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Prototyping Dissection Puzzles with Layered Manufacturing

This project explores the design and fabrication of dissection puzzles using layered manufacturing techniques. It provides an educational component for the UCB "CS 285" graduate course in solid modeling and rapid prototyping, fostering 3-D spatial thinking and hands-on feedback on accuracy and tolerances. The puzzles can serve as fun artifacts to take home as souvenirs and act as motivators for students.

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Prototyping Dissection Puzzles with Layered Manufacturing

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  1. SMI / FASE, May 22, 2012 Carlo H. Séquin EECS Computer Science Division University of California, Berkeley Prototyping Dissection Puzzleswith Layered Manufacturing

  2. Dissection Puzzles A good educational component for UCB “CS 285”: Graduate course: Solid Modeling and Rapid Prototyping • They train 3-D spatial thinking • “Hands-on” feedback on accuracy & tolerances • Fun artifacts to take home as souvenirs •  Good “motivators”

  3. Hamiltonian Dissections of Platonic Solids

  4. Higher-Genus Dissection Parts A more intriguing dissection of a Platonic solid

  5. Intriguing Dissection of a Tetrahedron

  6. Problem Statement Execution • Design a two- or three-piece geometrical puzzle in which a shape splits into all congruent parts via a helical screw motion. • Teams of 3-4 students • Conceptual discussions in class • A first design + Individual feedback • Initial design to be fabricated on FDM machine • 2nd, “final” design, hopefully yielding a working puzzle

  7. Simple Helicoidal Dissections Based on linear, twisting sweeps z The basic “ramp” Cross section Tailored envelope

  8. Simple Helicoidal Dissections A sweep producing a tear-drop shape z 3-part CAD model Cross section Scaling function

  9. First FDM Parts

  10. Rapid Prototyping with FDM

  11. A Look Into the FDM Machine 2 NOZZLES A sculpture-build in progress; note grey support!

  12. A Second Set of Parts There are still problems: The parts may not slide together completely!

  13. Simple Helicoidal Dissections A second approach – using a helical sweep path 2-part FDM model Sweep path Scaling function

  14. Clean-up and Sanding the Parts

  15. More Helicoidal Dissections • Bio-Hazard Symbol

  16. Advanced Helicoidal Dissections • This design started with the outer shape: a cube • then partitioned it in to 3 parts with helicoidal cuts

  17. The Parts of the Cube Dissection • Cannot be modeled with a sweep • Needs a CAD program with CSG operations

  18. Helicoidal Dissection of Tetrahedron(done with SLIDE by C.H. Séquin) Helicoidal axis

  19. Helicoidal Dissections of Rhombic Dodecahedron (George Hart) Too loose !

  20. Generalization: Multi-Prong Dissections Design a straight configuration and then twist the whole thing

  21. Two 3-Prong Parts

  22. . . . and they fit together!

  23. Another Variant Four prongs of different width unevenly spaced

  24. . . . and they also fit together!

  25. Multi-Prong, High-Genus Parts

  26. PART IIFabrication issues • A New Problem Statement: • Realize a given puzzle geometry with a particular fabrication process.

  27. A neat puzzle … If only it were larger ! Price increases with 3rd power of scale !! Enlarging a Cubic Burr Puzzle

  28. Burr Puzzle: Unit Elements 45o 45 Save building- and support-material: • Construct edge-frames of cubelets only • Shape all overhangs to minimize need of support

  29. Details for Cubelet Frame Replicated, abutting geometry

  30. A First Little Test Piece Just two cubelets

  31. One Puzzle Part

  32. All 4 Puzzle Parts

  33. Burr Puzzle Assembly

  34. Puzzle Part as a Sculpture

  35. Conclusions • Designing and fabricating dissection puzzleshas been a highly valuable experience . . .for the students – as well as for me! • It is also a rewarding activity:Students can take home artifacts that appeal toand are readily understandable by lay persons.

  36. More . . . SIGGRAPH 2011

  37. More Inspiration SIGGRAPH 2009

  38. Interested in Burr Puzzles ?

  39. Frederick Doering’s 3x3x3 Burr Puzzle

  40. Burr Puzzle Theory and Software

  41. Helicoidal Tiling of 3D Space Matthias Goerner 2007

  42. What is this ?

  43. It needs a coordinated action of several (groups of) parts to be disassembled A Puzzle That Cannot Be Taken Apart With Only Two Hands SNOEYINK, J. and STOLFY, J. 1993. Objects that cannot be taken apart with two hands. SCG '93 San Diego, pp 247-256.

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