Gears

Gears are like a continuously rotating lever. By using different sizes of wheels, and different numbers of teeth, you can use gears as force multipliers or as distance multipliers.

Figure above shows two cogs one with twice as many teeth as the other. The cog teeth fit together, so as when one cog turns it makes the other turn as well.

As cog A rotates once, nine of its teeth pass between the teeth on cog B. So cog B only turns half way round. It turns in the opposite direction to cog A. Cog A, the one which is starting the movement is called the driving wheel. Cog B is the driven wheel. If energy is transferred perfectly from cog A to cog B, then

Force x distance moved for cog A = Force x distance moved for cog B

As cog B does not turn as fast as cog A, the force it exerts must be larger. When a small cog and a large cog turn together, the larger cog always turns more slowly and with greater force than the smaller cog.

The easiest way to calculate how much the large cog multiplies the force exerted by the small cog is to count the teeth of the cogs. You can then multiply the force of the driving wheel by the following formula:

So the force exerted by the large cog is twice the force exerted by the small cog.

Relation between Number of Teeth (N_A/N_B), Radii (r_A/r_B) and Speed of Rotation (n_A/n_B)

In figure above, you can see that the two gears are rotating in opposite directions; that the smaller gear is spinning twice as fast as the larger gear, and that the axis of rotation of the smaller gear is to the right of the axis of rotation of the larger gear,

The fact that one gear is spinning twice as fast as the other is because of the ratio between the gears - gear ratio. In this figure, the diameter of the gear on the left is twice that of the gear on the right. The gear ratio is therefore 2 : 1. Everytime the larger gear goes around one, the smaller gear goes around twice. If both gears had the same diameter, they would rotate at the same speed but in opposite directions.

Most gears in real life have teeth. The teeth have three advantages:

prevent slippage

• They between the gears. Therefore, axles connected by gears are always synchronized exactly with one another.

determine exact gear ratios

• They make possible to . Let us take an example to illustrate this. If one gear has 60 teeth and another has 20, the gear ratio when these two gears are connected together, is 3:1,

control the gear ratios

• They , even if the diameter are a bit off.

The velocity ratio of a pair of gears is defined as the ratio of the number of revolutions per second of the driving wheel to the number of revolutions per second of the driven wheel.

If r_A and r_B are the radii of the driving wheel and the driven wheel respectively, then

where n_A and n_B are the number of teeth in the driving and the driven wheel respectively.

Advantages of Gears

Gear systems are very efficient at transferring energy. Some gear boxes are 95% efficient i.e., they only waste 5% of the energy they transfer.

Gears are useful for transferring energy at different speeds. A rotating motor could be made to turn a wheel very fast or very slowly, depending on the relative sizes of the cogs used. By using different gear ratios, a cyclist can adjust to varying riding conditions. A low gear ratio provides little force but easier pedalling for uphill climbs, while a high ratio offers greater force for level or downhill stretches where pedalling is easy.

In brief, gears are generally used for one of four different reasons:

• To reverse the direction of rotation.

• To increase or decrease the speed of rotation.

• To move rotational motion to a different axis.

• To keep the rotation of two axes synchronized.