Addendum: Height of tooth above
pitch circle or the radial distance between the pitch circle and
the top of the tooth.
Approach Ratio: The ratio of the arc
of approach to the arc of action.
Arc of Action: Arc of the pitch
circle through which a tooth travels from the first point of
contact with the mating tooth to the point where contact ceases.
Arc of Approach: Arc of the pitch
circle through which a tooth travels from the first point of
contact with the mating tooth to the pitch point.
Arc of Recess: Arc of the pitch
circle through which a tooth travels from its contact with the
mating tooth at the pitch point to the point where its contact
Axial Plane: In a pair of gears it
is the plane that contains the two axes. In a single gear, it
may be any plane containing the axis and a given point.
Backlash: The amount by which the
width of a tooth space exceeds the thickness of the engaging
tooth on the pitch circles. As actually indicated by measuring
devices, backlash may be determined variously in the transverse,
normal, or axial planes, and wither in the direction of the
pitch circles or on the line of action. Such measurements
should be converted to corresponding values on transverse pitch
circles for general comparison.
Base Circle: The circle from which
an involute tooth curve is generated or developed.
Base Helix Angle: The angle, at the
base cylinder of an involute gear, that the tooth makes with the
Base Pitch: In an involute gear it
is the pitch on the base circle or along the line of action.
Corresponding sides of involute teeth are parallel curves, and
the base pitch is the constant and fundamental distance between
them along a common normal in a plane of rotation. The
Normal Base Pitch is the base pitch in the normal plane, and
the Axial Base Pitch is the base pitch in the axial
Center Distance: The distance
between the parallel axes of spur gears and parallel helical
gears, or between the crossed axes of crossed helical gears and
worm gears. Also, it is the distance between the centers of the
Central Plane: In a worm gear this
is the plane perpendicular to the gear axis and contains the
common perpendicular of the gear and worm axes. In the usual
case with the axes at right angles, it contains the worm axis
Chordal Addendum: The height from
the top of the tooth to the chord subtending the
Chordal Thickness: Length of the
chord subtended by the circular thickness arc (the dimension
obtained when a gear-tooth caliper is used to measure the
thickness at the pitch circle).
Circular Pitch: Length of the arc of
the pitch circle between the centers or other corresponding
points of adjacent teeth. Normal Circular Pitch is the
circular pitch in the normal plane.
Circular Thickness: The length of
arc between the two sides of a gear tooth, on the pitch circle
unless otherwise specified. Normal Circular Thickness is
the circular thickness in the normal plane.
Clearance: The amount by which the
dedendum in a given gear exceeds the addendum of its mating
gear. It is also the radial distance between the top of a tooth
and the bottom o the mating tooth space.
Contact Diameter: The smallest
diameter on a gear tooth with which the mating gear makes
Contact Ratio: The ratio of the arc
of action to the circular pitch. It is sometimes thought of as
the average number of teeth in contact. For involute gears, the
contact ration is obtained most directly as the ration of the
length of action to the base pitch.
Contact Stress: The maximum
compressive stress within the contact area between mating gear
tooth profiles. It is also called Hertz stress.
Cycloid: The curve formed by the
path of a point on a circle as it rolls along a straight line.
When this circle rolls along the outer side of another circle,
the curve is called an Epicycloid; when it rolls along
the inner side of another circle it is called a Hypocycloid.
These curves are used in defining the former American
Standard composite tooth form.
Dedendum: The depth of tooth space
below the pitch circle or the radial dimension between the pitch
circle and the bottom of the tooth space.
Diametral Pitch: The ratio of the
number of teeth to the number of inches of pitch diameter-equals
number of gear teeth to each inch of pitch diameter. Normal
Diametral Pitch is the diametral pitch as calculated in the
normal plane and is equal to the diametral pitch divided by the
cosine of the helix angle.
