EML 2023 – Modeling, Parts

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

2. Equation Driven Curve y= 2 x2 – 3 x + 2, x = 0.. 2

3. Parametric Equations x = sin(t) y = 2 cos(t) t = 0 .. 1.25

4. Parametric Equations x = sin(t) y = 2 cos(t) + t t = 0 .. 4

5. What is a cam?

6. cam and follower

7. disc cam with flat follower

8. rocker cam

9. 4 cycle engine

10. Our Problem L1 = 2” L2 = 3” α = 120

11. Our problem • Design a disc cam (for use with a flat follower) such that: • follower height is L1 when cam angle is 0° • follower height is L2 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.

12. Determine cam profile equation • Would like to have y = f(x). • We want a linear relationshipbetween L and . L = A  + B Determine A and B. • When  = 0, L = L1; when  = , L = L2 L1 = A (0) + B L2 = A () + B

13. Cam profile equation A • Now we’ll get the x and y coordof point A (an arbitrary point) xA = L cos yA = L sin substitute for L

14. Cam profile equation A • We would like to have y as a functionof x. • Instead we have y and x as a function of . This is called a parametric representation of x and y.

15. Cam profile equation A • Let’s look at a numerical example: L1 = 2” (when  = 0) L2 = 3” corresponding to  = (120°)

16. Cam profile equation A • Plot the x,y coordinates as  variesfrom 0 to

17. 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 L1 = 2” L2 = 3” α = 120

18. Cam Profile L1 = 2” L2 = 3” α = 120 equation driven curve (parametric)

19. complete the profile

20. complete the profile

21. complete the profile

22. profile working region of cam