Hiscox movement 921 is a hunting-tooth worm gear: a double worm-gear wheel has one or more teeth in one section than the other, and worm motion advances one section relative to the other according to that difference.
Two Worm-wheels with One Tooth Difference Interactive Calculator
Enter tooth counts for the reference and compared sections. Results are ideal differential count kinematics only—not tooth geometry, contact, efficiency, torque, backlash or a build specification.
Equation Used
- The worm is treated as single-start.
- Both ideal wheel sections are referenced to the same worm input.
- Only relative angular motion magnitude is reported; direction depends on which section has more teeth.
- Entered tooth counts are exact integers.
- Tooth form, module, lead angle, center distance, contact ratio, interference, efficiency, torque, load sharing, friction, backlash, bearings, strength, wear, lubrication, tolerances and manufacturability are omitted.
Hiscox Movement 921: Double Hunting-Tooth Worm Wheel
Hiscox shows a single worm acting on a double worm-gear wheel whose two coaxial sections have different tooth counts. He says the worm advances one section relative to the other in proportion to the tooth-count difference.
For sections with Nf and No teeth, one worm revolution corresponds to ideal section advances of 1/Nf and 1/No revolution. Their relative advance magnitude is |1/Nf - 1/No|.
What This Calculator Represents
The tool computes only ideal relative count kinematics. Hiscox mentions planetary or clock motion and gives 100 and 101 teeth as an example, for which 10,100 worm revolutions produce one relative revolution.
The source does not provide modern precision tolerances, load capacity, efficiency or manufacturing guidance.
Ideal Differential Tooth-Count Arithmetic
relative revolution per worm revolution = d/(Nf No)
worm revolutions per relative revolution = Nf No/d
relative step = 360° d/(Nf No)
worm revolutions per compared-wheel tooth = Nf/d
If d=0, both ideal sections advance equally and there is no differential motion.
Worked Hiscox Example
With 100 and 101 teeth, d=1 and the ideal differential reduction is 100×101/1 = 10,100 worm revolutions per relative revolution, exactly the count stated by Hiscox. The relative step is about 0.03564° per worm revolution.
Model Boundary
- Historical arrangement: double worm-wheel sections, differing tooth counts and relative advance from their difference.
- Calculated: ideal relative angular count only.
- Not calculated: tooth and worm geometry, simultaneous engagement feasibility, lead angle, contact ratio, interference, efficiency, torque, load sharing, backlash, bearings, strength, wear, lubrication, thermal behavior, tolerances or suitability.
Frequently Asked Questions
Why is the reduction so large?
It comes from the small difference between two individually small advances.
What happens when the tooth counts are equal?
There is no relative motion and no finite differential reduction.
Does the calculator report direction?
No; it reports magnitude only.
Does it design the worm teeth?
No.
Are efficiency and torque included?
No.
Can this specify a manufacturable precision drive?
No.
References
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