List of gear nomenclature 1

List of gear nomenclature

Gears have a wide range of unique terminology known as gear nomenclature. Many of the terms defined cite the
same reference work.[1]

Addendum
The addendum is the height by which a tooth of a gear projects
beyond (outside for external, or inside for internal) the standard pitch
circle or pitch line; also, the radial distance between the pitch circle
and the addendum circle.[1]

Addendum angle
Addendum angle in a bevel gear, is the angle between elements of the
Principal dimensions
face cone and pitch cone.[1]

Addendum circle
The addendum circle coincides with the tops of the teeth of a gear and is
concentric with the standard (reference) pitch circle and radially distant from
it by the amount of the addendum. For external gears, the addendum circle
lies on the outside cylinder while on internal gears the addendum circle lies
on the internal cylinder.[1]

Internal gear diameters

Root circle
List of gear nomenclature 2

Apex to back
Apex to back, in a bevel gear or hypoid gear, is the distance in the direction
of the axis from the apex of the pitch cone to a locating surface at the back of
the blank.[1]

Back angle
The back angle of a bevel gear is the angle between an element of the back
cone and a plane of rotation, and usually is equal to the pitch angle.[1]
Apex to back

Mounting distance

Back cone
The back cone of a bevel or hypoid gear is an imaginary cone tangent to the
outer ends of the teeth, with its elements perpendicular to those of the pitch
cone. The surface of the gear blank at the outer ends of the teeth is
customarily formed to such a back cone.[1]

Back cone distance

Back cone distance in a bevel gear is the distance along an element of the
back cone from its apex to the pitch cone.[1]
Principal dimensions
List of gear nomenclature 3

Base circle
The base circle of an involute gear is the circle from which involute tooth
profiles are derived.[1]

Involute teeth

Base cylinder
The base cylinder corresponds to the base circle, and is the cylinder from
which involute tooth surfaces are developed.[1]

Base cylinder

Base diameter
The base diameter of an involute gear is the diameter of the base circle.[1]

Bull gear
The term bull gear is used to refer to the larger of two spur gears that are in
engagement in any machine. The smaller gear is usually referred to as a
pinion.

Base diameter
List of gear nomenclature 4

Center distance
Center distance (operating) is the shortest distance between non-intersecting
axes. It is measured along the mutual perpendicular to the axes, called the line
of centers. It applies to spur gears, parallel axis or crossed axis helical gears,
and worm gearing.[1]

Center distance

Central plane
The central plane of a worm gear is perpendicular to the gear axis and
contains the common perpendicular of the gear and worm axes. In the usual
case with axes at right angles, it contains the worm axis.[1]

Central plane

Composite action test

The composite action test (double flank) is a method of inspection in
which the work gear is rolled in tight double flank contact with a
master gear or a specified gear, in order to determine (radial)
composite variations (deviations). The composite action test must be
made on a variable center distance composite action test device.[1]

Schematic of the composite action test

List of gear nomenclature 5

Cone distance
Cone distance in a bevel gear is the general term for the distance along
an element of the pitch cone from the apex to any given position in the
teeth.[1]
Outer cone distance in bevel gears is the distance from the apex of the
pitch cone to the outer ends of the teeth. When not otherwise specified,
the short term cone distance is understood to be outer cone distance.
Mean cone distance in bevel gears is the distance from the apex of the
pitch cone to the middle of the face width.
Inner cone distance in bevel gears is the distance from the apex of the
pitch cone to the inner ends of the teeth.
Cone distance

Conjugate gears
Conjugate gears transmit uniform rotary motion from one shaft to another by means of gear teeth. The normals to
the profiles of these teeth, at all points of contact, must pass through a fixed point in the common centerline of the
two shafts.[1]

Crossed helical gear

A crossed helical gear is a gear that operate on non-intersecting, non-parallel axes.
The term crossed helical gears has superseded the term spiral gears. There is theoretically point contact between the
teeth at any instant. They have teeth of the same or different helix angles, of the same or opposite hand. A
combination of spur and helical or other types can operate on crossed axes.[1]

