A cam is a shaped wheel; a follower rests on it and rises and falls as it turns. The cam's shape decides the follower's path, which a displacement graph shows. Students read graphs from four cams, match cams to jobs, and choose a cam for a toy.
A toy bird must pop up, wait, and drop. A motor just turns. What shape of wheel turns one into the other?
A cam is a wheel with a shaped edge, turned by an axle. A follower rests on the edge and slides up and down in a guide as the cam turns. A displacement graph shows the follower's height against how far the cam has turned.
Cams time things: engine valves, toys, sewing machines, music boxes.
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.
A round cam off centre
TryTry it on the board and compare the result with your prediction.
Try: four cams
Was your prediction right? The round cam's follower moved 20 mm: twice the offset.
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Turn the eccentric cam once and watch the graph.
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Choose the pear cam and turn it.
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Choose the snail cam and turn it.
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Choose the heart cam and turn it.
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InvestigateWork out why it happens, one step at a time.
Worked example: read the graph
Worked exampleBefore each step, say what you think comes next.
heart cam, lift 20 mmIt rises steadily for half a turn (180°), then falls steadily.
90÷180=21At 90°, the cam has turned half of its rising part.
21×20=10 mmA steady rise is a straight line, so the height is the same fraction of the lift.
at 270∘: (360−270)÷180×20=10 mmOn the way down, count the degrees left until 360°.
Now a snail cam, which rises for the whole turn.
A snail cam with a 30 mm lift rises steadily for a whole turn. How high is the follower after 120°, in mm?
Match each cam to its follower's path.
Eccentric
Pear
Snail
Heart
ModifyChange the problem on purpose and see what happens.
Vary: choose the cam
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A toy bird must rest for half a turn, then pop up and down. Choose the cam and turn it.
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A toy hammer must lift slowly and fall with a bang. Choose the cam and turn it.
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A model pump rod must move up and down smoothly, with no sudden changes, by 10 mm. Choose the cam, set the lift and turn it.
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PractiseA few on your own, to check you have it.
Cams
An eccentric cam's axle is 8 mm off centre. What is the follower's lift, in mm?
A heart cam with a 24 mm lift. How high is the follower at 45°, in mm?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
A cam for a toy
Need a hint?
Steady rise and steady fall: which graph is made of straight lines?
Another hint
The heart cam. Now set how far it must rise.
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A toy fish must rise 25 mm at a steady speed and sink at a steady speed, over and over. Choose the cam, set the lift and turn it.
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For teachers
Students turn four cams (eccentric, pear, snail, heart) and read each follower's displacement graph, find that an eccentric cam lifts by twice its offset, calculate heights on straight-line rises, choose cams for toys, and design one. About 40 minutes.
I can explain how a cam's shape decides its follower's path.
I can read a displacement graph: rise, fall and rest (dwell).
I can choose a cam for a motion I need.
Before class
Cardboard cams on a pencil axle with a straw follower make this concrete in ten minutes. Automata (cam toys) are a good Make extension in class.
Simplifications: the follower is a roller that always touches the cam (real followers need a spring or gravity to keep contact), the cam turns slowly, and the profiles are idealised (a real snail cam's drop is a short curve, not a cliff).
Curriculum hooks: Design and Technologies, engineering principles and systems (primary); Maths, reading graphs, proportion.
Running the lesson
Predict: draw a circle with an off-centre dot; ask where the edge is nearest and farthest from the dot.
Try: pause after the pear cam and ask what a flat line on the graph means.
Worked example: point out that steady rises are straight lines, so height is a fraction of the lift.
Make: invite students to sketch their own toy's graph before choosing the cam.
The hard part (on purpose)
Students read the graph as a picture of the cam. Keep asking: what does the follower do while the cam turns from here to here?
When students get stuck
A student says a round cam can't move the follower. Ask: Where is the axle? Is the edge always the same distance from it? Fix: Off centre, the edge's distance from the axle changes.
A student reads the graph as the cam's outline. Ask: What is on the across axis? Fix: Angle turned; the up axis is the follower's height.
A student picks the heart cam for a sudden drop. Ask: Is there a vertical line on the heart's graph? Fix: Only the snail cam drops suddenly.
Stretch and support
Stretch: Sketch the displacement graph for a cam that rests, rises, rests at the top, then falls. What shape is the cam?
Support: Print the four displacement graphs and four cam pictures to match before the board.
Where it leads
Next: Four-bar linkages, the third way of changing motion.
Real examples: engine valves (camshaft), sewing machines, music boxes, automata, toy pull-alongs.
a round cam off centre: An eccentric cam is a circle on an off-centre axle. Students expect the follower to rise by the offset; it rises by twice the offset, the same move as the crank's stroke.
Try: four cams: Turning each cam and reading its graph builds the link between shape and path before any rules: rest (dwell), steady rise, sudden drop.
Worked example: read the graph: A steady rise is a straight line, so height is a proportion of the angle; students read and calculate heights at an angle. A match ties each shape to its path, and a question names why a snail cam must turn one way.
Vary: choose the cam: Students choose a cam for each job from the motion it needs: the move from graph to design.
cams: Lift from an eccentric's offset, heights from straight-line rises, and which cam fits a description.
a cam for a toy: Students turn a written motion into a cam and a lift, then test it: the full move from brief to mechanism.
Now you can
Explain how a cam's shape decides its follower's path.
Read a displacement graph: rise, fall and rest (dwell).