A gear ratio trades speed for turning force: a small gear driving a big gear turns the output slower but stronger, by the same factor. Students test gears on a winch, work out the ratio, speed, strength and lift time, then choose a pair that meets a brief, and find a brief where the constraints conflict.
A small motor can lift 200 g. The bucket is 450 g. You can't change the motor, but you have a box of gears. How do you lift it, and what do you give up?
A motor turns fast but can only lift a little. A winch winds rope onto a drum to lift a load. Put a gear on the motor (the driver) and a gear on the winch (the driven gear), and the teeth push each other round.
The brief: the motor turns 120 times a minute and lifts 200 g with no gears. The drum winds 0.1 m of rope each turn. Lift a 450 g bucket 1 m in 15 s or less. The kit has one each of 8, 16, 24 and 40-tooth gears.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Small gear, big gear
TryTry it on the board and compare the result with your prediction.
Try: turn it and load it
Was your prediction right? Slower and stronger, by the same 3.
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Press Turn the motor once and watch the orange dot on the winch gear. How far round does it go?
Use the board. This ticks when you get there.
Add 50 g at a time and lift, until the winch stalls.
Use the board. This ticks when you get there.
What is the heaviest bucket the winch lifted (in grams)?
InvestigateWork out why it happens, one step at a time.
Worked example: does 8 → 24 meet the brief?
Worked exampleBefore each step, say what you think comes next.
ratio=24÷8=3Ratio = driven teeth ÷ driver teeth. The winch needs 3 motor turns for each of its own.
120÷3=40 turns a minuteSlower by the ratio: divide the motor's speed.
200×3=600 gStronger by the same ratio: multiply what the motor lifts.
1÷0.1=10 winch turnsThe drum winds 0.1 m each turn, so 1 m takes 10 turns.
10÷40=0.25 min=15 sTime = turns ÷ turns a minute; times 60 for seconds.
600≥450✓15≤15✓Check both criteria: strong enough and fast enough. 8 → 24 passes.
Now do the same for 16 → 40. The ratio is 40÷16=2.5. Start with the winch's speed.
Sam wants a faster lift, so swaps the gears round.
Now 16 → 40 (ratio 2.5). How many turns a minute does the winch make?
16 → 40: what is the heaviest bucket it can lift, in grams?
16 → 40: how many seconds to lift the bucket 1 m?
Sam's winch stalls with the 450 g bucket. Click the line where Sam's working first goes wrong.
ModifyChange the problem on purpose and see what happens.
Vary: change one thing
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The bucket is now 300 g. Find the pair that lifts it fastest within 15 s, and lift with it.
Use the board. This ticks when you get there.
A faster motor: 180 turns a minute, and the 450 g bucket again. Which pair is fastest now? Lift with it.
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The bucket is now 700 g. Find a pair that can lift it at all, and lift.
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Ratios
The 16-tooth gear on the motor drives the 24-tooth gear on the winch. What is the ratio?
Motor 120 turns a minute, ratio 5. How many turns a minute does the winch make?
The 24-tooth gear on the motor drives the 16-tooth gear on the winch. The motor lifts 200 g with no gears. What is the heaviest lift now, to the nearest gram?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Write a brief
Need a hint?
Start from a pair and its numbers: what is the most it can lift, and how long does it take?
Another hint
Choose a load only one pair is strong enough for, or a time limit only one pair is fast enough for.
Another hint
For example 550 g: only 8 → 24 (600 g) and 8 → 40 (1000 g) are strong enough. Now pick a time limit only one of them meets.
Stretch: write a brief where no pair passes, then argue which constraint the client should relax, and why.
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Change the bucket and the time limit until exactly one pair in the kit meets the brief.
Use the board. This ticks when you get there.
For teachers
Students fit gears to a motor-driven winch, find by testing that a small gear driving a big one is slower and stronger by the same factor, work out ratio, speed, strength and lift time, choose pairs for a brief, meet a brief where constraints conflict, then write a brief of their own. About 45 minutes.
