KEVOS® MAKEOS · Threads
Three-Wire Measurement with Lead Angle (Buckingham)
What should the measurement over wires read for this coarse-lead or multi-start thread or worm?
Measurement over three wires including the effect of lead angle by Buckingham’s simplified formula, with the wire size the formula requires, for worms, Acme and multi-start threads.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Included thread angle | ° | Included angle of the thread form (60° unified/metric, 29° Acme and worms, 40° worms). |
| Angle measured in | choice | Whether the stated angle is in the axial plane or the normal plane. |
| Axial pitch | mm or in | Axial pitch (distance between adjacent threads), in the same unit as the pitch diameter. |
| Number of starts | starts | Number of thread starts; lead = starts × pitch. |
| Pitch diameter | mm or in | Pitch diameter to be checked. |
Method and formulas
- Lead angle B = atan(lead ÷ πE); half-angle A = included ÷ 2.
- Normal half-angle An: tan An = tan A cos B (axial form) or An = A (normal form). Axial thickness T = P/2.
- Wire diameter W = T cos B ÷ cos An; M = E + W(1 + sin An) (Buckingham’s formula 3).
- The simple formula without lead angle is shown for comparison.
- Example: a 2-start 29° thread, pitch 6.35, on 40 pitch diameter needs 3.2618 wires and reads 44.075.
Limitations
- Very accurate for lead angles below about 8–10°; for extreme accuracy at larger angles use the involute helicoid method.
- The wire diameter must equal the calculated value for the formula to apply directly.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect worms and multi-start threads accurately
- Choose wire size for a coarse-lead thread
- See how much lead angle changes the reading
Who it is for
- Quality inspectors
- Toolmakers
- Metrology technicians
What you get
- Lead angle
- Normal half-angle
- Wire diameter required by the formula
- Measurement over wires and the simple-formula reading
Interpreting the result
- If your wires differ from W, use the closest available set and the simple formula with a correction, or measure with balls.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1990–2003. Topic reference; no source tables or recommended settings are reproduced.
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