KEVOS® MAKEOS · Gears
Crossed Helical Gears (Shafts at Right Angles)
What diameters and centre distance does this crossed helical gear pair at 90° have?
Pitch and outside diameters, centre distance, leads and ratio of a pair of helical gears on shafts at right angles, from normal diametral pitch, tooth counts and the gear helix angle.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal diametral pitch | 1/in | Normal diametral pitch (the pitch of the cutter). |
| Pinion teeth | teeth | Teeth on the pinion. |
| Gear teeth | teeth | Teeth on the gear. |
| Gear helix angle (pinion = 90° − this) | ° | Helix angle of the gear; the two helix angles add to 90° for shafts at right angles. |
Method and formulas
- Gear D = N ÷ (Pn cos ψ); pinion d = n ÷ (Pn cos(90° − ψ)).
- Centre distance C = (D + d)/2; outside diameters add 2/Pn.
- Lead = π × pitch diameter ÷ tan(helix angle); ratio = N ÷ n.
- Example: 20/40 teeth at 8 normal DP and 45° give a centre distance of 5.3033 in.
Limitations
- Point contact: crossed helical gears carry light loads and wear faster than parallel-axis gears.
- Both gears must have the same hand of helix for shafts at right angles.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design or replace spiral gears on right-angle drives
- Find the centre distance for given tooth counts
- Choose helix angles to fit a centre distance
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pitch and outside diameters
- Centre distance
- Leads
- Ratio
Interpreting the result
- Equal 45° helix angles give the same diameter ratio as the tooth ratio.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2195–2203. Topic reference; no source tables or recommended settings are reproduced.
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Open the Crossed Helical Gears (Shafts at Right Angles) calculator
