# Mechanism of gear rotation

Is the smaller gear (pinion) always mounted to the input shaft when meshed with a bigger gear that is mounted on the output shaft? Are there places where the bigger gear drives the smaller gear?

• Who says it's never the other way around? I've seen lots of examples, such as the common "salad spinner". – Dave Tweed Mar 7 '15 at 12:01
• @DaveTweed - yes, that is what he is asking. – Russell McMahon Mar 7 '15 at 12:40

## 3 Answers

Two meshed gears are used to transfer rotational drive between two shafts.
The relative speeds of rotation are inversely proportional to the number of teeth on each gear. That is -

$$\text{Input}_{\text{RPM}} / \text{Output}_{\text{Rpm}} = \text{Output gear}_{\text{teeth}} / \text{Input gear}_{\text{teeth}}$$

So, if it is desired that the output shaft rotate more slowly than the input shaft then the output gear is larger. But, if it is desired that the output shaft rotate faster than the input shaft then the output gear is smaller.

The reason for the relationship above becomes obvious "by inspection".

With the arrangement shown below, for every complete (360 degree) rotation of the small gear the large gear rotates only part of a turn. The large gear has a lower RPM rate than the small gear.

IF the small gear was the DRIVING or INPUT gear then the large DRIVEN or OUTPUT gear would be turning more slowly.

But

IF the large gear was the DRIVING or INPUT gear then the small DRIVEN or OUTPUT gear would be turning more rapidly

Which arrangement is used depends on whether an increase or decrease in RPMs is required.

Torque or "twisting force" is inversely proportional to speed.
That is the slower turning shaft will have proportionately more torque.

Diagram from Wikipedia - Gear ratio

Look at the examples below and you will see how the gear size relates to relative shaft speed:

Several animated examples

3 meshed gears animated example

Animated 2 to 1 speed example

1:1 and 1:2 example from Essentially unrelated stack exchange biology question

There are many examples of low input speed to high output speed gearing:

• kitchen "salad spinner"
• old-fashioned hand-cranked siren
• electrical generator attached to a tractor PTO (power takeoff) — also wind-powered generators
• the "overdrive" gear in any vehicle transmission
• the speed regulator on a steam engine, or in many kinds of clockwork mechanisms

Indeed, any sort of spring- or weight-driven clock works this way. The spring or weight is used to apply torque to the slowest-moving gear in the mechanism, and the escapement (e.g., balance wheel or pendulum) at the other end of the system of gears regulates the speed.

In some cases, it's more efficient to use a belt drive for this kind of speed change. For example, an old-fashioned "spinning wheel" for making thread.

Any mechanical clock or watch relies on the motive power applied to the large gear (the "wheel") which drives the smaller one (the "pinion"). Thus the weight in a longcase clock is suspended by a cord, rope or chain from the "great wheel" (usually making a rotation every 12 hours) and the rate of rotation is geared up to the escape wheel (which often has the seconds hand mounted on it).

Note that the tooth form is usually different when gearing up : friction is critically important in a clock, transmitting high forces is usually less so (and is usually catered for by making the great wheel thicker than the others). So the teeth are usually cycloidal in form, where the deep part of the slot in a tooth is approximately rectangular, which means the base of a pinion tooth is undercut. This is a fundamentally weaker tooth form, especially since pinions may have as few as 6 teeth, but runs freely with little friction and zero pressure angle (see below).

For example

(from this page)

An extreme case is the lantern pinion

(from this page) where the pinion tooth is completely undercut!

You never lubricate the teeth of a clock or watch wheel : that only adds viscosity (i.e. friction), wasting power, and does nothing to eliminate wear. This is because the contact surfaces of the teeth roll over each other, there is no sliding motion involved. (The pivots, unless running in ballraces, do need lubrication. John Harrison employed ballraces for a prototype marine chronometer).

In contrast, while gearing speed down also involves contact surfaces rolling over each other, the purpose is usually to amplify force, and to do that with the least material, a stronger tooth form is required. This is normally an involute tooth form, where each tooth is wider at the base, like a wedge.

This means the teeth press each other outwards as well as turning each other, at an angle known as the pressure angle (usually 20 degrees in modern gears, formerly 14.5 degrees). Thus the axles are pushed apart, increasing friction on the pivots and requiring a stronger gearbox. (The animation on the Wikipedia page exaggerates the pressure angle). Traditionally, involute pinions are only cut down to 12 teeth, with the 20 degree PA making for more friction but stronger teeth with wider roots.

So : yes, gearing can be used to increase rotational speed, but it usually requires a different tooth form, otherwise it loses a lot of power to friction.
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