Exploring Additive Manufacturing: A Revolutionary Technology

Additive manufacturing, commonly known as 3D printing, has witnessed significant advancements since its inception in the 1980s. This technology allows for the creation of three-dimensional objects through various processes like extrusion, binding, and polymerization. With the rise of accessible 3D printers like MakerBot Replicator and services like Shapeways, individuals can now prototype and manufacture objects with ease. Spherical harmonics, a mathematical concept, are also explored in the context of Laplace's equation and Legendre polynomials. The potential of additive manufacturing and its applications in various industries make it a fascinating field to delve into.

• Additive manufacturing
• 3D printing
• Technology
• Prototyping
• Spherical harmonics

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1. Josh Grossman Abigail Taylor 13

2. 3D printing a.k.a. additive manufacturing computer file (STL) build up material 3D object Types: Extrusion Binding granular material Lamination Light polymerization CS AAPT2014

3. 3D printing Initiated in 1980 s Research industry DIY Exponential price drop Recently, rapid progress in capability materials, resolution, speed, Rapidly expanding market Used for prototyping and distributed manufacturing Compare: home/office publishing (2D printing) with resources of Internet CS AAPT2014

4. Printer #1: MakerBot Replicator Extrusion: fused deposition modeling (FDM) In-house; inexpensive Thanks to Alan Jamieson, SMCM Comp Science CS AAPT2014

5. Printer #2: Shapeways service Bound granular material: selective laser sintering (SLS) Other materials & methods available Upload file, make payment, receive objects in mail Better resolution than MakerBot Replicator Much higher marginal cost per item, but don t have to buy printer Marketplace uploading and purchasing designs SMCM MakerBot printer broke during project CS AAPT2014

6. CS AAPT 2014

7. Spherical Harmonics Angular solutions to Laplace s equation Specified by l, m l = 0, 1, 2, and m = -l, , l Associated Legendre polynomials Legendre polynomials CS AAPT2014

8. Spherical Harmonics Often initially confusing to students Geometric properties not immediately evident CS AAPT2014

9. Spherical Harmonics CS AAPT2014

10. Process Equations Export["00441.STL", RegionPlot3D[315*Abs[SphericalHarmonicY[0,0,Arc Cos[z/(x^2+y^2+z^2)^(1/2)],ArcTan[y/x]]^2]<(x^2+y^2 +z^2)^(1/2)<315*Abs[SphericalHarmonicY[0,0,ArcCos [z/(x^2+y^2+z^2)^(1/2)],ArcTan[y/x]]^2]+1.1,{x,- 45,45},{y,-45,45},{z,-45,45},PlotPoints->150]] Mathematica STL file Additional processing (optional) e.g. ReplicatorG for MakerBot Software converts for printing Finishing (optional) Print CS AAPT2014

11. MakerBot models ~$1 each Honeycomb for solid interiors Overhangs problematic print s or s, then glue Zero thickness at origin Individual plastic strands apparent sand and paint CS AAPT2014

12. Shapeways models $15-$45 each Add thickness CS AAPT2014

13. Uses Spherical harmonic manipulatives used in Quantum Mechanics class and Atomic Physics study group Illustrated geometric features Prompted student discussion CS AAPT2014

14. Whats next? Models of other 3D mathematical abstractions PvT phase surfaces for Thermodynamics classes, Real objects for experiments diagram from Hyperphysics Gears, wheels, moment of inertia test objects, What would you do? Fluid filters by user siderits on Thingiverse http://faculty.smcm.edu/jmgrossman/research/ed/3Dprinting.html By user ngoodger on Thingiverse CS AAPT2014