Crossing point
The crossing point is the point of intersection of bevel gear axes; also the apparent point of intersection of the axes
in hypoid gears, crossed helical gears, worm gears, and offset face gears, when projected to a plane parallel to both
axes.[1]

Crown circle
The crown circle in a bevel or hypoid gear is the circle of intersection of the back cone and face cone.[1]

Crowned teeth
List of gear nomenclature 6

Crowned teeth have surfaces modified in the lengthwise direction to

produce localized contact or to prevent contact at their ends.[1]

Dedendum angle
Dedendum angle in a bevel gear, is the angle between elements of the
root cone and pitch cone.[1]

Crowned gear

Equivalent pitch radius

Equivalent pitch radius is the radius of the pitch circle in a cross
section of gear teeth in any plane other than a plane of rotation. It is
properly the radius of curvature of the pitch surface in the given cross
section. Examples of such sections are the transverse section of bevel
gear teeth and the normal section of helical teeth.

Back cone equivalent

Face (tip) angle

Face (tip) angle in a bevel or hypoid gear, is the angle between an element of the face cone and its axis.[1]

Face cone
The face cone, also known as the tip cone is the imaginary surface that coincides with the tops of the teeth of a bevel
or hypoid gear.[1]

Face gear
A face gear set typically consists of a disk-shaped gear, grooved on at
least one face, in combination with a spur, helical, or conical pinion. A
face gear has a planar pitch surface and a planar root surface, both of
which are perpendicular to the axis of rotation.[1] It can also be referred
to as a face wheel, crown gear, crown wheel, contrate gear or
contrate wheel.

Face worm gear

List of gear nomenclature 7

Face width
The face width of a gear is the length of teeth in an axial plane. For
double helical, it does not include the gap.[1]
Total face width is the actual dimension of a gear blank including the
portion that exceeds the effective face width, or as in double helical
gears where the total face width includes any distance or gap
separating right hand and left hand helices.
For a cylindrical gear, effective face width is the portion that contacts
the mating teeth. One member of a pair of gears may engage only a
portion of its mate.
For a bevel gear, different definitions for effective face width are
applicable.

Face width

Form diameter
Form diameter is the diameter of a circle at which the trochoid (fillet curve)
produced by the tooling intersects, or joins, the involute or specified profile.
Although these terms are not preferred, it is also known as the true involute
form diameter (TIF), start of involute diameter (SOI), or when undercut
exists, as the undercut diameter. This diameter cannot be less than the base
circle diameter.[1]

Front angle
The front angle, in a bevel gear, denotes the angle between an element of the Form diameter
front cone and a plane of rotation, and usually equals the pitch angle.[1]
List of gear nomenclature 8

Front cone
The front cone of a hypoid or bevel gear is an imaginary cone tangent to the inner ends of the teeth, with its
elements perpendicular to those of the pitch cone. The surface of the gear blank at the inner ends of the teeth is
customarily formed to such a front cone, but sometimes may be a plane on a pinion or a cylinder in a nearly flat
gear.[1]

Gear center
A gear center is the center of the pitch circle.[1]

Heel
The heel of a tooth on a bevel gear or pinion is the portion of the tooth
surface near its outer end.
The toe of a tooth on a bevel gear or pinion is the portion of the tooth
surface near its inner end.[1]

Helical rack
A helical rack has a planar pitch surface and teeth that are oblique to
the direction of motion.[1] Heel and toe

Index deviation
The displacement of any tooth flank from its theoretical position, relative to a datum tooth flank.
Distinction is made as to the direction and algebraic sign of this reading. A condition wherein the actual tooth flank
position was nearer to the datum tooth flank, in the specified measuring path direction (clockwise or
counterclockwise), than the theoretical position would be considered a minus (-) deviation. A condition wherein the
actual tooth flank position was farther from the datum tooth flank, in the specified measuring path direction, than the
theoretical position would be considered a plus (+) deviation.
The direction of tolerancing for index deviation along the arc of the tolerance diameter circle within the transverse
plane.[1]
List of gear nomenclature 9

Inside cylinder
The inside cylinder is the surface that coincides with the tops of the
teeth of an internal cylindrical gear.[1]

