Hiscox’s hunting tooth worm gear uses two wheel sections with different tooth counts to produce a slow relative motion for planetary or clockwork applications. The calculator below is a separate exercise in worm-start and wheel-tooth pairing. It describes modular contact patterns; it does not calculate that two-wheel differential motion, wear or service life.
Hunting Tooth Worm Gear Interactive Calculator
Explore repeat interval, per-start tooth coverage, pairing-group count and average total wheel-tooth engagements over an entered number of worm revolutions.
Equation Used
- Integer worm-start and wheel-tooth counts.
- Nominal indexing advances S wheel-tooth pitches per worm revolution.
- Each worm start is distinguished when discussing pairing subsets.
- No tooth geometry, simultaneous contact, load sharing, alignment, friction, thermal, lubrication, wear, stress, fatigue, duty or life model.
All wheel teeth participate overall. When gcd(S,N)>1, each individual worm start pairs with one subset of N/g wheel teeth; the GCD counts the pairing groups. Coprime counts give one group.
Modular start-tooth pairings
A worm with S starts advances the wheel by S tooth pitches per worm revolution. For one distinguished worm start, the sequence of paired wheel teeth advances by S modulo N. It visits N/g distinct wheel teeth and repeats after N/g worm revolutions, where g=gcd(S,N).
Across all starts and wheel rotation, all wheel teeth participate; the GCD partitions pairings rather than making teeth inactive.
Use as a pairing-pattern check
The arithmetic identifies coprime counts and the number of modular pairing groups. It can help describe indexing patterns, but it cannot select a worm set or quantify wear, smoothness, noise or life.
Coverage and average engagement count
Repeat interval is N/g worm revolutions and one selected start pairs with N/g wheel teeth, or 100/g percent. Over R worm revolutions, there are nominally RS tooth-passage events in total, averaging RS/N per wheel tooth. The average is taken over all N wheel teeth, rather than just the subset associated with one start.
Worked pairing example
For S=2 and N=30, g=2. One selected start pairs with 15 teeth (50%) and its sequence repeats after 15 worm revolutions; the other start supplies the other pairing group. Over 30 worm revolutions, 60 nominal tooth-passage events average 2 per wheel tooth overall.
Scope and limitations
Actual worm design requires module/diametral pitch, pressure and lead angles, centre distance, profiles, materials, heat treatment, efficiency and self-locking behavior, contact and bending stress, load sharing, deflection, alignment, lubrication, thermal capacity, scuffing and full duty-cycle analysis.
Questions
Are some wheel teeth inactive when g is greater than one?
No. The teeth are partitioned among start-pairing groups.
Does gcd=1 guarantee long life?
No. It describes pairing arithmetic only.
Why is the engagement result an average?
An arbitrary entered revolution count may not complete a repeat cycle, and real simultaneous contact is outside the model.
Historical source and calculation basis
Hiscox, Mechanical Movements, Powers, Devices and Appliances, entry 921, describes a worm driving two wheel sections with slightly different tooth counts. Their relative motion is distinct from the single-wheel pairing exercise shown here.
KHK’s worm gear reference explains that a wheel advances by one tooth per worm revolution for each worm start. Applying that indexing step modulo N gives the GCD pairing groups and repeat interval. Geometry, loading, lubrication and materials are needed separately to assess a real gear set.
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