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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