---
title: "Spur gear terminology and standard tooth system"
subject: "Machine Design I"
chapter: 9
key: "semester_6/machine_design_i:spur-gear-terminology"
source: https://www.bctengineer.com/q/semester_6/machine_design_i/spur-gear-terminology
site: BCT Engineering
---

# Spur gear terminology and standard tooth system

Machine Design I · Chapter 9: Gear design

- Asked in: year not given, 5 marks
- Video: [Gear Terminology](https://www.youtube.com/watch?v=8hkmFClpwPU) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/machine_design_i/spur-gear-terminology
- Whole chapter: https://www.bctengineer.com/md/semester_6/machine_design_i/chapter-9

## Question

Define the following terms for a spur gear with the help of a neat sketch: pitch circle, circular pitch, module, diametral pitch, addendum, dedendum, clearance, pressure angle, backlash. State the relation between module, circular pitch and diametral pitch.

## Short answer

Pitch circle: imaginary rolling circle of diameter mz. Circular pitch pc=πm=π/Pd. Module m=d/z (mm); diametral pitch Pd=z/d (in⁻¹). Addendum=m, dedendum=1.25m, clearance=0.25m. Pressure angle (commonly 20°) is the angle between the line of action and the common tangent to the pitch circles. Backlash is the intentional gap between non‑working tooth flanks.

## Answer

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

```text
              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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which set of relations among module, circular pitch and diametral pitch is correct?
   A. p_c = pi m and p_c = pi / P_d
   B. p_c = m / pi and P_d = m z
   C. p_c = m and P_d = pi m
   D. p_c = pi m and P_d = pi / m
   Answer: A. Circular pitch p_c = pi d / z = pi m = pi / P_d, and P_d (per inch) = 25.4 / m. (Key point: Module relations)

2. How is the pressure angle defined?
   A. Angle between the line of action (common normal) and the common tangent to the pitch circles
   B. Angle between the tooth axis and the shaft
   C. Angle between the addendum and dedendum circles
   D. Angle between two adjacent teeth
   Answer: A. It is measured between the common normal at the contact point and the pitch circle tangent; standard values are 14.5 and 20 degrees. (Key point: Pressure angle)

3. Which statement is correct?
   A. Clearance is the gap between non-working flanks along the pitch circle
   B. Backlash is the gap between non-working flanks along the pitch circle, preventing jamming; clearance is tip-to-root space (0.25 m)
   C. Backlash equals the addendum
   D. Clearance equals the module
   Answer: B. Backlash allows for lubrication, thermal expansion and errors. Clearance is the space between a tooth top and the mating root, 0.25m. (Key point: Clearance and backlash)

## Related in Machine Design I

- [Lewis method module for spur gears](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Alewis-spur-gear-module-design) — Machine Design I, chapter 9
- [Compound gear train speeds, torques and tooth forces](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Acompound-gear-train-forces) — Machine Design I, chapter 9
- [Diameter of a shaft carrying a spur gear](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Agear-loaded-shaft-diameter) — Machine Design I, chapter 5
- [Lewis equation for beam strength of a gear tooth](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Alewis-beam-strength-derivation) — Machine Design I, chapter 9
- [Dynamic and wear load check, spur pair](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Abuckingham-dynamic-wear-check) — Machine Design I, chapter 9
- [Gear tooth failure and surface durability](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Agear-tooth-failure-surface-durability) — Machine Design I, chapter 9

## Related in other subjects

- [Spur gear pair dimensions numerical](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Aspur-gear-pair-geometry-numerical) — Theory of Mechanism and Machine I, chapter 4
- [Tooth forces on a spur gear pinion](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Aspur-gear-tooth-forces-numerical) — Theory of Mechanism and Machine I, chapter 8
- [Gear tooth vernier: chordal thickness](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Agear-tooth-vernier-chordal-thickness) — Metrology, chapter 11
- [Gearbox shaft design with spur gear](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Agearbox-shaft-design-asme) — Machine Design II, chapter 5