Effective Face Width: That portion
of the face width that actually comes into contact with mating
teeth, as occasionally one member of a pair of gears may have a
greater face width than the other.
Efficiency: The actual torque ratio
of a gear set divided by its gear ratio.
External Gear: A gear with teeth on
the outer cylindrical surface.
Face of Tooth: That surface of the
tooth which is between the pitch circle and the top of the
Fillet Curve: The concave portion of
the tooth profile where it joins the bottom of the tooth space.
The approximate radius of this curve is called the Fillet
Fillet Stress: The maximum tensile
stress in the gear tooth fillet.
Flank of Tooth: That surface which
is between the pitch circle and the bottom land. The flank
includes the fillet.
Helical Overlap: The effective face
width of a helical gear divided by the gear axial pitch; also
called the Face Overlap.
Helix Angle: The angle that a
helical gear tooth makes with the gear axis at the pitch circle
unless otherwise specified.
Hertz Stress: See Contact Stress.
Highest Point of Single Tooth Contact:
The largest diameter on a spur gear at which a single tooth
is in contact with the mating gear. Often referred to as HPSTC.
Internal Diameter: The diameter of a
circle coinciding with the topes of the teeth of an internal
Internal Gear: A gear with teeth on
the inner cylindrical surface.
Involute: The curve formed by the
path of a point on a straight line, called the generatrix, as it
rolls along a convex base curve. (The base curve is usually a
circle.) This curve is generally used as the profile of gear
Land: The Top Land is the top
surface of a tooth, and the Bottom Land is the surface of
the gear between the fillets of adjacent teeth.
Lead: The distance a helical gear or
worm would thread along its axis in one revolution if it were
free to move axially.
Length of Action: The distance on an
involute line of action through which the point of contact moves
during the action of the tooth profile.
Line of Action: The path of contact
in involute gears. It is the straight line passing through the
pitch point and tangent to the base circles.
Lowest Point of Single Tooth Contact:
The smallest diameter on a spur gear at which a single tooth
of one gear is in contact with its mating gear. Often referred
to as LPSTC. Gear set contact stress is determined with a load
placed at this point on the pinion.
Module: Ration of the pitch diameter
to the number of teeth. Ordinarily, module is understood to
mean ration of pitch diameter in millimeters to the
number of teeth. The English Module is a ratio of the
pitch diameter in inches to the number of teeth.
Normal Plane: A plane normal to the
tooth surfaces at a point of contact, and perpendicular to the
Pitch: The distance between similar,
equally-spaced tooth surfaces, in a given direction and along a
given curve or line. The single word “pitch” without
qualification has been used to designate circular pitch, axial
pitch, and diametral pitch, but such confusing usage should be
Pitch Circle: A circle the radius of
which is equal to the distance from the gear axis to the pitch
Pitch Diameter: The diameter of the
pitch circle. In parallel shaft gears the pitch diameters can
be determined directly from the center distance and the numbers
of teeth by proportionality. Operating Pitch Diameter is
the pitch diameter at which the gears operate. Generating
Pitch Diameter is the pitch diameter at which the gear is
generated. In a bevel gear the pitch diameter is understood to
be at the outer ends of the teeth unless otherwise specified.
(See also reference to standard pitch diameter under Pressure
Pitch Plane: In a pair of gears it
is the plane perpendicular to the axial plane and tangent to the
pitch surfaces. In a single gear it may be any plane tangent to
its pitch surface.
Pitch Point: This is the point of
tangency of two pitch circles (or of a pitch circle and a pitch
line) and is on the line of centers. The pitch point of a tooth
profile is at its intersection with the pitch circle.
Plane of Rotation: Any plane
perpendicular to a gear axis.
Pressure Angle: The angle between a
tooth profile and a radial line at its pitch point. In involute
teeth, pressure angle is often described as the angle between
the line of action and the line tangent to the pitch circle.
