---
title: "Short notes on gear standardisation"
subject: "Theory of Mechanism and Machine I"
chapter: 4
key: "semester_6/theory_of_mechanism_and_machine_i:gear-standardization-notes-module"
source: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/gear-standardization-notes-module
site: BCT Engineering
---

# Short notes on gear standardisation

Theory of Mechanism and Machine I · Chapter 4: Spur Gears

- Asked in: year not given, 5 marks
- Video: [GEARS BASICS - Nomenclature and Main Relations in Just Over 10 Minutes!](https://www.youtube.com/watch?v=NF8fpuczU5I) — Less Boring Lectures
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/gear-standardization-notes-module
- Whole chapter: https://www.bctengineer.com/md/semester_6/theory_of_mechanism_and_machine_i/chapter-4

## Question

Write short notes on: (a) module and diametral pitch, (b) standard tooth systems for involute gears, (c) undercutting.

## Short answer

Module m=d/z (mm) and diametral pitch P=z/d (in⁻¹) with P=25.4/m define tooth size. Standard systems: 14.5° full depth (addendum m, dedendum 1.157m), 20° full depth (addendum m, dedendum 1.25m), 20° stub (addendum 0.8m, dedendum m). Undercutting removes root below base circle when teeth < 2/sin²φ; prevented by profile shifting, stub teeth, or larger pressure angle.

## Answer

#### (a) Module and diametral pitch
- **Module** $m = d/z$ (mm): pitch circle diameter divided by number of teeth. It is the metric size of the tooth. Gears must have the same module to mesh. Standard modules (ISO/IS) include 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12 mm.
- **Diametral pitch** $P = z/d$ (teeth per inch) in the inch system, with $P = 25.4/m$.
- **Circular pitch** $p_c = \pi m = \pi d/z$.

#### (b) Standard tooth systems
| System | Pressure angle | Addendum | Dedendum |
|---|---|---|---|
| 14.5 degree composite / full depth | 14.5 | $m$ | $1.157m$ |
| 20 degree full depth | 20 | $m$ | $1.25m$ |
| 20 degree stub | 20 | $0.8m$ | $m$ |

- Gears from the same system and module are interchangeable.
- The 20 degree system has a stronger tooth (thicker at the root) and a smaller $z_{min}$ (18) than the 14.5 degree system (32).
- Stub teeth are stronger and avoid undercutting but have a smaller contact ratio.

#### (c) Undercutting
When a gear is cut with a hobbing cutter or rack cutter and the number of teeth is below $z_{min}$, the cutter tip removes part of the tooth root below the base circle. The tooth becomes thin at the root and weak, and the useful involute is shortened.

Remedies: use a larger pressure angle (20 or 25 degrees), stub teeth, or **profile shifting** (the cutter is moved outward by $xm$ so that the tooth gets a thicker root).

The minimum number of teeth to avoid undercutting for a rack cutter is $z_{min} = 2/\sin^2\phi$.

## Check yourself

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

1. Module is defined as:
   A. Number of teeth per inch of diameter
   B. Pitch circle diameter divided by number of teeth (mm)
   C. Pitch circle circumference divided by diameter
   D. Tooth thickness divided by pitch
   Answer: B. m = d/z in mm. Gears must have the same module to mesh. (Key point: Module definition)

2. The relation between diametral pitch P and module m is:
   A. P = m/25.4
   B. P = pi m
   C. P = 25.4 m
   D. P = 25.4/m
   Answer: D. Diametral pitch P = z/d in teeth per inch, so P = 25.4/m. (Key point: Module and diametral pitch relation)

3. Compared with the 14.5° system, the 20° full-depth system has:
   A. A thicker root and a smaller z_min (18 versus 32)
   B. A weaker root and a larger z_min
   C. The same z_min but longer teeth
   D. No difference in strength
   Answer: A. The 20° system has a stronger tooth (thicker at the root) and z_min of 18 against 32. (Key point: Standard tooth systems)

4. Which is a remedy for undercutting?
   A. Using fewer teeth
   B. Using a smaller pressure angle
   C. Profile shifting (moving the cutter outward by xm)
   D. Using a coarser module
   Answer: C. Profile shifting gives a thicker root. Larger pressure angle (20 or 25°) and stub teeth also help. (Key point: Remedy for undercutting)

## Related in Theory of Mechanism and Machine I

- [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
- [Force components on a helical gear tooth](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Ahelical-gear-force-components-axial-thrust) — Theory of Mechanism and Machine I, chapter 8
- [Involute tooth profile and its properties](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Ainvolute-profile-properties-law-of-gearing) — Theory of Mechanism and Machine I, chapter 4
- [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
- [Helical gears on parallel shafts numerical](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Ahelical-gear-parallel-shafts-geometry) — Theory of Mechanism and Machine I, chapter 5
- [Tooth force components on a bevel pinion](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Abevel-gear-tooth-forces-numerical) — Theory of Mechanism and Machine I, chapter 8

## Related in other subjects

- [Spur gear terminology and standard tooth system](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aspur-gear-terminology) — Machine Design I, chapter 9
- [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
- [Pitch, bearing contact and composite gear tests](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Agear-testing-methods-notes) — Metrology, chapter 11
- [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