--- title: "Cams and followers" subtitle: "Linkages and cams · Changing motion · Lesson 2" --- # Cams and followers **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A toy bird must pop up, wait, and drop. A motor just turns. What shape of wheel turns one into the other? :::teacher-note **In one sentence:** 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. **Students should be able to say:** 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. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **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 My prediction, and why: {{lines-3}} ::: :::teacher-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. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: read the graph :::keep-together ### A heart cam's height 1. $\text{heart cam, lift } 20 \text{ mm}$ — It rises steadily for half a turn (180°), then falls steadily. 2. $90 \div 180 = \tfrac{1}{2}$ — At 90°, the cam has turned half of its rising part. 3. $\tfrac{1}{2} \times 20 = 10 \text{ mm}$ — A steady rise is a straight line, so the height is the same fraction of the lift. 4. $\text{at } 270^\circ\text{: } (360 - 270) \div 180 \times 20 = 10 \text{ mm}$ — On 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?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 10 120 is a third of 360, and a third of 30 is 10 mm. ::: :::keep-together ### Shape and path **Match each cam to its follower's path.** A. Slow steady rise, then a sudden drop B. Steady rise, steady fall C. Rests for half a turn, then up and down D. Smooth wave up and down {{columns 60% 40%}} {{rows 1}} | Part | Letter | |---|---| | `Eccentric` | | | `Pear` | | | `Snail` | | | `Heart` | | ::: :::teacher-note **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 Where the edge is the same distance from the axle, the follower rests; where it gets farther away steadily, the follower rises steadily. ::: :::keep-together ### 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 ::: :::teacher-note **Answer:** 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. ::: :::typical ## Vary: choose the cam **A bird.** **A hammer.** **A pump.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Cams :::keep-together ### Eccentric **An eccentric cam's axle is 8 mm off centre. What is the follower's lift, in mm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 16 2 × 8 = 16 mm. ::: :::keep-together ### Heart **A heart cam with a 24 mm lift. How high is the follower at 45°, in mm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6 45 ÷ 180 = 1/4, and 1/4 of 24 = 6 mm. ::: :::keep-together ### 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 ::: :::teacher-note **Answer:** 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. ::: ## Make: a cam for a toy **A fish.** **Your own toy.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A snail cam has a 36 mm lift. How high is the follower at 90°, and what happens at 360°?** {{lines-3}} ::: :::teacher-note **Answer:** 90 ÷ 360 × 36 = 9 mm; at 360° it drops suddenly back to 0. :::