Diameters, Internal Gear

Inside diameter
Inside diameter is the diameter of the addendum circle of an internal
gear, this is also known as minor diameter.[1]

Internal gear diameters

Involute polar angle

Expressed as θ, the involute polar angle is the angle between a radius vector
to a point, P, on an involute curve and a radial line to the intersection, A, of
the curve with the base circle.[1]

Involute polar angle

List of gear nomenclature 10

Involute roll angle

Expressed as ε, the involute roll angle is the angle whose arc on the base
circle of radius unity equals the tangent of the pressure angle at a selected
point on the involute.[1]

Involute roll angle

Involute teeth
Involute teeth of spur gears, helical gears, and worms are those in which the
profile in a transverse plane (exclusive of the fillet curve) is the involute of a
circle.[1]

Involute teeth

Lands

Bottom land
The bottom land is the surface at the bottom of a gear tooth space adjoining
the fillet.[1]

Top land
Top land is the (sometimes flat) surface of the top of a gear tooth.[1]
Top and bottom lands
List of gear nomenclature 11

Line of centers
The line of centers connects the centers of the pitch circles of two engaging gears; it is also the common
perpendicular of the axes in crossed helical gears and wormgears. When one of the gears is a rack, the line of centers
is perpendicular to its pitch line.[1]

Mounting distance
Mounting distance, for assembling bevel gears or hypoid gears, is the
distance from the crossing point of the axes to a locating surface of a
gear, which may be at either back or front.[1]

Normal module
Normal module is the value of the module in a normal plane of a
helical gear or worm.[1]

Mounting distance

Normal plane
A normal plane is normal to a tooth surface at a pitch point, and
perpendicular to the pitch plane. In a helical rack, a normal plane is normal to
all the teeth it intersects. In a helical gear, however, a plane can be normal to
only one tooth at a point lying in the plane surface. At such a point, the
normal plane contains the line normal to the tooth surface.
Important positions of a normal plane in tooth measurement and tool design
of helical teeth and worm threads are: Planes at a pitch point on a helical tooth

1. the plane normal to the pitch helix at side of tooth;

2. the plane normal to the pitch helix at center of tooth;
3. the plane normal to the pitch helix at center of space between two teeth
In a spiral bevel gear, one of the positions of a normal plane is at a mean point and the plane is normal to the tooth
trace.[1]
List of gear nomenclature 12

Offset
Offset is the perpendicular distance between the axes of hypoid gears
or offset face gears.[1]
In the diagram to the right, (a) and (b) are referred to as having an
offset below center, while those in (c) and (d) have an offset above
center. In determining the direction of offset, it is customary to look at
the gear with the pinion at the right. For below center offset the pinion
has a left hand spiral, and for above center offset the pinion has a right
hand spiral.

Offset

Outside cylinder
The outside (tip or addendum) cylinder is the surface that coincides
with the tops of the teeth of an external cylindrical gear.[1]

Cylindrical surfaces
List of gear nomenclature 13

Outside diameter
The outside diameter of a gear is the diameter of the addendum (tip)
circle. In a bevel gear it is the diameter of the crown circle. In a
throated wormgear it is the maximum diameter of the blank. The term
applies to external gears, this is can also be known from major
diameter.[1]

Wormgear diameters

Conical surfaces

Pitch angle
Pitch angle in bevel gears, is the angle between an element of a pitch
cone and its axis. In external and internal bevel gears, the pitch angles
are respectively less than and greater than 90 degrees.[1]

Pitch circle
A pitch circle (operating) is the curve of intersection of a pitch surface
of revolution and a plane of rotation. It is the imaginary circle that rolls
without slipping with a pitch circle of a mating gear.[1]
Angle relationships
List of gear nomenclature 14

Angles

Pitch cone
A pitch cone is the imaginary cone in a bevel gear that rolls without slipping
on a pitch surface of another gear.[1]

Pitch cones

Pitch cylinder
A pitch cylinder is the imaginary cylinder in a spur or helical gear that rolls
without slipping on a pitch plane or pitch cylinder of another gear.[1]

Pitch cylinder
List of gear nomenclature 15

Pitch helix
The pitch helix is the intersection of the tooth surface and the pitch
cylinder of a helical gear or cylindrical worm.[1]

Base helix
The base helix of a helical, involute gear or involute worm lies on its
base cylinder.
Tooth helix

Base helix angle

Base helix angle is the helix angle on the base cylinder of involute helical teeth or threads.

