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.
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Students will be able to
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.
Timing
Predict and Try 10 min · Worked example 10 min · Vary 8 min · Practise and Make 12 min
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
What you will see
A question to ask
The fix
A student says a round cam can't move the follower.
Where is the axle? Is the edge always the same distance from it?
Off centre, the edge's distance from the axle changes.
A student reads the graph as the cam's outline.
What is on the across axis?
Angle turned; the up axis is the follower's height.
A student picks the heart cam for a sudden drop.
Is there a vertical line on the heart's graph?
Only the snail cam drops suddenly.
Answers to the checks
a round cam off centre: A round cam has its axle 10 mm off centre. As it turns once, the follower moves up and down by… 20 mm. The edge is 10 mm closer than average on one side and 10 mm farther on the other: twice the offset, like a crank's stroke.
Eccentric: Turn the eccentric cam once and watch the graph.
A smooth rise and fall: the graph is a wave.
Pear: Choose the pear cam and turn it.
The follower rests for half a turn (a dwell), then rises and falls quickly.
Snail: Choose the snail cam and turn it.
A slow, steady rise for a whole turn, then a sudden drop.
Heart: Choose the heart cam and turn it.
A steady rise for half a turn and a steady fall for the other half: straight lines on the graph.
A heart cam's height: A snail cam with a 30 mm lift rises steadily for a whole turn. How high is the follower after 120°, in mm? 10 120 is a third of 360, and a third of 30 is 10 mm.
Shape and path: Match each cam to its follower's path. Eccentric → C. Smooth wave up and down; Pear → B. Rests for half a turn, then up and down; Snail → D. Slow steady rise, then a sudden drop; Heart → A. Steady rise, steady fall Where the edge is the same distance from the axle, the follower rests; where it gets farther away steadily, the follower rises steadily.
One way only: Why must a snail cam always turn the same way? Turned backwards, the follower would hit the step and jam Forwards, the follower drops off the step. Backwards, it would have to climb a vertical step, so it jams.
A bird: A toy bird must rest for half a turn, then pop up and down. Choose the cam and turn it.
The pear cam: a dwell for half a turn, then a rise and fall.
A hammer: A toy hammer must lift slowly and fall with a bang. Choose the cam and turn it.
The snail cam: a slow rise and a sudden drop.
A pump: 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.
The eccentric cam with a 10 mm lift (its axle 5 mm off centre).
Eccentric: An eccentric cam's axle is 8 mm off centre. What is the follower's lift, in mm? 16 2 × 8 = 16 mm.
Heart: A heart cam with a 24 mm lift. How high is the follower at 45°, in mm? 6 45 ÷ 180 = 1/4, and 1/4 of 24 = 6 mm.
Dwell: On a displacement graph, a flat line means… The follower is resting (a dwell) A flat line: the follower's height doesn't change while the cam turns, because that part of the edge is a circle round the axle.
A fish: 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.
The heart cam with a 25 mm lift: straight-line rise and fall.
Solutions
One possible solution for each task. Other correct programs are fine.
Vary: choose the cam › A bird
Open task: any program that does what the step asks.
Vary: choose the cam › A hammer
Open task: any program that does what the step asks.
Vary: choose the cam › A pump
Open task: any program that does what the step asks.
a cam for a toy › A fish
Open task: any program that does what the step asks.
a cam for a toy › Your own toy
Open task: any program that does what the step asks.
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.
Exit ticket
A snail cam has a 36 mm lift. How high is the follower at 90°, and what happens at 360°?
90 ÷ 360 × 36 = 9 mm; at 360° it drops suddenly back to 0.
What each step is for
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.
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.