---
title: "Spiral bevel, hypoid and crossed helical gears"
subject: "Theory of Mechanism and Machine I"
chapter: 5
key: "semester_6/theory_of_mechanism_and_machine_i:spiral-hypoid-crossed-helical-notes"
source: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/spiral-hypoid-crossed-helical-notes
site: BCT Engineering
---

# Spiral bevel, hypoid and crossed helical gears

Theory of Mechanism and Machine I · Chapter 5: Bevel, Helical and Worm Gears

- Asked in: year not given, 5 marks
- 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/spiral-hypoid-crossed-helical-notes
- Whole chapter: https://www.bctengineer.com/md/semester_6/theory_of_mechanism_and_machine_i/chapter-5

## Question

Write short notes on (a) spiral bevel gears, (b) hypoid gears, and (c) crossed helical gears (helical gears on non-parallel shafts), stating one application of each.

## Short answer

Spiral bevel gears have curved oblique teeth, smooth engagement, high strength; used in vehicle final drives. Hypoid gears have offset axes, a larger stronger pinion, sliding contact needing EP lube; used in automotive differentials. Crossed helical gears connect non-parallel non-intersecting shafts with point contact, suited for light loads such as oil pumps.

## Answer

#### (a) Spiral bevel gears
- Bevel gears with **curved, oblique teeth**; the spiral angle is about 35 degrees. 
- Teeth engage gradually, so contact is smooth, quiet and the contact ratio is higher than straight bevel gears.
- Stronger and can run at high speeds.
- Produce axial thrust, whose direction depends on spiral hand and rotation.
- Shafts intersect. Application: final drive of rear-wheel drive vehicles (older cars), machine tool gearboxes.

#### (b) Hypoid gears
- Similar to spiral bevel gears but the shaft axes are **offset** (do not intersect); pitch surfaces are hyperboloids.
- The pinion is larger and stronger than in a spiral bevel set of the same ratio, and can be mounted with bearings on both sides.
- There is sliding along the tooth length, so a special hypoid (EP) lubricant is needed.
- Application: automobile differential (propeller shaft is lowered, giving a lower floor).

#### (c) Crossed helical gears
- Two helical gears of **any helix angle (and hand)** on non-parallel, non-intersecting shafts. Shaft angle $\Sigma = \psi_1 + \psi_2$ (for like hand).
- Theoretically **point contact**, so only light loads can be carried; sliding velocity along the teeth is high.
- Velocity ratio $\dfrac{N_1}{N_2} = \dfrac{z_2}{z_1} = \dfrac{d_2\cos\psi_2}{d_1\cos\psi_1}$, so it depends on the pitch diameters too.
- Application: oil pumps, distributor drives, light instrument drives.

| Gear | Shafts | Contact |
|---|---|---|
| Spiral bevel | Intersecting | Line (gradual) |
| Hypoid | Offset, non-parallel | Line |
| Crossed helical | Non-parallel, non-intersecting | Point |

## Check yourself

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

1. Why are spiral bevel gears smoother and quieter than straight bevel gears?
   A. Their teeth engage gradually because they are curved and oblique, giving a higher contact ratio
   B. Their shafts are offset so there is no sliding
   C. They have point contact which reduces friction
   D. They use a smaller pressure angle
   Answer: A. Curved, oblique teeth come into mesh gradually, so contact is smooth and the contact ratio is higher than for straight bevel gears. (Key point: Spiral bevel advantage)

2. How do hypoid gears differ from spiral bevel gears?
   A. Their shafts are parallel
   B. Their shaft axes are offset and do not intersect
   C. Their teeth are straight
   D. They have point contact only
   Answer: B. Hypoid gears are like spiral bevel gears but with offset, non-intersecting axes; the pitch surfaces are hyperboloids. (Key point: Hypoid shaft geometry)

3. Why does a hypoid gear set need a special EP lubricant?
   A. Because the pinion is smaller than in a spiral bevel set
   B. Because the shafts intersect
   C. Because there is sliding along the tooth length
   D. Because the gears run at low speed
   Answer: C. Sliding along the tooth length in hypoid gears gives high contact stress and rubbing, so a hypoid (EP) lubricant is needed. (Key point: Hypoid lubrication)

4. Why can crossed helical gears carry only light loads?
   A. Their helix angle must be 45 degrees
   B. They need parallel shafts
   C. They have too many teeth
   D. Theoretically they have point contact, with high sliding along the teeth
   Answer: D. Crossed helical gears touch at a point, so the load is concentrated and sliding is high; only light loads can be carried. (Key point: Crossed helical contact)

## Related in Theory of Mechanism and Machine I

- [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
- [Straight bevel gear geometry and formative teeth](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Astraight-bevel-gear-geometry-formative-teeth) — Theory of Mechanism and Machine I, chapter 5