A crank and slider turns rotation into back-and-forth motion: one turn is one stroke out and back, and the stroke is twice the crank's radius, whatever the rod's length. Students find the stroke by turning, work out a pump's flow, and size a crank to a brief.
A motor turns round and round. A pump needs a piston that goes in and out. How do you get one from the other?
Motors spin. Many machines need something to go back and forth instead: a pump's piston, a saw blade, a sewing machine's needle. A crank (an arm or a pin on a wheel) and a connecting rod turn one into the other: the slider at the end of the rod runs along a straight track.
The stroke is how far the slider moves from one end of its travel to the other.
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.
How far does it go?
TryTry it on the board and compare the result with your prediction.
Try: turn it
Was your prediction right? The stroke is twice the crank radius; the rod only sets where along the track it happens.
Try it yourselfYour edits are saved in this browser.
Press Turn the crank once and watch the graph of the slider's position.
Use the board. This ticks when you get there.
Read the graph: how far does the slider move from one end to the other (in mm)?
Make the rod longer, then turn the crank again. Does the stroke change?
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Worked example: a pump
Worked exampleBefore each step, say what you think comes next.
stroke=2×25=50 mm=5 cmThe pin goes 25 mm one side of the centre and 25 mm the other.
per stroke=4×5=20 cm3A piston 4 cm² in area moving 5 cm sweeps 20 cm³ of water.
60 turns a minute=60 strokes a minuteOne turn of the crank is one stroke.
20×60=1200 cm3 a minuteThat is 1.2 litres a minute.
Now a 30 mm crank and a piston 5 cm² in area, at 40 turns a minute. Start with the water per stroke.
A 30 mm crank drives a piston 5 cm² in area. How much water does it push each stroke, in cm³?
At 40 turns a minute, how much water a minute, in cm³?
Noah thinks his pump gives 600 cm³ a minute. Click the line where his working first goes wrong.
ModifyChange the problem on purpose and see what happens.
Vary: size the crank
Try it yourselfYour edits are saved in this browser.
The brief asks for a 60 mm stroke. Set the crank and turn it.
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Cranks
A crank of radius 35 mm. What is the stroke, in mm?
A saw blade must move 80 mm each stroke. What crank radius does it need, in mm?
A sewing machine's crank turns 900 times a minute. How many times does the needle go down each second?
A pump with a 4 cm stroke and a 3 cm² piston turns 50 times a minute. How much water a minute, in cm³?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
A pump to a brief
Need a hint?
Per stroke = flow ÷ strokes a minute: 900 ÷ 30.
Another hint
Stroke = water per stroke ÷ piston area.
Another hint
30 cm³ ÷ 6 cm² = 5 cm = 50 mm, so the radius is 25 mm.
Try it yourselfYour edits are saved in this browser.
A garden pump must move 900 cm³ a minute at 30 turns a minute, with a piston 6 cm² in area. Set the crank radius and turn it.
Use the board. This ticks when you get there.
For teachers
Students turn a crank and read the slider's position on a graph, find that the stroke is twice the crank radius whatever the rod's length, work out a pump's flow from stroke, piston area and turns a minute, and size a crank for a pump brief. About 40 minutes.
I can explain how a crank and slider turns rotation into back and forth.
I can work out a crank's stroke from its radius, and the radius from a stroke.
I can work out how much a crank-driven pump moves in a minute.
Before class
Do Mechanisms first if you can: this course assumes the idea of a brief and of a mechanism trading one thing for another.
A bicycle upside down makes a good start: the pedal is a crank, and a pencil taped to the pedal traces the circle. Sewing machines, toy steam engines and old pump jacks are good pictures.
Simplifications: rigid parts, no friction, and the crank turns slowly and steadily. Real pumps leak a little, so they move slightly less than the model says.
Curriculum hooks: Design and Technologies, engineering principles and systems (primary); Maths, measurement, volume and rates.
Running the lesson
Predict: draw the crank at 0° and 180° on the board, and mark where the pin is.
Try: after a longer rod gives the same stroke, ask what the rod does change.
Worked example: keep the units in centimetres for the volume line.
Vary: the engine question flips the mechanism; ask who has seen a car engine diagram.
The hard part (on purpose)
Students take the radius as the stroke, and mix up the rod and the crank. Keep pointing at the pin: where is it at each end of the stroke?
When students get stuck
A student takes the radius as the stroke. Ask: Where is the pin at each end of the stroke? Fix: From one side of the centre to the other: twice the radius.
A student changes the rod to change the stroke. Ask: Turn it with a longer rod. Did the stroke change? Fix: Only the crank radius sets the stroke.
A student mixes millimetres and centimetres in a volume. Ask: What units is the piston area in? Fix: Convert the stroke to cm before multiplying by cm².
Stretch and support
Stretch: A pump has two pistons on one crank, half a turn apart. How does that change the flow, and why might it be smoother?
Support: Give a drawing of the crank at four positions (0°, 90°, 180°, 270°) with the slider; students measure the slider's position at each.
Where it leads
Next: Cams and followers, where the shape of a wheel sets the path.
how far does it go?: The crank's radius is the number on show, so students expect it to be the stroke. Committing first makes the result stick: the pin goes from one side of the centre to the other, so the stroke is twice the radius.
Try: turn it: The trace settles the stroke; changing the rod and finding the same stroke separates the two lengths, which students tend to mix up.
Worked example: a pump: The worked example turns the crank into a useful number: stroke × piston area is the water per stroke, and turns a minute are strokes a minute. The faded example uses a 30 mm crank. Noah uses the radius as the stroke, planted after the method.
Vary: size the crank: Reasoning from the stroke back to the radius, then a question that reverses the mechanism: in an engine the slider (piston) drives the crank.
cranks: Stroke from radius and back, strokes a minute from turns a minute, and volume from area × stroke.
a pump to a brief: Students work back from the flow to the stroke and the radius, then test it on the board: the same brief-first reasoning as the other Mechanisms lessons.
Now you can
Explain how a crank and slider turns rotation into back and forth.
Work out a crank's stroke from its radius, and the radius from a stroke.
Work out how much a crank-driven pump moves in a minute.