--- title: "Cranks and sliders" subtitle: "Linkages and cams · Changing motion · Lesson 1" --- # Cranks and sliders **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A motor turns round and round. A pump needs a piston that goes in and out. How do you get one from the other? :::teacher-note **In one sentence:** Students turn a crank and read the slider's position on a graph, find that the stroke is twice the crank radius whatever the rod's length, work out a pump's flow from stroke, piston area and turns a minute, and size a crank for a pump brief. **Students should be able to say:** I can explain how a crank and slider turns rotation into back and forth. I can work out a crank's stroke from its radius, and the radius from a stroke. I can work out how much a crank-driven pump moves in a minute. **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's pin is 20 mm from the centre, and the rod is 80 mm long. How far does the slider move from one end of its travel to the other?** ☐ 100 mm ☐ 40 mm ☐ 20 mm ☐ 80 mm My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 40 mm: twice the radius. The pin goes from 20 mm on one side of the centre to 20 mm on the other, and the slider follows it. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: a pump :::keep-together ### A 25 mm crank, then a 30 mm crank 1. $\text{stroke} = 2 \times 25 = 50 \text{ mm} = 5 \text{ cm}$ — The pin goes 25 mm one side of the centre and 25 mm the other. 2. $\text{per stroke} = 4 \times 5 = 20 \text{ cm}^3$ — A piston 4 cm² in area moving 5 cm sweeps 20 cm³ of water. 3. $60 \text{ turns a minute} = 60 \text{ strokes a minute}$ — One turn of the crank is one stroke. 4. $20 \times 60 = 1200 \text{ cm}^3 \text{ a minute}$ — That is 1.2 litres a minute. Now a 30 mm crank and a piston 5 cm² in area, at 40 turns a minute. Start with the water per stroke. **A 30 mm crank drives a piston 5 cm² in area. How much water does it push each stroke, in cm³?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 30 Stroke 2 × 30 = 60 mm = 6 cm, so 5 × 6 = 30 cm³. ::: :::keep-together ### A minute **At 40 turns a minute, how much water a minute, in cm³?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1200 30 cm³ × 40 strokes = 1200 cm³ (1.2 litres) a minute. ::: :::keep-together ### Find the mistake **Noah thinks his pump gives 600 cm³ a minute. Click the line where his working first goes wrong.** ``` 1 Noah's pump: a 30 mm crank and a piston 5 cm² in area. 2 The piston moves as far as the crank is long: 30 mm = 3 cm. 3 Water per stroke = 5 × 3 = 15 cm³. 4 At 40 turns a minute: 15 × 40 = 600 cm³ a minute. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: the piston moves twice the crank's length, 6 cm, because the pin goes from one side of the centre to the other. So 30 cm³ a stroke and 1200 cm³ a minute. ::: :::typical ## Vary: size the crank **A 60 mm stroke.** **Backwards.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Cranks :::keep-together ### Stroke **A crank of radius 35 mm. What is the stroke, in mm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 70 2 × 35 = 70 mm. ::: :::keep-together ### Radius **A saw blade must move 80 mm each stroke. What crank radius does it need, in mm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 40 80 ÷ 2 = 40 mm. ::: :::keep-together ### Speed **A sewing machine's crank turns 900 times a minute. How many times does the needle go down each second?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 15 900 strokes a minute ÷ 60 = 15 a second. ::: :::keep-together ### Flow **A pump with a 4 cm stroke and a 3 cm² piston turns 50 times a minute. How much water a minute, in cm³?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 600 3 × 4 = 12 cm³ a stroke, × 50 = 600 cm³. ::: ## Make: a pump to a brief **A garden pump.** **Evaluate.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A crank of radius 15 mm drives a piston 4 cm² in area at 50 turns a minute. What is the stroke, and how much water a minute?** {{lines-3}} ::: :::teacher-note **Answer:** Stroke 30 mm = 3 cm; 4 × 3 = 12 cm³ a stroke; 12 × 50 = 600 cm³ a minute. :::