Gear Terms & Definitions

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 ceases. 

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 gear axis. 

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 plane. 

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 pitch circles. 

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 circular-thickness arc. 

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. 

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 tooth. 

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 Radius.

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. 

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 gear. 

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 teeth. 

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 plane.

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 avoided. 

Pitch Circle: A circle the radius of which is equal to the distance from the gear axis to the pitch point.

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 Angle.)

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 mating gear. 

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 circle.

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 rotation coincide. 

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. 

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