EML 2023 – Modeling, Parts Lecture 1.11 – Equation Driven Curve

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

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

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

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

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

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

EML 2023 Department of Mechanical and Aerospace Engineering rocker cam 8

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

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

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

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

EML 2023 Department of Mechanical and Aerospace Engineering Cam profile equation Now we’ll 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

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

EML 2023 Department of Mechanical and Aerospace Engineering Cam profile equation Let’s look at a numerical example: L 1 = 2” (when  = 0) L 2 = 3” corresponding to  = (120 °) A 15

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

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” α = 120 

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

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

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

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

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

EML 2023 Department of Mechanical and Aerospace Engineering 23