Spur gear terminology and standard tooth system

A spur gear has straight teeth cut parallel to the axis and transmits motion between parallel shafts.

              top land
             ________
            /        \       <- addendum circle
           /          \      ^  addendum a = m
   -------/------------\-----v-------- pitch circle
          |            |     ^
          |            |     |  dedendum = 1.25m
   _______|            |_____v___ <- root circle
          |<-- tooth ->|
            thickness

   clearance c = dedendum - addendum = 0.25m
   backlash = gap between the non-working flanks
              of mating teeth on the pitch circle

Terms

• Pitch circle: the imaginary circle that rolls without slipping on the pitch circle of the mating gear. Its diameter is the pitch diameter $d = mz$.
• Circular pitch $p_c$: the distance along the pitch circle from a point on one tooth to the corresponding point on the next tooth, $p_c = \pi d/z = \pi m$.
• Module $m$: pitch diameter divided by the number of teeth, $m = d/z$ (mm). It is the standard size parameter in SI.
• Diametral pitch $P_d$: number of teeth per unit pitch diameter, $P_d = z/d$ (per inch).
• Addendum $a$: radial height of the tooth above the pitch circle, $a = m$ for standard teeth.
• Dedendum $b_d$: radial depth of the tooth below the pitch circle, $1.25m$ (full depth, 20 degrees).
• Clearance $c$: the space between the top of a tooth of one gear and the root of the mating gear, $c = 0.25m$.
• Pressure angle $\phi$: the angle between the common normal (line of action) at the contact point and the common tangent to the pitch circles. Standard values are 14.5 degrees and 20 degrees (20 degrees is more common, as it gives stronger teeth and allows fewer teeth without undercut).
• Backlash: the gap between the non-working flanks of mating teeth, measured along the pitch circle. It allows for lubrication, thermal expansion and errors, and prevents jamming.

Relation

$$p_c = \pi m = \frac{\pi}{P_d}, \qquad P_d\ [\text{per inch}] = \frac{25.4}{m\ [\text{mm}]}$$

Standard modules (IS) include 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8 and 10 mm. Gears must have the same module and pressure angle to mesh.