SMI / FASE, May 22, 2012SMI / FASE, May 22, 2012

Prototyping Prototyping Dissection Puzzles

with Layered Manufacturing

Carlo H. SCarlo H. Sééquinquin

EECS Computer Science DivisionEECS Computer Science DivisionUniversity of California, BerkeleyUniversity of California, Berkeley

Dissection PuzzlesDissection 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”

Hamiltonian Dissections of Platonic SolidsHamiltonian Dissections of Platonic Solids

Higher-Genus Dissection PartsHigher-Genus Dissection Parts

A more intriguing dissection of a Platonic solid

Intriguing Dissection of a TetrahedronIntriguing Dissection of a Tetrahedron

Problem StatementProblem Statement

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

ExecutionExecution

Simple Helicoidal DissectionsSimple Helicoidal Dissections

The basic “ramp” Cross section Tailored envelope

Based on linear, twisting sweeps

z

Simple Helicoidal DissectionsSimple Helicoidal Dissections

3-part CAD model Cross section Scaling function

A sweep producing a tear-drop shape

z

First FDM PartsFirst FDM Parts

Rapid Prototyping with FDMRapid Prototyping with FDM

A Look Into the FDM MachineA Look Into the FDM Machine

A sculpture-build in progress; note grey support!

2 NOZZLES

A Second Set of PartsA Second Set of PartsThere are still problems: The parts may not slide together completely!

Simple Helicoidal DissectionsSimple Helicoidal DissectionsA second approach – using a helical sweep path

2-part FDM model Sweep path Scaling function

Clean-up and Sanding the PartsClean-up and Sanding the Parts

More Helicoidal DissectionsMore Helicoidal Dissections

Bio-Hazard Symbol

Advanced Helicoidal DissectionsAdvanced Helicoidal Dissections

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

The Parts of the Cube DissectionThe Parts of the Cube Dissection

• Cannot be modeled with a sweep• Needs a CAD program with CSG operations

Helicoidal Dissection of TetrahedronHelicoidal Dissection of Tetrahedron

(done with SLIDE by C.H. S(done with SLIDE by C.H. Sééquin)quin)

Helicoidal axis

Helicoidal Dissections of Rhombic Helicoidal Dissections of Rhombic Dodecahedron Dodecahedron (George Hart)(George Hart)

Too loose !

Generalization: Multi-Prong DissectionsGeneralization: Multi-Prong Dissections

Design a straight configuration and then twist the whole thing

Two 3-Prong PartsTwo 3-Prong Parts

. . . and they fit together!. . . and they fit together!

Another VariantAnother Variant

Four prongs of different width unevenly spaced

. . . and they also fit together!. . . and they also fit together!

Multi-Prong, High-Genus PartsMulti-Prong, High-Genus Parts

PART IIPART II

Fabrication issuesFabrication issues

A New Problem Statement:

Realize a given puzzle geometry with a particular fabrication process.

Enlarging a Cubic Burr PuzzleEnlarging a Cubic Burr Puzzle

A neat puzzle …

If only it were larger !

Price increases with 3rd power of scale !!

Burr Puzzle: Unit ElementsBurr Puzzle: Unit Elements

Save building- and support-material:

Construct edge-frames of cubelets only

Shape all overhangs to minimize need of support

4545o

Details for Cubelet FrameDetails for Cubelet Frame

Replicated, abutting geometry

A First Little Test PieceA First Little Test Piece

Just two cubelets

One One Puzzle PartPuzzle Part

All 4 Puzzle PartsAll 4 Puzzle Parts

Burr Puzzle AssemblyBurr Puzzle Assembly

Puzzle Part as a SculpturePuzzle Part as a Sculpture

ConclusionsConclusions

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.

More . . .More . . .

SIGGRAPH 2011

More InspirationMore Inspiration

SIGGRAPH 2009

Interested in Burr Puzzles ?Interested in Burr Puzzles ?

Frederick DoeringFrederick Doering’’s 3x3x3 Burr Puzzles 3x3x3 Burr Puzzle

Burr Puzzle Theory and SoftwareBurr Puzzle Theory and Software

Helicoidal Tiling of 3D SpaceHelicoidal Tiling of 3D Space

Matthias Goerner 2007

What is this ?What is this ?

A Puzzle That Cannot Be Taken Apart A Puzzle That Cannot Be Taken Apart With Only Two HandsWith Only Two Hands

It needs a coordinated action of several (groups of) parts to be disassembled

SNOEYINK, J. and STOLFY, J. 1993. Objects that cannot be taken apart with two hands. SCG '93 San Diego, pp 247-256.