Grade by Grade
D. Structures and Mechanisms · Machines and Mechanisms

Gears: Teeth That Mesh

D2.2 D2.3 D2.4 A1.2 A2.1About 40 minutes
Learning goals
  • I can name the parts of a gear system: teeth, axle, driver gear, follower gear and idler gear.
  • I can explain that two meshing gears turn in opposite directions.
  • I can predict the direction of every gear in a gear train.
  • I can explain how an idler gear makes the follower turn the same way as the driver.
  • I can follow and write simple code that predicts gear directions.

Words to know

gear
A wheel with teeth around its edge. Gears pass turning motion to each other.
teeth
The bumps around the edge of a gear that fit into the gaps of another gear.
mesh
When the teeth of two gears fit together so that one gear turns the other.
driver gear
The gear that is turned first, by a handle, a motor or your hand. It drives the others.
follower gear
A gear that is turned by another gear. It is also called the driven gear.
idler gear
A gear placed between the driver and the follower. It makes the follower turn the same way as the driver.
gear train
Two or more gears meshed together in a row.
clockwise
Turning the same way the hands of a clock turn.
counterclockwise
Turning the opposite way to the hands of a clock.

Remember from Grade 2

In Grade 2 you learned that a gear is a wheel with teeth, and that one gear can turn another. Now let's look closely: which way does each gear turn, and why?

What happens when gears mesh?

Put two gears side by side so their teeth mesh (fit together). Turn one gear. Its teeth push the teeth of the other gear, and that gear turns too.

  • The gear you turn first is the driver.
  • The gear it turns is the follower (or driven gear).
  • Each gear turns on its own axle.

Here is the big rule: two meshing gears turn in opposite directions. If the driver turns clockwise, the follower turns counterclockwise.

Close-up of brass gears inside a mechanical clock, with their teeth meshing together.
Inside a mechanical clock, many gears mesh. Look for a small gear touching a big one: when one turns, it pushes the other the opposite way. AI-generated image
driver(12 teeth)turnsclockwisefollower(24 teeth)turns counter-clockwise
The driver turns clockwise. Where the teeth meet, the driver's teeth push the follower's teeth the same way, so the follower turns counterclockwise.

Why opposite?

Look where the teeth touch. On the clockwise driver, the teeth on its right side are moving down. They push the teeth on the left side of the follower down too. When the left side of a wheel moves down, that wheel turns counterclockwise. Try it with your two fists, knuckles touching: roll them against each other.

Three gears: the idler

What if you want the follower to turn the same way as the driver? Put a third gear in the middle. It is called an idler gear.

  • Driver: clockwise.
  • Idler: counterclockwise (opposite to the driver).
  • Follower: clockwise (opposite to the idler, so the same as the driver).
driverclockwisefollowerclockwiseidler: counterclockwise
A gear train with an idler gear in the middle. The driver and the follower both turn clockwise.

The odd and even rule

In a single row of gears, each gear turns the opposite way to the one before it. So:

  • Gears in odd places (1st, 3rd, 5th...) turn the same way as the driver.
  • Gears in even places (2nd, 4th, 6th...) turn the opposite way.

The size of the gears does not change the direction. Only the order matters.

Worked example

Let's predict a gear train

Five gears are meshed in a row. Gear 1 (the driver) turns clockwise. Which way does gear 5 turn?

  1. Gear 1: clockwise.
  2. Gear 2: opposite, counterclockwise.
  3. Gear 3: opposite again, clockwise.
  4. Gear 4: counterclockwise.
  5. Gear 5: clockwise. Check with the rule: 5 is odd, so it turns the same way as the driver.

Gear 5 turns clockwise, the same as the driver.

Gears that don't touch: chains

On a bicycle, the front gear (chainring) and the back gear (sprocket) don't touch. A chain joins them. Gears joined by a chain turn in the same direction, because the chain wraps around the outside of both. You will see belts do this too.

Code it: a gear direction predictor

Computers can predict gear directions for engineers. Here is a simple program. It starts with the driver's direction and flips the direction once for each gear after it.

set direction to "clockwise" // gear 1, the driver
set numberOfGears to 5
repeat (numberOfGears - 1) times
if direction = "clockwise" then
set direction to "counterclockwise"
else
set direction to "clockwise"
say "The last gear turns " + direction

The loop runs 4 times (for gears 2, 3, 4 and 5). Output: The last gear turns clockwise.

Worked example

Let's trace the code

Change the program so numberOfGears is 4. What does the program say?

