Levers, linkages and gears

In this chapter, you will revise what you learnt in Grade 7 about different types of levers and linked levers. You will pay special attention to whether a lever or a system of levers gives a mechanical advantage or a distance advantage.

You will also revise what you learnt earlier this year about how gear systems can give a mechanical advantage or a speed advantage. Then you will learn about a type of gear called a bevel gear. Bevel gears change the direction of rotation.

It is important that you understand mechanical advantage very well, because you will be doing calculations about mechanical advantage in the next chapter.

Revision of levers and mechanical advantage

Mechanisms are parts of machines that help us to move things. Machines are usually made of many connected mechanisms. Some parts of a mechanism move, and other parts are used to hold the moving parts in place.

Mechanisms are useful because they help us to move things further, faster or by using less force.

Figures 4 to 7 show machines that you might have at home. Write down what each of these machines is used for, and how they make it easier to do the task.

1. A bottle opener

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2. A pair of scissors

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3. A hammer

4. A pair of pliers

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Levers allow you to change the direction of movement, the size of movement and the amount of input force that is needed for the output movement to happen.

Do you remember what mechanical advantage is?

You already know that:

• If the input force is smaller than the output force, there is a mechanical advantage. You can say the mechanical advantage is bigger than 1.
• If the input force is bigger than the output force, there is not a mechanical advantage, but rather a distance advantage. You can say the mechanical advantage is smaller than 1.

When engineers, scientists and technologists design mechanisms, they want to know exactly how big the mechanical advantage in a system is. It is not good enough for them to say that the mechanical advantage is bigger than 1 or smaller than 1. They need a number to tell them exactly how big or small the mechanical advantage is. We call this number the mechanical advantage.

If a lever makes it easier to lift a heavy weight, the input force is less than the output force, and the mechanical advantage is greater than 1.

For example, if the output force is 12 and the input force is 4, the mechanical advantage is calculated in the following way:

\(12 \div 4\). This can also be written as \(\frac{12}{4}\) or ¹²⁄₄

The answer to this calculation can be written in different ways:

a ratio of 3 to 1

OR 3 : 1

OR 3.

This means that the output force is threetimes greater than the input force. You can also saythat the lever gives a mechanical advantage of 3.

But you cannot get something for nothing. If the input force is 3 times less than the output force, you will have to move the input arm 3 times further than the output arm. Look at Figure 8 to see how this works.

Not all levers give a mechanical advantage. Sometimes the input force is greater than the output force. These levers make it harder to move something, but the output movement will be greater than the input movement.

On a lever, the distances moved by the input arm and the output arm are directly related to their distances away from the fulcrum.

• If the distances from the fulcrum are equal, the distances moved will be equal.
• If the fulcrum is closer to the input force, the distance moved by the input arm will be smaller.
• If the fulcrum is closer to the output force, the distance moved by the output arm will be smaller.

The first-class lever and mechanical advantage

A lever can change a large movement with a small input force into a small movement with a large output force. When you use a bottle opener, you use a small input force to pull up the long handle, and the lever mechanism makes the output force big enough to bend the top of the bottle.

The first-class lever and distance advantage

You can also use a lever the other way around. You can use a big input force over a small input distance. This gives a smaller output force over a bigger output distance. You can see this in Figure 11.

These kinds of levers are often used to help cranes lift things very high. If, for example, the input arm moves 1 cm down and lifts the output arm 4 cm up, the lever is giving you a distance advantage. But the input force has to be 4 times bigger than the output force, so the mechanical advantage is less than 1:

The pair of kitchen or braai tongs in Figure 12 is an example of a tool that gives a distance advantage.

Linked levers

Figures 13 and 14 show two types of tools that are used to cut twigs and branches from trees, called "pruning".

1. How do you know that both of these tools use levers?

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2. How do you know that the levers used are first-class levers?

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3. Do both of these tools give a mechanical advantage? Explain your answer.

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4. Which of these tools will give you greater mechanical advantage? Explain your answer.

