A Practical Guide to Tensegrity Design
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My studies of tensegrity have provided me with an interesting tour of human endeavor. The topic seemed to fit the skills I had and developed them in ways I appreciated. I would summarize these skill areas as mathematics, graphics, computer programming and geometry.
At Los Angeles Harbor Community College, where I started out studying physics but switched to economics, my good-humored physics professor, William Colbert, provided me with computer access even after I had stopped taking physics courses. He helped me get started in computer programming with APL and tolerated my interest in BASIC. I stuck with economics for quite awhile, and fortunately my economics professors encouraged me to get a rigorous background in mathematics. In particular Sheen Kassouf at the University of California at Irvine encouraged me to take rigorous courses in linear algebra and statistics, and Peter Diamond at the Massachusetts Institute of Technology advised me to take a rigorous calculus course. Frank Cannonito and Howard G. Tucker provided my introduction to rigorous mathematical thinking at UCI. Rudiger Dornbusch in the economics department at MIT emphasized the importance of paying attention to units in doing mathematical analysis which has helped me through many a conundrum.
After I left graduate school, I indulged a more serious interest in Buckminster Fuller's work. Gradually that interest focused on tensegrity where it seemed to me there was a dearth of information on designing these structures. Fuller's engineering orientation appealed to me, so I looked into getting more expertise in that vein. After taking a couple night courses in machine shop at Minuteman Tech and investigating vocational-technical schools, I ended up at the Lowell Institute School. There I learned electronics technology mostly, but I took a course in welding too.
At that time the School was located at MIT and being directed by Bruce Wedlock. I was surprised to find myself on the MIT campus again, and took advantage of the continued access to MIT's excellent libraries. I dug up a lot of the books in the references (Appendix C) there. (As far as libraries are concerned, I also found the General, Research and Art Libraries at the Boston Public Library to be very helpful.) Eventually, I landed a job at the School, first as a teaching assistant in electronics technology and then as an instructor teaching computer programming. At one point, Dr. Wedlock kindly let me offer a course on tensegrity through the School though the course finally had to be canceled due to insufficient enrollment.
Teaching at the Lowell Institute School brought me into contact with UNIX and the X Window System. UNIX systems of one sort or another finally provided the development environment for my continuing pursuit of the craft of tensegrity computation. I started out doing computations on a TI-55 programmable pocket calculator. From there, I graduated to a Commodore 64 and its successors, the 128 and the Amiga. Finally I wound up using Linux with occasional ports to Windows as opportunities arose. The software migrated from the TI's machine language, to BASIC, to C and is now written in C++. In UNIX environments, the Free Software Foundation's C and C++ compiler and emacs editor have proven very useful.
LaTeX provided an avenue where I could easily communicate the mathematical constructs I found useful in working with tensegrity. More recently, I've started working with MathML. mfpic, which allows diagrams to be developed using LaTeX's Metafont, has been useful for developing a lot of the illustrations in the book. POV-Ray has been a great visualization tool and has also been used to generate many of the illustrations. HTML and the World Wide Web have been a great avenue for communicating my work more widely. And let's give a cheer for pdflatex which puts LaTeX with embedded PNG illustrations into Adobe's PDF format.
Thanks to Buckminster Fuller for the long letter he wrote to me on tensegrity and for bringing the technology to my attention through his books. The variety and insight of the work of Kenneth Snelson and David Georges Emmerich have been a great source of inspiration. Several times I've made "discoveries" only to discover that one of them found the same thing years ago, and I might have saved myself some time by studying their work more closely. Snelson associate Philip Stewart's inquiries about a structure provided the stimulus for developing a lot of the material on complex hubs and vector constraints. Maxim Schrogin's inquiry about maximal strut clearances in prisms prompted the orthogonal tensegrity prism example of Section 7.3.6, and his structures have been the source of much inspiration. Grappling with the structures of Ariel Hanaor and René Motro has also been very instructive.
I thank Chris Fearnley for suggesting I put LaTeX into PDF format and especially for inviting me to talk at the January 25-26, 2003, gathering of the Synergeticists of the Northeast Corridor whose participants patiently listened to my presentation of the first four chapters of this book. Also at that gathering, Joe Clinton gave a talk on tensegrity which pointed out to me the importance of David Emmerich as a tensegrity pioneer.
Val Gómez Jáuregui's comprehensive Master's thesis on tensegrity (Gómez04) reminded me I left out a mention of the important cabledome technology in my review of recent tensegrity history. Mark Schenk notified me of the path-breaking work on tensegrity computation theory going on at the University of California at San Diego. I apologize for any names of others who have made useful comments on this book that I have inadvertently omitted.
In the end, I have no one to blame for all this but myself.
August 23, 2004 and July 20, 2006
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