  1. The loop runs 4 − 1 = 3 times.
  2. Start: clockwise. After loop 1 (gear 2): counterclockwise.
  3. After loop 2 (gear 3): clockwise.
  4. After loop 3 (gear 4): counterclockwise.

It says "The last gear turns counterclockwise." That matches the rule: 4 is even, so the last gear turns the opposite way to the driver.

Gears in daily life

You can find gears in hand egg beaters, wind-up toys, clocks and watches, hand drills, can openers, salad spinners, bicycles (with a chain) and many machines with motors, like car engines and washing machines.

Just for fun

Riddle: What has lots of teeth but never needs to visit the dentist?

A gear!

Hands-on activity

Make cardboard gears

You need: a piece of corrugated cardboard (from a delivery box), 3 jar lids of different sizes (or round cardboard circles), glue or double-sided tape, 3 pushpins or thumbtacks, a thick piece of cardboard or a box as a base, a marker, and scissors or a craft knife (for the grown-up).

  1. A grown-up peels the flat paper off one side of the corrugated cardboard, so the bumpy ridges show. Cut strips as wide as the lid's rim.
  2. Wrap a strip around the edge of each lid, ridges facing out, and glue it. The ridges are your gear teeth.
  3. A grown-up pushes a pushpin through the centre of each lid into the base. The pin is the axle. Wiggle each lid until it spins freely.
  4. Place two gears so the ridges mesh. Mark an arrow on each lid. Turn the driver clockwise. Which way does the follower turn? Record it.
  5. Add a third gear in a row. Predict the direction of each gear, then test.
  6. Bonus: Run the code above in your head with 3 gears. Does it match your test?

What to look for: meshing gears turn opposite ways; with three in a row, the first and third turn the same way. If the gears slip, push them closer so the ridges fit together better. Safety: a grown-up handles the scissors or knife and the pushpins; keep pins away from little children. (If you have building-set gears, you can use those instead.)

Your turn

1

What is a gear?

2

What does mesh mean?

3

A driver gear turns clockwise. Which way does the gear meshed with it turn?

4

What is an idler gear for?

5

Four gears are in a row. Gear 1 turns counterclockwise. Which way does gear 4 turn?

6

Does the size of a gear change which way it turns?

7

Two sprockets are joined by a chain. Do they turn the same way or opposite ways?

More practice: warm-up

1

What do we call the bumps around a gear's edge?

2

Which gear is turned first?

3

What is another name for a follower gear?

4

Name two things that have gears.

5

Which way do the hands of a clock turn?

More practice: on your own

1

Seven gears are meshed in a row. The driver turns clockwise. Which way does gear 7 turn? How do you know?

2

Ben wants the last gear of his gear train to turn the opposite way to the driver. Should he use 2, 3 or 5 gears in a row?

3

Explain in your own words why two meshing gears turn opposite ways.

4

In the code, what does the line repeat (numberOfGears - 1) times do?

5

Your cardboard gears slip instead of turning each other. Give two ways to fix them.

Challenge

1

Three gears are arranged in a triangle so that each gear meshes with both of the others. What happens when you try to turn one? Explain.

2

A toy has a driver gear, two idler gears and a follower in a row. The driver turns clockwise. Which way does the follower turn?

3

Change the code so it works for a driver that starts counterclockwise and a train of 6 gears. What will it say?

Check your understanding

Quiz

1.

Two gears mesh. The driver turns clockwise. The follower turns...

2.

The gear that is turned first is called the...

3.

Why put an idler gear between a driver and a follower?

4.

Six gears are in a row. Gear 1 turns clockwise. Gear 6 turns...

5.

What decides the direction a gear turns in a gear train?

6.

Two bicycle sprockets joined by a chain turn...

For parents and teachers

Big idea (D2.2, D2.3, D2.4): Gears transmit rotary motion. Meshing gears always turn in opposite directions; an idler gear makes the follower turn the same way as the driver. In a row of gears, odd-numbered gears turn like the driver and even-numbered gears turn the opposite way. Chains and open belts keep the same direction. Predicting with code is A2.1; testing predictions is A1.2.

How to help: Use your fists to act out meshing gears. If you have a building set with gears, let your child build trains of 2, 3, 4 and 5 gears and predict before turning.

Common difficulties:

  • Thinking a bigger gear turns the other way. Size changes speed (next lesson), not direction.
  • Forgetting to count the driver as gear 1.
  • Safety: a grown-up should cut the cardboard and push in the pushpins. Keep pins away from younger siblings.