Compound gear and pulley systems: Gears

are wheels with around the outside. When several wheels are interlocked, they can transfer motion from one place to another, eg in some hand whisks or on bikes.

A close-up image of the rear of a bicycle, including the chain, wheel and brakes.

Gears can change the direction or the speed of movement. As there are teeth around the edge of the gears they grip together and so can withstand a greater force, enabling them to move large items such as cars or bicycles.

Gear trains

are when two or more gears are joined together. In a simple gear train, the causes the to turn in the opposite direction.

Smaller gears with fewer teeth turn faster than larger gears with more teeth. This difference in speed is called the .

Example

The drive gear has 60 teeth and the driven gear has 15 teeth.

Gear ratio = 15 ÷ 60

= 0.25

For each rotation of the drive gear, the driven gear would rotate four times.

Gear ratio = 1:4

This is known as . If the drive gear had 15 teeth and the driven gear had 60 teeth, the gear ratio would be 4:1 which is known as .

Question

If a cyclist is pedalling with a drive gear of 50 teeth and a driven gear of 25 teeth, what is the gear ratio?

If the drive gear and the driven gear are separated by another gear, called the , they will move in the same direction.

A drive gear and driven gear separated by an idler gear. Directional arrows show drive and driven gears move in the same direction and the idler gear in the opposite direction.

Pulleys

use , similar to levers, to lift up loads. Pulleys are wheel shaped with a groove that allows a cord to sit inside the groove. They can be used by hand or attached to a motorised to increase the amount of weight that can be lifted.

Pulleys are a simple and manoeuvrable way to move large objects. They are easy to transport to where they are needed and set up, but they do require somewhere stable to hang.

A single pulley changes the direction of force, making pulling down easier than lifting up. Single pulley systems are demonstrated in cranes, lifting a bucket from a well, raising a flag or adjusting window blinds. Even though there is no actual mechanical advantage with one pulley, it is referred to as having a mechanical advantage of one.

Showing a rope over a single pulley system and an arrow to show the downward direction of effort to pull a load. — Figure caption,
A The mechanical advantage of a fixed pulley is one

One pulley doesn’t make a mechanical advantage, as the same amount of force is needed. However, if additional pulleys are added, a mechanical advantage is created. Using two pulleys together means you need half the force to lift. This is called a , and is used to lift large, difficult-shaped objects, such as furniture. Adding more wheels to the block and tackle increases the load it can lift.

Showing a rope over a two pulley system and an arrow to show the downward direction of effort to pull a load. — Figure caption,
A block and tackle pulley

Showing a rope under a moveable pulley system and fulcrum with an arrow to show the upward direction of effort to pull a load. — Figure caption,
The mechanical advantage of a movable pulley (one where the pulley can move freely along the rope) is two

Example

The 10 N load below would still require 10 N of force to lift as the extra pulley is not taking any additional strain in weight - the weight is still taken by only one section of rope.

Showing a load supporting rope under a fixed pulley holding a 10 N load. A redirecting rope from a second fixed pulley shows the downward effort to pull the load.

The 10 N load below would require half of the force to lift. There are two sections of rope taking the strain, so 5 N of force would be needed to lift it. The mechanical advantage would be 2.