--- title: "Four-bar linkages" subtitle: "Linkages and cams · Changing motion · Lesson 3" --- # Four-bar linkages **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A windscreen wiper swings back and forth, but its motor turns round and round. Four bars do it. Why can't they be any lengths you like? :::teacher-note **In one sentence:** Students turn a four-bar linkage, find that a longer crank jams, learn the rule for whether the crank can turn fully (shortest + longest ≤ the other two, with the crank shortest), design a wiper with a swing of at least 100°, and search for a linkage whose swing falls in a range. **Students should be able to say:** I can name the four bars of a four-bar linkage and what each one does. I can use the rule to say whether a crank can turn all the way round. I can change bar lengths to meet a swing criterion. **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 **The crank is 30 mm and turns all the way round. Make it 55 mm (the other bars stay the same). What happens?** ☐ It turns all the way, with the same swing ☐ It turns all the way, with a bigger swing ☐ It jams part of the way round ☐ The rocker turns all the way round too My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** It jams. With a 55 mm crank, at some angles the coupler and rocker together can't reach the crank's end, so the linkage locks. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: the rule :::keep-together ### Check 30, 80, 60, 70, then 55, 80, 60, 70 1. $\text{sorted: } 30, 60, 70, 80$ — List the four lengths, shortest to longest. 2. $30 + 80 = 110$ — Add the shortest and the longest. 3. $60 + 70 = 130$ — Add the other two. 4. $110 \le 130 \;\checkmark$ — No more than the other two: one bar can go all the way round. The crank is the shortest, so it is the crank. 5. $55 + 80 = 135 > 60 + 70 = 130 \;\times$ — With a 55 mm crank: more than the other two, so no bar can go all the way round. It jams. **Bars 40, 90, 60 and 70 mm (crank 40). Can the crank turn all the way?** ☐ Yes: 40 + 90 = 130 is no more than 60 + 70 = 130 ☐ No: 40 + 90 is more than 60 + 70 ☐ Yes: 40 + 60 = 100 is less than 90 + 70 ☐ No: the coupler is too long ::: :::teacher-note **Answer:** Yes: 40 + 90 = 130 is no more than 60 + 70 = 130 Shortest + longest = 40 + 90 = 130, the other two = 130. Not more, and the crank is the shortest, so it turns (only just). ::: :::keep-together ### Find the mistake **Ava thinks her crank turns all the way. Click the line where her working first goes wrong.** ``` 1 Ava's bars: crank 55, coupler 80, rocker 60, ground 70 (mm). 2 Shortest + second shortest = 55 + 60 = 115. 3 The other two = 80 + 70 = 150. 4 115 is less than 150, so the crank turns all the way round. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: add the shortest and the longest: 55 + 80 = 135. That is more than 60 + 70 = 130, so the crank jams. ::: :::typical ## Vary: a wiper **A wiper.** **Shortest frame.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## The rule :::keep-together ### Yes or no **Bars 20, 50, 40 and 45 mm (crank 20). Can the crank turn all the way?** ☐ Yes ☐ No ::: :::teacher-note **Answer:** Yes 20 + 50 = 70, no more than 40 + 45 = 85. ::: :::keep-together ### Again **Bars 35, 100, 50 and 70 mm (crank 35). Can the crank turn all the way?** ☐ Yes ☐ No ::: :::teacher-note **Answer:** No 35 + 100 = 135, more than 50 + 70 = 120: it jams. ::: :::keep-together ### A limit **Coupler 90, rocker 70 and ground 80 mm. What is the longest crank (shorter than all of them) that still turns all the way, in mm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 60 crank + 90 ≤ 70 + 80 = 150, so the crank can be up to 150 − 90 = 60 mm. ::: ## Make: a wiper to a range **Into range.** **Evaluate.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Bars 25, 75, 55 and 60 mm, with the 25 mm bar as the crank. Can the crank turn all the way? Show the sums.** {{lines-3}} ::: :::teacher-note **Answer:** 25 + 75 = 100, 55 + 60 = 115; 100 ≤ 115 and the crank is shortest, so yes. :::