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First-class levers

Systems of linked levers

The bolt cutter in Figure 17 has two pairs of linked levers that are connected to each other. Figure 2 at the start of the chapter shows the movement of the parts of a bolt cutter.

• The pair of dark grey levers on the right have the handles on them. They share a single fulcrum.
• The pair of light grey levers on the left have the cutting blades on them. They have a separate fulcrum for each lever.
• There are also two pivot points in the middle of the two pairs of levers, to link them together. They have a different purpose from the other fulcrums, because they move together with the levers, instead of the levers rotating around them.

1. Are both the pairs of levers used in the bolt cutter first-class levers? Explain your answer.

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2. What can you say about the total mechanical advantage of the two pairs of levers linked to each other?

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3. Look at the cutting levers (the end that cuts). What is different about the fulcrums of these levers compared to a pair of scissors?

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4. Compare the arrangements of the fulcrums in the bolt cutter and the pair of scissors. Why are the fulcrums arranged in a different way in a bolt cutter than in a pair of scissors?

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Second-class levers give a mechanical advantage

Second-class levers have the fulcrum at one end and the input at the other end. The output is between the input and the fulcrum.

A second-class lever always gives a mechanical advantage. The input is always further away from the fulcrum than the output, so the input arm always moves further than the output arm. This means that the output force will always be bigger than the input force.

So the MA is always greater than 1:

MA = output force ÷ input force > 1.

1. Give one more example of your own for each of the following types of levers.

(a) first-class lever

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(b) second-class lever

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Third-class levers give a distance advantage

Third-class levers also have the fulcrum at one end, but the output is at the other end. The input is between the fulcrum and the output.

The input is always closer to the fulcrum than the output, so the output arm always moves further than the input arm.

This means that the output force will always be smaller than the input force.

So the mechanical advantage is always smaller than 1:

MA = output force ÷ input force < 1.

Gear systems

You learnt about gears in Term 1 this year. Do you remember? Here are a few reminders:

Mechanical advantage and speed advantage

Torque and revolutions per minute

A small driver and a large driven gear

Look at the two connected gears in Figure 20. Gears that have teeth like these are called spur gears. Now answer the questions that follow:

1. If the driver gear turns clockwise, which way will the driven gear turn?

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2. Count the numbers of teeth on the two gears in Figure 20. How many revolutions will the driver gear need to turn to make the driven gear turn once? Explain why this happens.

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3. Will this system give a mechanical advantage? How do you know?

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A large driver and a small driven gear

Look at the two gears in Figure 21. The driver gear is now large and the driven gear is smaller.

1. Will the driven gear turn faster or slower than the driver gear? Explain your answer.

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2. A driver gear has 10 teeth and the driven gear has 5 teeth. How many revolutions will the driver gear need to turn to make the driven gear turn once? Explain why this happens.

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3. Will this gear system give a mechanical advantage or a speed advantage? How do you know?

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Idler gears

Look at Figure 22. The driver and the driven gear are the same size. In the middle there is a small gear called an idler gear.

What does an idler gear do?

1. Will the idler gear turn faster or slower than the driver gear? Explain.

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2. Will the idler gear turn faster or slower than the driven gear? Explain.

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3. Will the driver gear and the driven gear turn at different speeds? Explain.

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4. Will the driver gear and the driven gear turn in different directions? Explain.

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Bevel gears

Bevel gears are used when you want to change the direction of turning. Look at Figure 23. It shows how two bevel gears mesh together.

• The top gear will turn on a horizontal axle.
• The bottom gear will turn a on a vertical axle.
• The bevel gear system changes the direction of rotation by 90°.

Figure 24 on the next page shows a hand drill and an egg beater.

• The driver gear is a large bevel gear attached to a crank handle.
• The driven gears are the small bevel gears. The bottom bevel gear forces the drill to turn and the egg beater to rotate its blades.

1. Do you think the hand drill gives you a speed advantage or a mechanical advantage? Explain your answer.

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2. Explain how the bevel gears on the drill work.

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Something you could do at home: make a can crusher

Next week

Next week, you will learn how to do mechanical advantage calculations for levers and gears.