EML 2023 – Modeling, Parts
Lecture 1.11 – Equation Driven Curve
Equation Driven Curve
y= 2 x2 – 3 x + 2, x = 0.. 2
EML 2023
Department of Mechanical and Aerospace Engineering
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Parametric Equations
x = sin(t)
y = 2 cos(t)
t = 0 .. 1.25
EML 2023
Department of Mechanical and Aerospace Engineering
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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?
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Department of Mechanical and Aerospace Engineering
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cam and follower
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Department of Mechanical and Aerospace Engineering
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disc cam with flat follower
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Department of Mechanical and Aerospace Engineering
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rocker cam
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Department of Mechanical and Aerospace Engineering
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4 cycle engine
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Department of Mechanical and Aerospace Engineering
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Our Problem
L1 = 2”
L2 = 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 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.
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 = L1 ; when  = , L = L2
L1 = A (0) + B
L2 = A () + B
B  L1
A
L 2  L1

EML 2023
Department of Mechanical and Aerospace Engineering
12
Cam profile equation
L = A  B
 L 2  L1 
L= 
  L1

  
A
• Now we’ll get the x and y coord
of point A (an arbitrary point)
xA = L cos
yA = L sin
 L 2  L1 

x = 
  L1  cos 

substitute for L
  

 L 2  L1 

y = 
  L1  sin

  

EML 2023
Department of Mechanical and Aerospace Engineering
13
Cam profile equation
 L 2  L1 

x = 
  L1  cos 

  

 L 2  L1 

y = 
  L1  sin

  

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
 L 2  L1 

x = 
  L1  cos 

  

 L 2  L1 

y = 
  L1  sin

  

A
• Let’s look at a numerical example:
L1 = 2” (when  = 0)
L2 = 3” corresponding to  = 2
 3
x = 
 2


   2 cos 


 3 

y = 
  2 sin

 2 

3
(120°)
EML 2023
Department of Mechanical and Aerospace Engineering
15
Cam profile equation
 3
x = 
 2


   2 cos 


 3 

y = 
  2 sin

 2 

A
• Plot the x,y coordinates as  varies
from 0 to
2
3
EML 2023
Department of Mechanical and Aerospace Engineering
16
Cam profile
L1 = 2”
L2 = 3”
α = 120
 3
x = 
 2


   2  cos 


 3
y = 
 2


   2  sin


• How do we get this exact curve into SolidWorks?
– 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
L1 = 2”
L2 = 3”
α = 120
equation driven curve (parametric)
 3
x = 
 2


   2  cos 


 3
y = 
 2


   2  sin


EML 2023
Department of Mechanical and Aerospace Engineering
18
complete the profile
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Department of Mechanical and Aerospace Engineering
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complete the profile
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Department of Mechanical and Aerospace Engineering
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complete the profile
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Department of Mechanical and Aerospace Engineering
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profile
working region of cam
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Department of Mechanical and Aerospace Engineering
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Department of Mechanical and Aerospace Engineering
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