"Using lego to create a time table calculator"
by Callum and James
What is a lego computer?
A lego computer is made by connecting cogs together and working out the gear ratios. This is just how the first computers ever worked. They were sometimes called "difference engines."
A gear with 40 teeth will turn a gear with 8 teeth 5 times round for each turn because 8 goes into 40, 5 times.
The lego gears have 8, 16, 24 and 40 teeth which means you can make simple calculators for the two, three and five times table. To make other times tables you have to combine gears together. E.g To multiply by six, you need to multiply by two using a 16 and an 8 tooth gear and then multiply that output by three by using a 24 and an 8 tooth gear. You have to put the middle gears on the same axle.
You can with a bit of thought create machines for many times tables. By turning small gears with big gears the computers become dividers.
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You need a big box of Lego and some space to work. |
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This is Pieran's lego calculator. He's the so called cog master he taught me how to use cogs and I think he could make most of the times tables such as 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 20 (etc.) |
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If you look closely you can see that it times by 3 and then by 2 which makes a computer that times by 6. But if you turn the follower it divides by 6. |
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As you can see this one times by 5 and then by 3 to make a 15 times table computer. |
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As you can see on this one it's a trick because you think it's a fifteen but it's actually a five. The sixteen and the twenty four gears are just to hold the axles in. |
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This computer is another way of multiplying by 15.
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We could also make a machine to multiply by nine by using two sets of gears with ratio of 1 to 3 each.
We think you can make any times table if you have enough Lego cogs.
We noticed that as the times tables became bigger they were much harder to turn to make multiplications but easier to do division.
We also found that a lego differential gearbox halves the input.
Worm gears divide by twenty four but they can't multiply because they only go one way!
We still can't make the 7, 11, 13 and the other prime number times tables. Can you?
e-mail the thecogmaster@ambleside.schoolzone.co.uk with your solutions.
(We think you will have to use a differential gearbox to add two sets of multiplications together such as times 8 and times 5 but we did not get time to test it.- The teacher)