Notes on the design of the "Evolving Trefoil"
=============================================

On Dec. 20 the new generator program became fully functional.
I immediately started a maquette (yellow) with the specs of: "tref24_12-11b_360tw.gif"
Picture is at:  Tref22_FDMc.JPG
On Dec. 21 I used it for a tentative design based on feedback received from Brent on Dec. 7:
-- The outer diameter of the sculpture should fit into a sphere of 11 feet in diameter.
-- The flange width should be at least as thick as it was in the "Millennium Arch".

With the settings shown in "segm21-design.jpg", I obtain the following data, when scaled up to 11 feet:
-- flange thickness of 0.91"  [Millennium Arch was 0.69"]
-- arm diameter about 24"   [Millennium Arch was 21"]
-- volume = 10'000 cubic inches = 43 gallons   [Millennium Arch was 35 gallons]
The unique geometry designed with these values is in: "segm21-design.jpg"
The STL version of this part is depicted in: "segm21-side-STL.jpg"
A close-up of one end showing the cross section in mid-story is shown in: "segm21-Xsect-STL.jpg"
All these files are in:      
http://www.cs.berkeley.edu/~sequin/BC/Trefoil_Design

Based on a closer inspection of this latest design,
I am inclined to make some small changes to make the sculpture lighter, and also appear more lightweight.
With that goal, I decreased the arm thickness by 10%.
I also contemplated reducing the flangewidth by 10%, but I feel that this structure with only 3-way saddles needs a little more substance in the flanges -- so I left the setting at 1.2, and used a semicircular bulge: = "1.02".
Flange thickness is kept at 0.05.  The result is shown in: "Tref22.jpg".

Later I made some stereo pictures, where I increased the arm-scale again by 5% -- (to 0.19).
The design result is in:  Tref24st_r0.19.jpg.
A corresponding high-res STL file is in:  Tref24st_OneSixth.stl
A picture of this part is in:  Tref24st_r0.19_STL.jpg

I also experimented with making a single-sided sculpture (with arm-scale 0.18).
The result is in Tref27st_r0.18.jpg. ===> This also looks good!
This sculpture would have one of the joints between the 6 identical pieces of geometry going through the saddle; thus the master geometry would have to be split there, and the cast pieces would have to be joined there. The difficulty is that my generator currently cannot produce "half-stories" with the split in that place, but I think that Rob Arps could make the split when he cuts up the master geometry into suitable modules. We would also have to check whether a joining and glueing operation in this place would cause any problems.
A file that shows 1/3 of the total geometry with the split point indicated is in:  Tref27st_1-3STL.jpg

------------------------ CHS,  Dec. 22, 2010  ---------------------------------------------------------------

I took a final look at the design and also made three maquettes of the 1/6 geometry part.
For these maquettes, I scaled the nominal STL file by a factor of 3.3 and oriented the part to lay as flat as possible.
The compressed STL file from QuickSlice is in:  Tref24st_OneSixth.stl.gz.
Maquettes in the FDM machine: ET_24_a.JPG
and three of them assembled: ET_24_b.JPG, ET_24_c.JPG, ET_24_d.JPG
==> Everything seems to look good!

Today I ran the whole design once more in the sweep generator:  EvolTref_final.gif
and also produced an STL file of the whole design at somewhat lesser tessellation fineness:  EvolTref_final.stl
In QuickSlice I checked the nominal dimensions, and now suggest a   SCALE FACTOR of 50. 
==> This would give us a sculpture just slightly smaller than 12 feet in diameter.

Some specific data in STL units        (inches)  ==>  and the real geometry size when scaled up by a facor of 50:
Radius of overall sculpture:            1.41"    ==>   70.5"
Thickness of the trefoil knot:          1.39"    ==>   69.5"
"Worm" diameter in middle of story:     0.49"    ==>   24.5"
Lateral flange/ribbon width:            0.15"    ==>    7.5"
Thickness of the flanges:               0.02"    ==>    1.0"

------------------------ CHS,  Jan. 28, 2011  --------------------------------------------------------------