3D Printing in the Classroom With Mathematica
Copyright © 2012 Board of Trustees, University of Illinois. All rights reserved. Last modified 2/10/12
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Today
• Hear about how and why scientists are
creating micro and nano-sized 3-D objects
• Learn about how this can be done using
polymerization initiated by light
• Use this technology and math functions to
have students create their own 3-D objects!
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Micromanufacturing
• Micromanufacturing refers to methods used
to create structures of micrometer sizes or
smaller.
One micrometer, or micron, is
one-millionth of a meter ( )
One nanometer is one-billionth of
a meter ( )
1.0x106m
1.0x109m
50 microns
Micro Gears Photonic Crystal Bioreactor
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3-Dimensional Printing
• Micro-sterolithograpry is a type of 3-D printing process
• Structures are made one layer at a time and built from the bottom-up.
• Work of Professor Nicholas Fang in nanoscale optical imaging
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3-Dimensional Printing
• So, we can’t
take a
$500,000
machine into
classroom –
what can
students do?
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3-Dimensional Printing
Cross Section Image
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How Can Light Create An Object?
The solution used in this process is made
from three different chemicals, each has a
unique purpose in producing a 3D object
1. IRGACURE – The initiator that reacts to Ultraviolet Light
2. SUDAN I –UV absorber that determines the thickness of each layer
3. HDDA or PEG – Provides “bulk” to make each layer
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Light-Activated Polymer
• UV light reacts
with and splits
the initiator to
create two free
radicals
• Radicals each
have single free
electron looking
for something to
bond to
+
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Light Activated Polymer
• Radical bonds
with monomer
• Now single free
electron at end of
chain
+
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Light Activated Polymer
• Repeats until two
ends with free
electrons interact
and bond
• These “chains”
solidify the
solution to form a
layer
+
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Preparation slides
• Polymer reacts with uv light
• Polymer does NOT react with red light, but
we can see red.
• Red is good color to use for preparing
apparatus
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Slicing the 3D Object
• 3D object are
constructed by
slices
• Overlapping
between layers is
generally required
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Taking it to the Math Classroom
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Getting Started
• Open the Mathematica application and follow
the instructions on the top of the screen
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Mathematica Application
• To create an object, you will begin by determining a
2-D region between two different functions
• The shaded region is rotated around the y-axis to
create a 3-D object
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Entering Your Own Functions
• Enter a “Lower Bound Eqn (Red)” (ex: x-5)
• Enter an “Upper Bound Eqn (Blue)” (ex: -x+10)
• Press “Enter” to graph. (2D region: 0≤x≤10 & 0≤y≤10)
• Drag “Slicer (Purple)” to view cross sections
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Rotating Around The Y-Axis
• Here are 3 different views of the 3-D object made
by the 2-D region on the left
Lowerbound: (x - 5) ^ 2
Upperbound: .1x + 5 View From Top
View From Side
View From Bottom
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Matching Game!
• Challenge! Try and match each 3-D object with its
corresponding 2-D region.
A
B
C
1
2
3
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Horizontal Cross Sections
• Drag the “Slicer (Purple)” to view the cross section
layer that will be printed at different heights.
“Slicer” at y = 2
“Slicer” at y = 5
“Slicer” at y = 8
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Matching Game!
• Challenge! Try and match each cross section with
the appropriate “slicer” height.
Lowerbound: Abs[x-4]
Upperbound: Sin[x]+6
A
1
B
2
C
3
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Typing Functions in Mathematica
Function Typed in Mathematica
3/4x+4
-3(x-2)^2+5
-2Abs[x-2]+5
Sin[2x-4]+3
10(.5)^(x-2)
.1x(x-2)^2(x-5)^2
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3 xy
5)2(3 2 xy
522 xy
3)42( xSiny
2)5(.10 xy
22 )5()2(1. xxxy
Learning to “Tame” Functions
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“Match Me!”
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Printing Your Object
• Once your functions are chosen, click “Generate
Slideshow” Button. This will create the slideshow
that contains each individual layer of your object.
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Examples of Objects
Upper Bound Function:
Lower Bound Function:
y .1(x 2)6
y .9(x 2)2 2
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Examples of Objects
Upper Bound Function:
Lower Bound Function:
y 0.11(x 6)(x 5)(x 4)(x 3)(x 2)(x 1)(x 1.5)(x 5.5) 4
y 0.05(x 3.5)6
Student Objects
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Student Objects
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Any Questions?
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End
The following slides are
only for additional
applications
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A Different Application!
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One Layer at a Time
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Mathematical Sculpture
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Mathematical Sculptures
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The Holy Grail
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Engagement Ring!
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Other 3-D Applications (Powerpoint)
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Other 3-D Applications (Powerpoint)
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