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.
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Students will be able to
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.
Timing
Predict and Try 8 min · Worked example 12 min · Vary 6 min · Practise and Make 14 min
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
What you will see
A question to ask
The fix
A student takes the radius as the stroke.
Where is the pin at each end of the stroke?
From one side of the centre to the other: twice the radius.
A student changes the rod to change the stroke.
Turn it with a longer rod. Did the stroke change?
Only the crank radius sets the stroke.
A student mixes millimetres and centimetres in a volume.
What units is the piston area in?
Convert the stroke to cm before multiplying by cm².
Answers to the checks
how far does it go?: The crank's pin is 20 mm from the centre, and the rod is 80 mm long. How far does the slider move from one end of its travel to the other? 40 mm: twice the radius. The pin goes from 20 mm on one side of the centre to 20 mm on the other, and the slider follows it.
One turn: Press Turn the crank once and watch the graph of the slider's position.
One turn of the crank is one stroke out and one back.
The stroke: Read the graph: how far does the slider move from one end to the other (in mm)? 40 40 mm: twice the 20 mm radius.
A longer rod: Make the rod longer, then turn the crank again. Does the stroke change?
No: still 40 mm. The rod's length moves where the slider runs, not how far.
A 25 mm crank, then a 30 mm crank: A 30 mm crank drives a piston 5 cm² in area. How much water does it push each stroke, in cm³? 30 Stroke 2 × 30 = 60 mm = 6 cm, so 5 × 6 = 30 cm³.
A minute: At 40 turns a minute, how much water a minute, in cm³? 1200 30 cm³ × 40 strokes = 1200 cm³ (1.2 litres) a minute.
Find the mistake: Noah thinks his pump gives 600 cm³ a minute. Click the line where his working first goes wrong. line 2 Line 2: the piston moves twice the crank's length, 6 cm, because the pin goes from one side of the centre to the other. So 30 cm³ a stroke and 1200 cm³ a minute.
A 60 mm stroke: The brief asks for a 60 mm stroke. Set the crank and turn it.
A 30 mm crank: 2 × 30 = 60 mm.
Backwards: In a car engine, which way does the motion go? The pistons push back and forth and turn the crank The same mechanism works both ways: a pump turns rotation into back and forth, an engine turns back and forth into rotation.
Stroke: A crank of radius 35 mm. What is the stroke, in mm? 70 2 × 35 = 70 mm.
Radius: A saw blade must move 80 mm each stroke. What crank radius does it need, in mm? 40 80 ÷ 2 = 40 mm.
Speed: A sewing machine's crank turns 900 times a minute. How many times does the needle go down each second? 15 900 strokes a minute ÷ 60 = 15 a second.
Flow: A pump with a 4 cm stroke and a 3 cm² piston turns 50 times a minute. How much water a minute, in cm³? 600 3 × 4 = 12 cm³ a stroke, × 50 = 600 cm³.
A garden pump: 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.
900 ÷ 30 = 30 cm³ a stroke; 30 ÷ 6 = 5 cm stroke; radius 25 mm.
Solutions
One possible solution for each task. Other correct programs are fine.
Vary: size the crank › A 60 mm stroke
Open task: any program that does what the step asks.
Vary: size the crank › Backwards
Open task: any program that does what the step asks.
a pump to a brief › A garden pump
Open task: any program that does what the step asks.
a pump to a brief › Evaluate
Open task: any program that does what the step asks.
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.
Exit ticket
A crank of radius 15 mm drives a piston 4 cm² in area at 50 turns a minute. What is the stroke, and how much water a minute?
Stroke 30 mm = 3 cm; 4 × 3 = 12 cm³ a stroke; 12 × 50 = 600 cm³ a minute.
What each step is for
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.
Where it leads
Next: Cams and followers, where the shape of a wheel sets the path.