EML 2023 Modeling Parts Lecture 1 11 Equation

EML 2023 – Modeling, Parts Lecture 1. 11 – Equation Driven Curve

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

Parametric Equations x = sin(t) y = 2 cos(t) t = 0. . 1. 25 EML 2023 Department of Mechanical and Aerospace Engineering 3

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

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

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

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

rocker cam EML 2023 Department of Mechanical and Aerospace Engineering 8

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

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

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 Solid. Works that exactly models this profile. EML 2023 Department of Mechanical and Aerospace Engineering 11

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 EML 2023 Department of Mechanical and Aerospace Engineering 12

Cam profile equation A • 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 EML 2023 Department of Mechanical and Aerospace Engineering 13

Cam profile equation A • 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. EML 2023 Department of Mechanical and Aerospace Engineering 14

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

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

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

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

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

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

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

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

EML 2023 Department of Mechanical and Aerospace Engineering 23