Belt & Pulley Speed
Driven speed, ratio, and belt velocity from pulley diameters.
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The engineering
Diameters do for belts what tooth counts do for gears — set the ratio — except belts creep 1–2% under load, so treat the answer as nominal, not exact. That slip is a feature as much as a flaw: a belt drive is its own overload clutch and vibration isolator.
Belt velocity is the number that bites at the extremes: V-belts get unhappy above roughly 30 m/s as centrifugal tension eats the grip budget, and below a few m/s you're transmitting power with tension you have to crank in at the bearings. It also sets flex-cycle frequency — small pulleys at high speed fatigue belts fastest, which is why minimum sheave diameters appear in every catalog.
Where this math comes from
Belt drives are the quiet workhorse of the machine age — flat leather belts running from mill line shafts powered whole factories through the nineteenth century, with the ratio arithmetic on this card decided by which pulley the millwright slid the belt onto. A factory floor plan was literally a belt-drive diagram.
The modern chapter starts in 1917 when John Gates of the Gates Rubber Company introduced the rubber V-belt, whose wedging action in a grooved sheave multiplied grip and let drives shrink from ceiling shafts to motor-and-sheave pairs. Electric motors killed the line shaft; the V-belt gave every machine its own.
- 1801Textile mill era (circa)Flat-belt line shafting becomes the standard factory transmission.
- 1917John GatesRubber V-belt invented — the compact machine drive.
- 1979Gates / industry (circa)Synchronous (toothed) belts mature, adding exact ratios to belt drives.
See the full timeline of the math behind every calculator →
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