Gear Engineering Glossary

Addendum Dimension

The radial distance from the pitch circle to the top (tip) of the gear tooth. For standard gears, the addendum equals one module.

Addendum = m (Module)

Backlash Clearance

The gap between the mating tooth surfaces of meshing gears when measured along the pitch circle. Some backlash is intentional to prevent jamming due to thermal expansion, manufacturing tolerances, and lubrication needs.

Base Circle Geometry

The circle from which the involute tooth profile is generated. It is the fundamental reference for tooth shape. The base circle diameter is always smaller than the pitch circle diameter.

d_b = d × cos(α)

Bevel Gear Gear Type

A conical gear used to transmit motion between intersecting shafts, typically at 90 degrees. Teeth are cut on a cone surface rather than a cylinder. Common in differentials and power tools.

Bore Dimension

The central hole in a gear through which a shaft passes. The bore diameter must be smaller than the root diameter of the gear to maintain structural integrity.

Center Distance Assembly

The distance between the axes of two meshing gears. For standard spur gears, center distance equals half the sum of the two pitch diameters.

C = (d₁ + d₂) / 2

Circular Pitch Dimension

The distance measured along the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth. It is the fundamental measurement of tooth spacing.

p = π × m = π × d / N

Clearance Clearance

The radial distance between the top of a tooth and the bottom of the mating gear's tooth space. Clearance prevents tooth tips from touching the mating gear's root. Typically 0.25 × module.

c = 0.25 × m

Cone Angle Bevel

The angle between the pitch cone element and the gear axis in a bevel gear. For a pair of bevel gears at 90°, the cone angles of the two gears sum to 90°.

Dedendum Dimension

The radial distance from the pitch circle to the bottom (root) of the tooth space. For standard gears, the dedendum equals 1.25 times the module to provide clearance.

Dedendum = 1.25 × m

Diametral Pitch (DP) Imperial

The Imperial system measurement for tooth size, defined as the number of teeth per inch of pitch diameter. Higher DP values mean finer (smaller) teeth. It is the reciprocal relationship of the metric module.

DP = N / d (inches) = 25.4 / m

Face Width Dimension

The length of the gear tooth measured along the axis of the gear. A wider face width increases load capacity but also increases weight and potential for uneven load distribution.

Gear Ratio Performance

The ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. Determines the speed reduction (or increase) and torque multiplication between shafts.

Ratio = N_driven / N_driver

Gear Train Assembly

A system of two or more meshing gears used to transmit motion and power. Gear trains can be simple (single pair), compound (multiple pairs on shared shafts), or epicyclic (planetary).

Helical Gear Gear Type

A gear with teeth cut at an angle (helix angle) to the axis. Provides smoother, quieter operation than spur gears due to gradual tooth engagement. Produces axial thrust that requires thrust bearings.

Helix Angle Helical

The angle between a helical gear tooth and the gear axis. Common values range from 15° to 30°. Higher angles increase smoothness but also increase axial thrust forces.

Interference Problem

A condition where the tip of a gear tooth digs into the root fillet of the mating gear during meshing. Occurs when gears have too few teeth for the given pressure angle. Prevented by profile shift or increasing tooth count.

Internal Gear (Ring Gear) Gear Type

A gear with teeth on the inside of a cylindrical surface, meshing with an external pinion rotating inside it. Key component of planetary/epicyclic gear systems.

Involute Profile Geometry

The curved shape of a gear tooth generated by unwinding a taut string from a circle (the base circle). The involute profile ensures a constant velocity ratio between meshing gears regardless of center distance variations.

Module (m) Metric

The metric measurement of tooth size, defined as pitch diameter divided by number of teeth (in mm). Standard ISO modules include 0.5, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10 mm. Larger module = bigger teeth.

m = d / N (mm)

Normal Module Helical

In helical gears, the module measured in the plane perpendicular to the tooth direction. Related to the transverse module by the helix angle.

m_n = m_t × cos(β)

Outside Diameter (OD) Dimension

The largest diameter of a gear, measured at the tips of the teeth. Also called the addendum circle diameter. This is the physical outer boundary of the gear.

d_a = m × (N + 2)

Pitch Circle Geometry

The theoretical circle on which gear calculations are based. When two gears mesh properly, their pitch circles are tangent to each other. The pitch circle lies between the addendum and dedendum circles.

d = m × N

Planetary (Epicyclic) Gear System Assembly

A gear system consisting of a central sun gear, multiple planet gears, and an outer ring (internal) gear. Provides high gear ratios in a compact space. Used in automatic transmissions, electric screwdrivers, and turbine engines.

Pressure Angle (α) Geometry

The angle between the line of action (force direction) and the tangent to the pitch circle at the point of contact. Common values: 14.5° (legacy), 20° (standard), 25° (heavy-duty). Higher angles produce stronger but noisier teeth.

Profile Shift (x) Correction

A correction applied to the gear tooth form by shifting the cutting tool radially during manufacturing. Used to avoid undercutting in gears with few teeth, adjust center distance, or balance sliding velocities between mating gears.

Rack Gear Type

A flat, linear gear with straight teeth that meshes with a pinion (circular gear) to convert rotational motion to linear motion. Can be thought of as a gear with infinite radius. Used in steering systems, CNC machines, and sliding gates.

Root Diameter Dimension

The diameter of the circle at the base of the tooth spaces. Also called the dedendum circle diameter. The gear material below this circle is the rim or web.

d_f = m × (N − 2.5)

Spur Gear Gear Type

The simplest and most common gear type with straight teeth parallel to the axis. Used to transmit motion between parallel shafts. Easy to manufacture but can be noisy at high speeds due to sudden tooth engagement.

Tooth Thickness Dimension

The width of a gear tooth measured along the pitch circle arc. For standard gears, tooth thickness equals half the circular pitch.

t = p / 2 = π × m / 2

Undercutting Problem

Removal of material at the root of a gear tooth during manufacturing, weakening the tooth base. Occurs when the number of teeth is below the minimum for a given pressure angle (e.g., fewer than 17 teeth at 20°). Prevented by profile shift correction.

N_min = 2 / sin²(α)

Whole Depth Dimension

The total depth of a tooth space, measured from the top of the tooth to the bottom of the space. Equals addendum plus dedendum.

h = 2.25 × m

Working Depth Dimension

The depth of engagement of two mating teeth, equal to the sum of their addenda. The remaining depth below is clearance.

h_w = 2 × m

Worm Gear Gear Type

A gear system consisting of a worm (screw-shaped driver) and a worm wheel. Provides very high gear ratios in a single stage and can be self-locking. Used in conveyor systems, tuning pegs, and elevator drives.