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# Cams and followers

Linkages and cams · Changing motion

<!-- Speaker note: 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 (Predict and Try 10 min · Worked example 10 min · Vary 8 min · Practise and Make 12 min). Sources: TeachEngineering: K-12 engineering design challenges (benchmark; the briefs and wording are our own), https://www.teachengineering.org/ (checked 12 October 2026). -->

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## Today

**We are learning to** 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.

- 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.

<!-- Speaker note: 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. Teacher: Try: pause after the pear cam and ask what a flat line on the graph means. Teacher: Worked example: point out that steady rises are straight lines, so height is a fraction of the lift. -->

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## Why it matters

> A toy bird must pop up, wait, and drop. A motor just turns. What shape of wheel turns one into the other?

<!-- Speaker note: 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. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Predict

**A round cam has its axle 10 mm off centre. As it turns once, the follower moves up and down by…**

- 0 mm: it is round
- 30 mm
- 20 mm
- 10 mm

<!-- Speaker note: What happens: 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. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: draw a circle with an off-centre dot; ask where the edge is nearest and farthest from the dot. -->

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## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fengineering%2Flinkages%2Fcams%2Fstep-2&code=widget%3A+motion%0Amode%3A+cam%0Acam%3A+eccentric%0Alift%3A+20%0Achoose%3A+on%0Anumbers%3A+off%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/engineering/linkages/cams/?full=step-2#step-2)

<!-- Speaker note:  -->

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## What happened?

* 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.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## A heart cam's height

Now a snail cam, which rises for the whole turn.

$$\text{heart cam, lift } 20 \text{ mm}$$

1) $90 \div 180 = \tfrac{1}{2}$ — At 90°, the cam has turned half of its rising part.
2) $\tfrac{1}{2} \times 20 = 10 \text{ mm}$ — A steady rise is a straight line, so the height is the same fraction of the lift.
3) $\text{at } 270^\circ\text{: } (360 - 270) \div 180 \times 20 = 10 \text{ mm}$ — On the way down, count the degrees left until 360°.

<!-- Speaker note: Model this live on the board before revealing anything: write each line and say why, pausing to ask the class what comes next. Then click to reveal the lines and compare. Script. Start: write heart cam, lift 20 mm and say "It rises steadily for half a turn (180°), then falls steadily." Line 1: write 90 ÷ 180 = 1 ÷ 2 and say "At 90°, the cam has turned half of its rising part." Line 2: write 1 ÷ 2 × 20 = 10 mm and say "A steady rise is a straight line, so the height is the same fraction of the lift." Line 3: write at 270^: (360 - 270) ÷ 180 × 20 = 10 mm and say "On the way down, count the degrees left until 360°." -->

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## 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?**

* Answer: 10

<!-- Speaker note: 120 is a third of 360, and a third of 30 is 10 mm. -->

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## Shape and path

**Match each cam to its follower's path.**

| | |
|---|---|
| `Eccentric` | A. Slow steady rise, then a sudden drop |
| `Pear` | B. Steady rise, steady fall |
| `Snail` | C. Rests for half a turn, then up and down |
| `Heart` | D. Smooth wave up and down |

* Answer: Eccentric → D. Smooth wave up and down; Pear → C. Rests for half a turn, then up and down; Snail → A. Slow steady rise, then a sudden drop; Heart → B. Steady rise, steady fall

<!-- Speaker note: Where the edge is the same distance from the axle, the follower rests; where it gets farther away steadily, the follower rises steadily. -->

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## One way only

**Why must a snail cam always turn the same way?**

- Turned backwards, the follower would hit the step and jam
- It would not matter
- It would rise too quickly
- The motor can only turn one way

* Answer: Turned backwards, the follower would hit the step and jam

<!-- Speaker note: Forwards, the follower drops off the step. Backwards, it would have to climb a vertical step, so it jams. -->

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## Vary: choose the cam



- **A bird:** 
- **A hammer:** 
- **A pump:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/engineering/linkages/cams/?full=step-4#step-4)

<!-- Speaker note: What this step is for: Students choose a cam for each job from the motion it needs: the move from graph to design. For students who need more support: Print the four displacement graphs and four cam pictures to match before the board. For early finishers: Sketch the displacement graph for a cam that rests, rises, rests at the top, then falls. What shape is 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. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Eccentric

**An eccentric cam's axle is 8 mm off centre. What is the follower's lift, in mm?**

* Answer: 16

<!-- Speaker note: 2 × 8 = 16 mm. -->

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## Heart

**A heart cam with a 24 mm lift. How high is the follower at 45°, in mm?**

* Answer: 6

<!-- Speaker note: 45 ÷ 180 = 1/4, and 1/4 of 24 = 6 mm. -->

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## Dwell

**On a displacement graph, a flat line means…**

- The follower is falling
- The follower is at its highest
- The follower is resting (a dwell)
- The cam has stopped

* Answer: The follower is resting (a dwell)

<!-- Speaker note: 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. -->

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## Make: a cam for a toy



- **A fish:** 
- **Your own toy:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/engineering/linkages/cams/?full=step-6#step-6)

<!-- Speaker note: What this step is for: Students turn a written motion into a cam and a lift, then test it: the full move from brief to mechanism. Hints, in order: Steady rise and steady fall: which graph is made of straight lines? / The heart cam. Now set how far it must rise. -->

<!-- Speaker note: Teacher: invite students to sketch their own toy's graph before choosing the cam. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## 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.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: Next: Four-bar linkages, the third way of changing motion. Real examples: engine valves (camshaft), sewing machines, music boxes, automata, toy pull-alongs. -->