Base lead angle

Base lead angle is the lead angle on the base cylinder. It is the complement of the base helix angle.

Outside helix
The outside (tip or addendum) helix is the intersection of the tooth surface and the outside cylinder of a helical gear
or cylindrical worm.

Outside helix angle

Outside helix angle is the helix angle on the outside cylinder.

Outside lead angle

Outside lead angle is the lead angle on the outside cylinder. It is the
complement of the outside helix angle.

Normal helix
A normal helix is a helix on the pitch cylinder, normal to the pitch
helix.

Normal helix
Pitch line
The pitch line corresponds, in the cross section of a rack, to the pitch circle (operating) in the cross section of a
gear.[1]
List of gear nomenclature 16

Pitch point
The pitch point is the point of tangency of two pitch circles (or of a pitch circle and pitch line) and is on the line of
centers.[1]

Pitch surfaces
Pitch surfaces are the imaginary planes, cylinders, or cones that roll
together without slipping. For a constant velocity ratio, the pitch
cylinders and pitch cones are circular.[1]

Pitch surfaces

Planes

Pitch cones

Pitch plane
The pitch plane of a pair of gears is the plane perpendicular to the axial plane
and tangent to the pitch surfaces. A pitch plane in an individual gear may be
any plane tangent to its pitch surface.
The pitch plane of a rack or in a crown gear is the imaginary planar surface
that rolls without slipping with a pitch cylinder or pitch cone of another gear.
The pitch plane of a rack or crown gear is also the pitch surface.[1]

Transverse plane
The transverse plane is perpendicular to the axial plane and to the pitch Pitch planes
plane. In gears with parallel axes, the transverse and the plane of rotation
coincide.[1]
List of gear nomenclature 17

Principal directions
Principal directions are directions in the pitch plane, and correspond to
the principal cross sections of a tooth.
The axial direction is a direction parallel to an axis.
The transverse direction is a direction within a transverse plane.
The normal direction is a direction within a normal plane.[1]

Principal directions

Profile radius of curvature

Profile radius of curvature is the radius of curvature of a tooth
profile, usually at the pitch point or a point of contact. It varies
continuously along the involute profile.[1]

Fillet radius

Radial composite deviation

Tooth-to-tooth radial composite deviation (double flank) is the
greatest change in center distance while the gear being tested is rotated
through any angle of 360 degree/z during double flank composite
action test.
Tooth-to-tooth radial composite tolerance (double flank) is the
permissible amount of tooth-to-tooth radial composite deviation. Total composite variation trace
Total radial composite deviation (double flank) is the total change in
center distance while the gear being tested is rotated one complete revolution during a double flank composite action
test.
Total radial composite tolerance (double flank) is the permissible amount of total radial composite deviation.[1]
List of gear nomenclature 18

Root angle
Root angle in a bevel or hypoid gear, is the angle between an element of the root cone and its axis.[1]

Root circle
The root circle coincides with the bottoms of the tooth spaces.[1]

Internal gear diameters

Root cone
The root cone is the imaginary surface that coincides with the bottoms
of the tooth spaces in a bevel or hypoid gear.[1]

Root cylinder
The root cylinder is the imaginary surface that coincides with the
bottoms of the tooth spaces in a cylindrical gear.[1]

Principal dimensions

Shaft angle
A shaft angle is the angle between the axes of two non-parallel gear
shafts. In a pair of crossed helical gears, the shaft angle lies between
the oppositely rotating portions of two shafts. This applies also in the
case of worm gearing. In bevel gears, the shaft angle is the sum of the
two pitch angles. In hypoid gears, the shaft angle is given when
starting a design, and it does not have a fixed relation to the pitch
angles and spiral angles.[1]

Spiral gear Shaft angle

See: Crossed helical gear.

