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Upon my completion of my initial reading of Buckminster Fuller's two Synergetics books (Synergetics, New York: Macmillan Publishing Co., Inc., 1975, and Synergetics 2, New York: Macmillan Publishing Co., Inc., 1979), or perhaps in the middle of that reading, I conceived a great interest in tensegrity structures and the mathematics involved in designing them. Bucky's idea of building a dome big enough to cover an entire city had a certain fascination for me as well.
The best mathematical resource I had found was Hugh Kenner's geodesic math and how to use it (Berkeley: University of California Press, 1976). It had all the details for determining strut lengths for geodesic domes, but only information on simple tensegrity structures. Still it was head and shoulders above anything I had found or was to find at that time. (More recently some civil engineers have come up with a design technique which seems to work very well although I have yet to unravel it. See the Hanaor92 reference in my tensegrity prospectus.)
So, I began a correspondence with Buckminster Fuller's office to see if I could find out more. I didn't save a copy of the first letter I sent, but the reply should give you the flavor. The pamphlet they kindly sent in response, TENSEGRITY: Introductory Theory and Model Construction by Robert Grip (Philadelphia: Buckminster Fuller, 1978), pretty much contained what I'd found in Anthony Pugh's an introduction to tensegrity (Berkeley: University of California Press, 1976) which was interesting for the variety of models it outlined but didn't bother with math at all. The basic design technique for complex structures seemed to be to build it with rubber bands or something very elastic to start with and then use those average tendon lengths to build with less elastic tendons.
In retrospect, I think that was the extent of the design theory available at that point, but I thought there might be more so I decided to press further. This conviction stemmed from reading Bucky's U.S. Patent #3,063,521 (Tensile-Integrity Structures), especially Figure 7 which gave member length data to seven decimal places. I felt this data must have been derived using some mathematical method. From the drift of the next reply I assume I must have sent a couple more letters, an initial letter seeking more information and a follow-up when that wasn't answered.
I followed up the referral to Joe Clinton the above letter gave me. The text of that letter should give you the drift of what I must have been requesting from Bucky's office. I don't know that I ever received a response to my letter to Clinton, but I later found through the New Alchemy Quarterly (Winter 1981/1982 No. 7, p. 7) that he seemed to be mostly interested in geodesic/tensegrity hybrid techniques, and didn't seem much interested in the "pure" tensegrity I was interested in. The New Alchemy people curiously claimed that pure tensegrities had "one fatal flaw: cut one cable and the entire structure will implode with great force." I'd never experienced anything approaching that behavior in my explorations. Maybe this is a behavior of some tensegrities made with elastic tendons like rubber bands. The few I've experimented with behave very differently from tensegrities with tendons made with relatively inelastic material like steel cable or even nylon twine. For example, a rubber band tensegrity icosahedron allows two opposite struts to be pressed inward without the rest following suit. When the tendons are made of inelastic materials, all the struts move inward. Certainly I can't imagine someone building a structural tensegrity using elastic tendons.
I also hadn't received the personal response from Bucky the above reply from his office makes reference to and so must have sent yet another letter. The reply to that informed me of the extended reply Bucky was preparing in response to my query. So I waited for that for a month or so, and finally sent a cautious feeler to see how it was coming. As the reply informed me, Bucky was still working on it.
Bucky's personal reply finally did arrive and was well worth the wait. It didn't have the mathematical key I was looking for, but more served to orient my development of the appropriate mathematics and designs. See A Practical Guide to Tensegrity Design for what I finally came up with. The dates on the original letter ran from February 2 to March 18, 1982. On checking the Buckminster Fuller Archives website at Stanford University, I found the following reference to the letter in the description for "Series 2. Dymaxion Chronofile":
From this and the cut-and-paste look of the letter (with the pastes left out occasionally), the letter gives the impression of a sort of pattern integrity that somewhat dissolved into its constituents once a copy of it had been made and sent to me.
[ Box: 491 ]
[ Folder: 1 ]
Dymaxion Chronofile, Vol. 831 [3 of 7] 1983 Aug.
Chronofile. 1982 June 20 - 1983 Aug. 19. Contains excerpt from 1982 May 30 Burkhardt "Tensegrity" letter.
Much of the letter was material I'd already seen in the Synergetics books, and some of the passages and figures were copied directly out of those books. I've indicated the copied passages with HTML's pre-formatted type face. Many of the copied figures were different in detail, either in the graphic or the caption. I imagine the differences indicated Bucky's current thinking on that material, or perhaps he remolded the figure or its caption to the more specific requirements of my letter. I've given the figures numbers and indicated the analogous material in Synergetics if I knew of some.
In 2002, after I published the letter on the web, Yasushi Kajikawa pointed out to me that much of the material of the letter was published in Bucky's last book, Cosmography, which appeared in 1992 and had managed to totally slip under my radar. Having finally read Cosmography in Spring, 2004, I went back through the letter and made additional notes to indicate the connections between the letter and Cosmography I'd found. I'd be very surprised if I've found all the connections and would appreciate hearing about ones you see that I missed.
Since the letter is so long, I've broken it into several sections. Most of the time, three asterisks (***) indicated a section break in the letter. Once there was an obvious shift in the content of the letter.
I make the letter available here with the kind permission of Jaime Snyder and Allegra Fuller Snyder, the co-executors of the Estate of Buckminster Fuller, and more recently through the attention of Estate administrator John Ferry. The email from Jaime Snyder contains the details of the original conditions. All the material of the letter is Copyright 1999, Estate of Buckminster Fuller, all rights reserved. My current license is automatically renewed in perpetuity unless I hear otherwise from the Estate. For more information contact:
The Estate of Buckminster Fuller|
P.O. Box 3248
Santa Barbara, CA 93130
The content of both Synergetics and Synergetics 2 is available on the Internet at http://www.rwgrayprojects.com/synergetics/synergetics.html. Those renderings of our common illustrations are nicer than what you'll find here. I've inserted links to those illustrations so you can refer to them when mine are too nebulous for you. My scans of tabular material are not very good at all, so for those you'll definitely want to refer to the alternative source. I did do an extra-good job on Table 1 (Table 223.64 from Synergetics) since the alternative source doesn't seem to have anything for that. In general, I've tried to go to a little more trouble when scanning things which are unique to this offering.
I would appreciate hearing any comments or questions you have on this. I can be reached at firstname.lastname@example.org or Box 426164, Cambridge, MA 02142-0021.
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