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EML 2023 Modeling, Parts Lecture 1.11 Equation Driven Curve

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EML 2023 Department of Mechanical and Aerospace Engineering Equation Driven Curve 2 y= 2 x 2 3 x + 2, x = 0.. 2

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EML 2023 Department of Mechanical and Aerospace Engineering Parametric Equations 3 x = sin(t) y = 2 cos(t) t = 0.. 1.25

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EML 2023 Department of Mechanical and Aerospace Engineering Parametric Equations 4 x = sin(t) y = 2 cos(t) + t t = 0.. 4

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EML 2023 Department of Mechanical and Aerospace Engineering What is a cam? 5

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EML 2023 Department of Mechanical and Aerospace Engineering cam and follower 6

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EML 2023 Department of Mechanical and Aerospace Engineering disc cam with flat follower 7

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EML 2023 Department of Mechanical and Aerospace Engineering rocker cam 8

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EML 2023 Department of Mechanical and Aerospace Engineering 4 cycle engine 9

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EML 2023 Department of Mechanical and Aerospace Engineering Our Problem L 1 = 2 L 2 = 3 = 120 10

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EML 2023 Department of Mechanical and Aerospace Engineering Our problem Design a disc cam (for use with a flat follower) such that: follower height is L 1 when cam angle is 0 follower height is L 2 when cam angle is the relationship between the height, L, and the cam angle, , is linear We need to get the function of the cam profile and then draw a curve in SolidWorks that exactly models this profile. 11

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EML 2023 Department of Mechanical and Aerospace Engineering Determine cam profile equation Would like to have y = f(x). We want a linear relationship between L and . L = A + B Determine A and B. When = 0, L = L 1 ; when = , L = L 2 L 1 = A (0) + B L 2 = A ( ) + B 12

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EML 2023 Department of Mechanical and Aerospace Engineering Cam profile equation Now well get the x and y coord of point A (an arbitrary point) x A = L cos y A = L sin substitute for L A 13

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EML 2023 Department of Mechanical and Aerospace Engineering Cam profile equation We would like to have y as a function of x. Instead we have y and x as a function of . This is called a parametric representation of x and y. A 14

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EML 2023 Department of Mechanical and Aerospace Engineering Cam profile equation Lets look at a numerical example: L 1 = 2 (when = 0) L 2 = 3 corresponding to = (120 ) A 15

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EML 2023 Department of Mechanical and Aerospace Engineering Cam profile equation Plot the x,y coordinates as varies from 0 to A 16

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EML 2023 Department of Mechanical and Aerospace Engineering Cam profile How do we get this exact curve into SolidWorks? make a sketch with an equation driven curve (parametric) button is under the spline button 17 L 1 = 2 L 2 = 3 = 120

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EML 2023 Department of Mechanical and Aerospace Engineering Cam Profile equation driven curve (parametric) 18 L 1 = 2 L 2 = 3 = 120

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EML 2023 Department of Mechanical and Aerospace Engineering complete the profile 19

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EML 2023 Department of Mechanical and Aerospace Engineering complete the profile 20

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EML 2023 Department of Mechanical and Aerospace Engineering complete the profile 21

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EML 2023 Department of Mechanical and Aerospace Engineering profile working region of cam 22

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EML 2023 Department of Mechanical and Aerospace Engineering 23