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 --------------------------------------------------------------