Gear train

Great — the gear train clearly caught your eye. Here are more challenges and curiosity questions that this Koumio® board will help you answer.

Challenges and curiosity questions

Try answering on your own first. The answer is hidden under the button.

With a partner, count out loud how many turns it takes for the kangaroo and the cheetah (top and bottom wheel) to return to their starting position.

The answer is 50/49.

On the board the kangaroo and the cheetah move at almost the same speed. Is that true in nature too?

Yes and no. The cheetah excels at extreme short-term speed, while the kangaroo is the master of efficient movement over long distances.

The cheetah is the fastest land mammal and can reach 110–120 km/h in a short sprint. The red kangaroo moves by hopping and tops out at around 60–70 km/h.

But the kangaroo is a master of endurance. Thanks to tendons in its legs that work like springs, hopping paradoxically costs it less energy the faster it goes. It can hold 40–50 km/h for a very long time and over 2 km would probably beat a tired cheetah.

What happens when we put another wheel between two wheels? Does force, speed or direction change?

Direction: yes, it changes. Without an extra wheel, neighbouring wheels turn in opposite directions; with an idler wheel in between, the first and last wheel turn the same way.

Force and speed: adding an idler usually does not change the overall gear ratio between the first and last wheel, so the resulting speed and force stay the same. The motion can still speed up or slow down depending on the size and tooth count of the first and last wheel. The idler mainly transmits motion and changes direction.

Why do we ride uphill in first gear?

We start in first gear because it is less demanding. We need less force to set the body in motion. We have to pedal more often, but it costs us less effort.

Why does a car pull away in first gear and not in fifth?

It is similar in a car. Starting in first gear makes setting the car in motion slower but much easier (low gear = easy pedalling / high force / low speed).

Why does a bicycle have so many different cogs (different sizes and tooth counts)?

The derailleur changes which wheels we are currently using. That controls how hard the pedalling is (force) and how fast we go.

Imagine the biggest cog were another 10 times larger. How hard would it be to turn?

Such a wheel would be very hard to turn. You would have to apply a large force for a relatively long time before it moved at all.

What is the gear ratio between the big and the small hand of an analogue clock? How many times does the minute hand pass twelve before one hour has gone by?

The minute hand (the driving one, in terms of speed) goes round the dial in 1 hour. The hour hand (driven) takes 12 hours. So the minute hand moves 12 times faster — a gear ratio of 1:12.

Teacher's guide: Gear train

What the guide covers:

Content – what the Koumio® board can explain and show.
A set of challenges, curiosity questions and application questions.
Use in lessons: what a teaching unit can look like (1–2 lessons).
Applications and examples of gears in practice.

1. What can the Koumio® board explain and show?

Simple and compound gearing.
Gear ratios and angular velocity (even though it is not directly visible, the board helps build the intuition).
Spreading force across several points of action (using several smaller sources).
Calculating the gear ratio with a formula.

2. Lesson outline

If you have several Koumio® boards available, split the class into groups. Let the children experiment freely, then ask them to explain the principles of gears and ratios to their classmates in their own words.

Suggested sequence of activities

1
Grab a cog and spin it (the motion passes to all the wheels).
2
Watch how the animals move (direction of motion).
3
Place each animal into its "house" (getting ready for the race).
4
Start the race – find out in what order the animals finish. Fun fact: the kangaroo and the cheetah move at almost the same speed. Is that true in nature too?
5
Observe how many times you must turn a wheel for two chosen cogs to return to their starting position. Try neighbouring wheels as well as distant ones. This gives you the ratio of turns, which matches the ratio of tooth counts (angular velocity).
6
Explore what role the number of teeth plays.

Further information and terms

Driving wheel (produces the action) vs. driven wheel (the one that "rides along"). The gear ratio i can be calculated:

from wheel revolutions: i = n₁ / n₂
from tooth counts: i = z₂ / z₁ (e.g. 20/10 = 2:1)
from wheel diameters: i = D₂ / D₁

Index 2 marks the driven wheel, index 1 the driving wheel.

If i > 1, the gearing slows the motion down. If i < 1, the gearing speeds it up.

The smaller the driving wheel, the more turns it needs to make to turn the big driven wheel once.

3. Applications and examples of gears in practice

Gears are part of many machines and do many different jobs. You find them in car engines, on bicycles, in motorcycles, hydraulic jacks and gearboxes.

They are the heart of mechanical watches and alarm clocks, but you also find them in can openers, kitchen grinders, mixers, cordless drills and printers. They are used in wind turbines, on excavators, escalators, in lifts and on conveyor belts.

Related terms

Gearbox: A mechanical device that transmits motion between a driving and a driven machine; it converts rotation into rotation with a different angular speed and torque.
Gear drive: The most common kind of drive, working by meshing (force transmitted by pressure) with the parts in direct contact.
Gear train: An assembly of a driving and a driven wheel; the smaller one is called the pinion, the larger one the gear.
Cog: A machine part for transmitting rotary motion and mechanical energy between shafts.

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