomenclature}}

===General===
[[File:Gear words.png|600px]]
<!--Further note on tooth
 force: If two rigid objects make contact, they always do so at a point (or points) where the tangents to their surfaces coincide—that is, where there is a common tangent. The perpendicular to the common tangent at the point of contact is called the common normal. Ignoring friction, the force exerted by the objects on each other is always directed along the common normal. Thus, for meshing gear teeth, the line of action is the common normal to the tooth surfaces. -->

; Rotational [[frequency]], ''n'' : Measured in rotation over time, such as [[revolutions per minute]] (RPM or rpm).
; [[Angular frequency]], ''ω'' : Measured in [[radians per second]]. 1{{nbsp}}RPM = 2{{pi}}{{nbsp}}rad/minute = {{sfrac|{{pi}}|30}}{{nbsp}}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 gear]]s, 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 : 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 design dimension and cannot be measured, but is a location where other measurements are made. Its value is based on the number of teeth (''N''), the normal '''module''' (''m<sub>n</sub>''; or normal diametral pitch, ''P<sub>d</sub>''), and the helix angle (<math>\psi</math>):
:: <math>d = \frac{Nm_n}{\cos\psi}</math> in metric units or <math>d = \frac{N}{P_d\cos\psi}</math> in imperial units.<ref name="Standardization, 2007">ISO/DIS 21771:2007 : "Gears – Cylindrical Involute Gears and Gear Pairs – Concepts and Geometry", ''International Organization for Standardization'', (2007)</ref>
; Module or modulus, ''m'': Since it is impractical to calculate circular pitch with [[irrational number]]s, mechanical engineers usually use a scaling factor that replaces it with a regular value instead. This is known as the ''module'' or ''modulus'' of the wheel and is simply defined as:
::<math>m = \frac{p}{\pi}</math>
: where ''m'' is the module and ''p'' the circular pitch. The [[Unit (measurement)|units]] of module are customarily [[millimeters]]; an ''English Module'' is sometimes used with the units of [[inches]]. When the diametral pitch, DP, is in English units,
:: <math>m = \frac{25.4}{DP}</math> in conventional metric units.
: The distance between the two axis becomes:
:: <math>a = \frac{m}{2}(z_1 + z_2)</math>
: where a is the axis distance, ''z''<sub>1</sub> and ''z''<sub>2</sub> 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 [[primes]] 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 [[relatively prime]] to each other; this occurs when the [[Greatest common divisor|greatest common divisor (GCD)]] 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 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 [[evolvent]] based straight cogs.<ref>{{citation|author=Gunnar Dahlvig |work=Konstruktionselement och maskinbyggnad|at=7 |language=sv |title=Construction elements and machine construction |year=1982|isbn=978-9140115546}}</ref>
; Operating pitch diameters : Diameters determined from the number of teeth and the center distance at which gears operate.<ref name="ansiagma"/> Example for pinion:
:: <math> d_w = \frac{2a}{u+1} = \frac{2a}{\frac{z_2}{z_1} + 1}. </math>
; 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]], ''θ'' : 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, ''D<sub>o</sub>'' : 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. <math>a = \frac{1}{2}(D_o - D)</math>
; Dedendum, ''b'' : Radial distance from the depth of the tooth trough to the pitch surface. <math>b = \frac{1}{2}(D - \text{root diameter})</math>
; Whole depth, ''h<sub>t</sub>'' : 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, ''DP'' :
:: <math>DP = \frac{N}{d} = \frac{\pi}{p}</math>
: 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
:: <math>DP = \frac{25.4}{m}</math> in imperial units
; Base circle : 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
; Base pitch, normal pitch, ''p<sub>b</sub>'' : 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 mates properly with any other

===Helical gear===
; Helix angle, ''ψ'' : 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 be considered as the hypotenuse angle as well.
; Normal circular pitch, ''p<sub>n</sub>'' : 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".
::<math>p_n = p\cos(\psi)</math>

