Transcript SMI / FASE, May 22, 2012 Prototyping Dissection Puzzles with Layered Manufacturing Carlo H.

SMI / FASE, May 22, 2012
Prototyping Dissection Puzzles
with Layered Manufacturing
Carlo H. Séquin
EECS Computer Science Division
University of California, Berkeley
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”
Hamiltonian Dissections of Platonic Solids
Higher-Genus Dissection Parts
A more intriguing dissection of a Platonic solid
Intriguing Dissection of a Tetrahedron
Problem Statement

Design a two- or three-piece geometrical puzzle
in which a shape splits into all congruent parts
via a helical screw motion.
Execution

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
Simple Helicoidal Dissections
Based on linear, twisting sweeps
z
The basic “ramp”
Cross section
Tailored envelope
Simple Helicoidal Dissections
A sweep producing a tear-drop shape
z
3-part CAD model
Cross section Scaling function
First FDM Parts
Rapid Prototyping with FDM
A Look Into the FDM Machine
2 NOZZLES
A sculpture-build in progress; note grey support!
A Second Set of Parts
There are still problems:
The parts may not slide together completely!
Simple Helicoidal Dissections
A second approach – using a helical sweep path
2-part FDM model
Sweep path
Scaling function
Clean-up and Sanding the Parts
More Helicoidal Dissections
 Bio-Hazard
Symbol
Advanced 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 Dissection
• Cannot be modeled with a sweep
• Needs a CAD program with CSG operations
Helicoidal Dissection of Tetrahedron
(done with SLIDE by C.H. Séquin)
Helicoidal axis
Helicoidal Dissections of Rhombic
Dodecahedron (George Hart)
Too loose !
Generalization: Multi-Prong Dissections
Design a straight configuration and then twist the whole thing
Two 3-Prong Parts
. . . and they fit together!
Another Variant
Four prongs of different width unevenly spaced
. . . and they also fit together!
Multi-Prong, High-Genus Parts
PART II
Fabrication issues

A New Problem Statement:

Realize a given puzzle geometry
with a particular fabrication process.
Enlarging a Cubic Burr Puzzle

A neat puzzle …

If only it were larger !

Price increases with 3rd power of scale !!
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
Details for Cubelet Frame
Replicated, abutting geometry
A First Little Test Piece
Just two cubelets
One
Puzzle Part
All 4 Puzzle Parts
Burr Puzzle Assembly
Puzzle Part as a Sculpture
Conclusions
 Designing
and fabricating dissection puzzles
has 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 to
and are readily understandable by lay persons.
More . . .
SIGGRAPH 2011
More Inspiration
SIGGRAPH 2009
Interested in Burr Puzzles ?
Frederick Doering’s 3x3x3 Burr Puzzle
Burr Puzzle Theory and Software
Helicoidal Tiling of 3D Space
Matthias Goerner 2007
What is this ?
A Puzzle That Cannot Be Taken Apart
With 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.