Standard Pressure Angles are established in connection with
standard gear-tooth proportions. A given pair of involute
profiles will transmit smooth motion at the same velocity ratio
even when the center distance is changed. Changes in center
distance, however, in gear design and gear manufacturing
operations, are accompanied by changes in pitch diameter, pitch,
and pressure angle. Different values of pitch diameter and
pressure angle therefore may occur in the same gear under
different conditions. Usually in a gear design, and unless
otherwise specified, the pressure angle is the standard
pressure angle at the standard pitch diameter, and is
standard for the hob or cutter used to generate teeth. The
Operating Pressure Angle is determined by the center
distance at which a pair of gears operates. The Generating
Pressure Angle is the angle at the pitch diameter in effect
when the gear is generated. Other pressure angles may be
considered in gear calculations. In gear cutting tools and
cutters, the pressure angle indicates the direction of the
cutting edge as referred to some principal direction. In
oblique teeth, that is helical, spiral, etc., the pressure angle
may be specified in the transverse, normal, or axial
plane. For a spur gear or a straight bevel gear, in which
only one direction of cross-section needs to be considered, the
general term pressure angle may be used without qualification to
indicate transverse pressure angel. In spiral bevel gears,
unless otherwise specified, pressure angle means normal pressure
angle at the mean cone distance.
Principle Reference Planes: These
are a pitch plane, axial plane, and transverse plane, all
intersecting at a point and mutually perpendicular.
Rack: A gear with teeth spaced along
a straight line, and suitable for straightline motion. A
Basic Rack is one that is adopted as the basis of a system
of interchangeable gears. Standard gear-tooth proportions are
often illustrated on an outline of the basic rack. A
Generating Rack is a rack outline used to indicate tooth
details and dimensions for the design of a required generating
tool, such as a hob or gear-shaper cutter.
Ratio of Gearing: Ratio of the
numbers of teeth on mating gear. Ordinarily the ratio is found
by dividing the number of teeth on the larger gear by the number
of teeth on the smaller gear or pinion. For example, if the
ratio is 2 or “2 to 1,” this usually means that the smaller gear
or pinion makes two revolutions to one revolution of the larger
Roll Angle: The angle subtended at
the center of a base circle from the origin of an involute to
the point of tangency of the generatrix from any point on the
same involute. The radian measure of this angle is the tangent
of the pressure angle of the point on the invlolute.
Root Circle: A circle coinciding
with or tangent to the bottoms of the tooth spaces.
Root Diameter: Diameter of the root
Tangent Plane: A plane tangent to
the tooth surfaces at a point or line of contact.
Tip Relief: An arbitrary
modification of a tooth profile whereby a small amount of
material is removed near the tip of the gear tooth.
Total Face Width: The actual width
dimension of a gear blank. It may exceed the effective face
width, as in the case of double-helical gears where the total
face width includes any distance separating the right-hand and
left-hand helical teeth.
Transverse Plane: A plane
perpendicular to the axial plane and to the pitch plane. In
gears with parallel axes, the transverse plane and the plane of
Trochoid: The curve formed by the
path of a point on the extension of a radius of a circle as it
rolls along a curve or line. It is also the curve formed by the
path of a point on a perpendicular to a straight line as the
straight line rolls along the convex side of a base curve. By
the first definition the trochoid is derived from the cycloid;
by the second definition it is derived from the involute.
True Involute Form Diameter: The
smallest diameter on the tooth at which the involute exists.
Usually this is the point of tangency of the involute tooth
profile and the fillet curve. This is usually referred to as
the TIF diameter.
Undercut: 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 lowest point.
Undercut may be deliberately introduced to facilitate finishing
operations, as in preshaving.
Whole Depth: The total depth of a
tooth space, equal to addendum plus dedendum, also equal to
working depth plus clearance.
Working Depth: The depth of
engagement of two gears, that is, the sum of their addendums.
The standard working distance is the depth to which a tooth
extends into the tooth space of a mating gear when the center
distance is standard.