Transcript Pax Mundi (fabrication process)

CS285
Designing Viae Globi
(Roads on a Sphere)
Carlo H. Séquin
University of California, Berkeley
Inspired by
Brent Collins
Gower, Missouri
Brent Collins’
Pax Mundi
1997: wood, 30”diam.
2006: Commission from
H&R Block, Kansas City
to make a 70”diameter
version in bronze.
My task:
to define the master geometry.
CAD tools played important role.
How to Model Pax Mundi ...

Already addressed that question in 1998:

Pax Mundi could not be done with
Sculpture Generator I

Needed a more general program !
 Used

the Berkeley SLIDE environment.
First:
Needed to find the basic paradigm   
Sculptures by Naum Gabo
Pathway on a sphere:
Edge of surface is like seam of tennis- or base-ball;
 2-period Gabo curve.
2-period “Gabo Curve”
 Approximation
with quartic B-spline
with 8 control points per period,
but only 3 DOF are used (symmetry!).
4-period “Gabo Curve”
Same construction as for as for 2-period curve
Pax Mundi Revisited

Can be seen as:
Amplitude modulated,
4-period Gabo curve
SLIDE-GUI for “Pax Mundi” Shapes
Good combination of interactive 3D graphics
and parameterizable procedural constructs.
2-period Gabo sculpture
Tennis ball –
or baseball –
seam
used as
sweep curve.
Viae Globi Family
2
3
(Roads on a Sphere)
4
5
periods
Modularity of Gabo Curve Generator
 Sweep

Gabo Curves as B-splines
 Cross

Curve Generator:
Section Fine Tuner:
Paramererized shapes
 Sweep
/ Twist Controller
Sweep / Twist Control

How do we orient, move, morph ...
the cross section along the sweep path ?
Natural orientation
with Frenet frame
Torsion Minimization:
Azimuth: tangential / normal
900° of twist
added.
Extension: Free-form Curve on a Sphere
Spherical Spline Path Editor (Jane Yen)
Nice smooth interpolating curves through sparse data points
Many Different Viae Globi Models
Maloja
Extending the Paradigm: Aurora-M
 Simple
path on sphere,
 but
more play with the
swept cross section.
 This
 It
is a Moebius band.
is morphed from a
concave shape at the
bottom to a flat ribbon
at the top of the flower.
Target Geometry
Constraints:
• Bronze, 70” diameter
• Less than 1500 pounds
• Less than $50’000
• Maintain beauty, strength
• Minimize master geometry
Emulation

Use smoother quintic spline

Make 4 identical parts
(needs extra control point)

Add a few “warp” parameters
Emulation; Define Master Pattern
 Master
to make
a mold from.
Alignment tab

Use 4 copies.
Model of Master Part Made with FDM

4 pieces make the whole sculpture
Joe Valasek’s CNC Milling Machine
 Styrofoam
milling
machine
Design of Two-Part Master
 Alignment
tabs for easy assembly
Subdivide into Two Master Segments
Machined Master Pattern #2
(Cut) Master  Silicone Rubber
Mold
Mold  Several (4) Wax Copies
Spruing the Wax Parts for Casting
Ceramic Slurry Shell Around Wax
Part
Shell Ready
for Casting
Casting with Liquid Bronze
The Freed Bronze Cast
Assembling the Segments
The “Growing” Ribbon
The Single Support Point
Grinding the Welded Seams,
Polishing the Surface
Applying Patina
Ready for Shipping
The Move Around the Building (Jan.18)
Front Door
H&R Block Building
Steve Tightening the Bolts
Brent Polishing Our Baby