List of gear nomenclature 19

Spur gear
A spur gear has a cylindrical pitch surface and teeth that are parallel to
the axis.[1]

Spur rack
A spur rack has a planar pitch surface and straight teeth that are at
right angles to the direction of motion.[1]

Standard pitch circle

The standard pitch circle is the circle which intersects the involute at
the point where the pressure angle is equal to the profile angle of the
basic rack.[1]

Standard pitch diameter

The standard reference pitch diameter is the diameter of the
standard pitch circle. In spur and helical gears, unless otherwise
specified, the standard pitch diameter is related to the number of teeth Spur gear
and the standard transverse pitch. The diameter can be roughly
estimated by taking the average of the diameter measuring the tips of the gear teeth and the base of the gear teeth.[1]
The pitch diameter is useful in determining the spacing between gear centers because proper spacing of gears implies
tangent pitch circles. The pitch diameters of two gears may be used to calculate the gear ratio in the same way the
number of teeth is used.

Where is the total number of teeth, is the circular pitch, is the diametrical pitch, and is the helix angle
for helical gears.

Standard reference pitch diameter

The standard reference pitch diameter is the diameter of the standard pitch circle. In spur and helical gears, unless
otherwise specified, the standard pitch diameter is related to the number of teeth and the standard transverse pitch. It
is obtained as:[1]
List of gear nomenclature 20

Test radius
The test radius (Rr) is a number used as an arithmetic convention established to simplify the determination of the
proper test distance between a master and a work gear for a composite action test. It is used as a measure of the
effective size of a gear. The test radius of the master, plus the test radius of the work gear is the set up center distance
on a composite action test device. Test radius is not the same as the operating pitch radii of two tightly meshing
gears unless both are perfect and to basic or standard tooth thickness.[1]

Throat diameter
The throat diameter is the diameter of the addendum circle at the central
plane of a wormgear or of a double-enveloping wormgear.[1]

Throat form radius

Throat form radius is the radius of the throat of an enveloping wormgear or
of a double-enveloping worm, in an axial plane.[1]

Wormgear diameters

Tip radius
Tip radius is the radius of the circular arc used to join a side-cutting edge and
an end-cutting edge in gear cutting tools. Edge radius is an alternate term.[1]

Tip radius

Tip relief
List of gear nomenclature 21

Tip relief is a modification of a tooth profile whereby a small amount of

material is removed near the tip of the gear tooth.[1]

Tip relief

Tooth surface

Profile of a spur gear Notation and numbering for an external gear

Notation and numbering for an internal gear

The tooth surface (flank) forms the side of a gear tooth.[1]

It is convenient to choose one face of the gear as the reference face and to mark it with the letter “I”. The other
non-reference face might be termed face “II”.
For an observer looking at the reference face, so that the tooth is seen with its tip uppermost, the right flank is on the
right and the left flank is on the left. Right and left flanks are denoted by the letters “R” and “L” respectively.

References
[1] Gear Nomenclature, Definition of Terms with Symbols. American Gear Manufacturers Association. ISBN 1-55589-846-7. OCLC 65562739.
ANSI/AGMA 1012-G05.
Article Sources and Contributors 22

Article Sources and Contributors

List of gear nomenclature  Source: http://en.wikipedia.org/w/index.php?oldid=429406147  Contributors: Biscuittin, Catsquisher, ClickRick, Incnis Mrsi, JohnBlackburne, Michael Hardy,
Open2universe, Peter Horn, Tommy2010, Wizard191, 14 anonymous edits

Image Sources, Licenses and Contributors

Image:Principal dimensions.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Principal_dimensions.jpg  License: GNU Free Documentation License  Contributors: GearHeads,
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Image:Tip relief.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tip_relief.jpg  License: GNU Free Documentation License  Contributors: GearHeads, Sfan00 IMG
Image:Tooth surface.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tooth_surface.jpg  License: GNU Free Documentation License  Contributors: GearHeads, Gerbrant
Image:External numbering.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:External_numbering.jpg  License: GNU Free Documentation License  Contributors: GearHeads
Image:Internal numbering.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Internal_numbering.jpg  License: GNU Free Documentation License  Contributors: GearHeads

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