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

===Worm gear===
; 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, ''λ'' : 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.
; Pitch diameter, ''d<sub>w</sub>'' : 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===
<gallery mode=packed>
File:Contact line.jpg|Line of contact
File:Action path.jpg|Path of action
File:Action line.jpg|Line of action
File:Action plane.jpg|Plane of action
File:Contact lines.jpg|Lines of contact (helical gear)
File:Action arc.jpg|Arc of action
File:Action length.jpg|Length of action
File:Limit diameter.jpg|Limit diameter
File:Face advance.svg|Face advance
File:Action zone.jpg|Zone of action
</gallery>
; 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<sub>t</sub>'' : 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<sub>a</sub>'' : 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<sub>r</sub>'' : The arc of the pitch circle through which a tooth profile moves from contact at the pitch point until contact ends.
; Contact ratio, ''m<sub>c</sub>'' or ''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 during which a tooth comes and goes out of contact with the mating gear.
; Transverse contact ratio, ''m<sub>p</sub>'' or ''ε<sub>α</sub>'' : 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<sub>F</sub>'' or ''ε<sub>β</sub>'' : 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<sub>t</sub>'' or ''ε<sub>γ</sub>'' : The sum of the transverse contact ratio and the face contact ratio.
:: <math> \epsilon_\gamma = \epsilon_\alpha + \epsilon_\beta </math>
:: <math> m_{\rm t} = m_{\rm p} + m_{\rm F} </math>
; Modified contact ratio, ''m<sub>o</sub>'' : For bevel gears, the square root of the sum of the squares of the transverse and face contact ratios.
:: <math> m_{\rm o} = \sqrt{m_{\rm p}^2 + m_{\rm F}^2} </math>
; 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===
<gallery mode=packed>
File:Tooth thickness.jpg|Tooth thickness
File:Thickness relationships.jpg|Thickness relationships
File:Chordial thickness.svg|Chordal thickness
File:Pin measurement.jpg|Tooth thickness measurement over pins
File:Span measurement.jpg|Span measurement
File:Addendum teeth.jpg|Long and short addendum teeth
</gallery>

; Circular thickness : Length of arc between the two sides of a gear tooth, on the specified [[wikt:datum circle|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 [[wikt:datum line|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 [[wikt:datum surface|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 wis 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.
[[File:Undercuts.svg|thumb|right|Undercut]]
; Undercut : An [[Undercut (manufacturing)|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.
; Root fillet : or fillet curve, the concave portion of the tooth profile where it joins the bottom of the tooth space.[[#Notes|<sup>2</sup>]]

===Pitch===
'''Pitch''' is the distance between a point on one tooth and the corresponding point on an adjacent tooth.<ref name="ansiagma"/> 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.

<gallery mode=packed>
File:Pitches.svg|Pitch
File:Tooth pitches.jpg|Tooth pitch
File:Base pitch.jpg|Base pitch relationships
File:Principal pitches.jpg|Principal pitches
</gallery>

; Circular pitch, ''p'' : Arc distance along a specified pitch circle or pitch line between corresponding profiles of adjacent teeth.
; Transverse circular pitch, ''p''<sub>t</sub> : Circular pitch in the transverse plane.
; Normal circular pitch, ''p''<sub>n</sub>, ''p''<sub>e</sub> : 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''<sub>x</sub> : 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''<sub>N</sub>, ''p''<sub>bn</sub> :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''<sub>b</sub>, ''p''<sub>bt</sub> : 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 plane.
; Diametral pitch (transverse), ''P''<sub>d</sub> : Ratio of the number of teeth to the standard pitch diameter in inches.
:: <math> P_{\rm d} = \frac{N}{d} = \frac{25.4}{m} = \frac{\pi}{p} </math>
; Normal diametral pitch, ''P''<sub>nd</sub> : Value of diametral pitch in a normal plane of a helical gear or worm.
:: <math> P_{\rm nd} = \frac{P_{\rm d}}{\cos\psi} </math>
; Angular pitch, ''θ''<sub>N</sub>, ''τ'' : Angle subtended by the circular pitch, usually expressed in radians.
:: <math> \tau = \frac{360}{z} </math> degrees or <math> \frac{2\pi}{z} </math> radians