I can work out a gear ratio as driven teeth ÷ driver teeth.
I can explain that a ratio makes the output slower and stronger by the same factor.
I can check a design against every criterion in a brief.
I can explain what to do when no design meets every constraint.
Before class
Try every board yourself. LEGO Technic or Meccano gears make a good start before the board: mark a tooth on each gear, turn the small one once and count.
Simplifications: no friction or losses (real gear meshes lose a few per cent each), the motor lifts exactly 200 g with no gears, and the bucket rises at a steady speed. Years 9–10 can add 80% efficiency per mesh.
Curriculum hooks: Design and Technologies, engineering principles and systems (primary); Science, forces and simple machines; Maths, ratio and rates (applied, not taught). If the class has not met ratio, do that first.
Maths for the time: 1 m ÷ 0.1 m a turn = 10 winch turns; turns ÷ turns a minute × 60 = seconds.
Running the lesson
Predict: ask a few students to say why they chose their option before the Try.
Try: the dot moves a third of a turn. Ask how many motor turns make one winch turn.
Worked example: model it live, line by line, before revealing the prepared lines.
Find the mistake: ask which gear is being driven in Sam's design.
Vary, too heavy: stop the class here. Who would they talk to, and what would they offer?
Make: compare briefs. Did anyone make one pass by speed and another by strength?
The hard part (on purpose)
Students treat speed and strength as separate. Keep returning to 'same factor, opposite directions', and to which gear is being driven.
When students get stuck
A student says the bigger gear turns faster. Ask: Count the winch turns for one motor turn. Is it more or less than one? Fix: The big gear has more teeth to push past, so it turns less.
A student divides the driver by the driven gear (the ratio upside down). Ask: Which gear is being driven? Put that one on top. Fix: Ratio = driven ÷ driver.
A student changes only the speed (or only the strength). Ask: Hang more load. Did the strength change as well as the speed? Fix: Both change, by the same ratio.
A student checks only the load. Ask: Your design lifts it. Is it fast enough? Fix: Check every criterion in the brief.
Stretch and support
Stretch: Two pairs in a row (a compound train): 8 → 24, then 8 → 40 on the same axle. What is the overall ratio? Could it lift 700 g, and how long would it take?
Support: Give a table with columns ratio, winch speed, heaviest lift, time, and fill the 8 → 24 row together.
Where it leads
Next: Gear trains (idlers and compound trains), then levers and pulleys (planned).
Code links: a short Python loop can test every gear pair against the brief; the board's Make does this for them.
Physical computing: a motor and a servo on a real winch (Power and motors).
small gear, big gear: Committing to what a small-to-big gear pair does tests the new move before students see it: slower and stronger, by the same factor. Each wrong option is a real slip: bigger is faster, or only one thing changes.
Try: turn it and load it: Counting winch turns settles the speed half of the prediction; adding load until it stalls settles the strength half. Numbers are hidden so students find both by testing.
Worked example: does 8 → 24 meet the brief?: The worked example models the move with numbers: ratio = driven ÷ driver, divide the speed, multiply the strength, then the time and both criteria. The faded example practises it on 16 → 40. Sam's upside-down ratio is planted after the method.
Vary: change one thing: Each task changes one thing in the brief: a lighter load, a faster motor, then a load so heavy that no pair meets both criteria. The last is the engineering point: constraints can conflict, and someone has to decide.
ratios: Ratio the right way up, divide for speed, multiply for strength, and a real-world trade-off.
write a brief: Writing a brief with exactly one passing pair reverses the process: students reason from the criteria to the gears, and the board tests every pair in the kit, as an engineer's checking tool would.
Now you can
Work out a gear ratio as driven teeth ÷ driver teeth.
Explain that a ratio makes the output slower and stronger by the same factor.
Check a design against every criterion in a brief.
Explain what to do when no design meets every constraint.