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A Practical Guide to Tensegrity Design: Revision History

Back to A Practical Guide to Tensegrity Design: Cover

17Sep08 In Section 2.2, elaborate the footnote on Gough98. Change the XHTML version to indent the first line of paragraphs and footnotes.
16Sep08 In the last sentence of Section 3.1.6, change "connector" to "vector" (XHTML only — should have been done when the PDF was changed). In the Preface, note that the discussion of vector constraints in Section 7.3 is the best claim of this book to be called "practical."
15Sep08 In Section 3.1.6, add two more commas to the second sentence of the first paragraph. In Section 7.1, mention that the terminology is sometimes loose, and "force" is used to refer to the corresponding signed magnitude. Note that the trivial generalization to consider member stresses is neglected. In Section 7.2.2, be precise and note that fim is a signed magnitude rather than a force. In this section of the PDF version, change three places where "stress" is used to "force" (change should have been made when XHTML was changed).
14Feb08 On the Cover, note the recent review in the IASS Journal.
26Jan08 In Acknowledgements, remove Motro CV link which no longer works (XHTML only).
12Nov07 Cosmetic change which affects only the PDF version: tone down (shrink the font sizes and subsidiary formatting) the chapter and section headings by escaping the LaTeX default values.
29Jun07 In Acknowledgements, change "Val Gómez" to "Val Gómez Jáuregui". In References, mention his book.
05Jun07 In Section 5.1, correct a confusion and note that Snelson's approach the the t-tripod approach are different. In Appendix A, include Snelson's truss in the comparative examination and include an illustration of his truss. Update the list of Figures accordingly.
31Aug06 In Section 1.3, don't call Fuller's 1944 construction "aspension." Fuller73 doesn't call it that, it doesn't look like aspension really though perhaps it's an aspension precursor, and the aspension patent (#3,139,957) of July 7, 1964, postdates even Fuller's tensegrity patent by almost two years. Apparently the 1944 technology never got a name. Thanks to Phil Earnhardt for prompting me to look at this issue more closely.
22Aug06 In Foreword and Chapter 1, mark off the blocks of foreign language using div elements with appropriate lang attributes (HTML only).
21Aug06 In Section 2.2 and Section 7.2, fix validation problems, and add xml:lang attribute to html element for all XHTML files (XHTML only). In List of Figures, fix link to Figure 5.1 (HTML only). For Figures 2.2, 2.3, 2.4, 2.5, 2.6, 4.1, 5.1, 5.10, 6.11 and 6.12, develop special version of the graphic for web browsers instead of letting the browser do a lower-quality reduction from the high resolution versions. Size these to convenient proportions, and size the high resolution versions to match the proportions. Size the PDF version of these figures to yield 300 dpi resolution (one at 250 dpi) for the high-resolution versions. The figure changes impact both the HTML/XHTML and the PDF versions to hopefully give a better appearance to these figures for the web offering.
17Aug06 In Section 2.4, indicate from the start that the triangle radii are fixed by replacing r with rbar. Put explicit dot -- ⋅ -- multiplication signs in trigonometric formula for the PDF version.
15Aug06 In Foreword, fix quote marks around Bob (PDF only) and use "a real discovery" instead of "such a discovery". In Figures 5.6, 5.11 and 7.1, make the outer tendon layer red instead of blue to better differentiate it from the black tendons.
10Aug06 Add Foreword.
28Jul06 In Chapter 8, Appendix A, Appendix B and References, link in style sheet, misc fixes to get through W3C validator, use id attribute rather than name and don't use it in anchors by itself but put it somewhere else and get rid of the anchor (XHTML/MathML/HTML only). In the second file, correct "Georges David" to "David Georges". This last change affects the PDF too. On Cover, note that the XHTML/MathML/HTML pages now work (to a reasonable extent) with Amaya.
27Jul06 In Section 7.1, Section 7.2 and Section 7.3, link in style sheet, misc fixes to get through W3C validator, use id attribute rather than name and don't use it in anchors by itself but put it somewhere else and get rid of the anchor (XHTML/MathML/HTML only). Validator doesn't like text in blockquote element in the second file!?
26Jul06 In Section 5.3 (second try), Section 6.1, Section 6.2.1, Section 6.2.2, Section 6.2.3, Section 6.2.4, Section 6.2.5 and Section 6.2.6, link in style sheet, misc fixes to get through W3C validator, use id attribute rather than name and don't use it in anchors by itself but put it somewhere else and get rid of the anchor (XHTML/MathML/HTML only).
25Jul06 In Chapter 3, Section 4.1, Section 4.2, Section 4.3, Section 5.1, Section 5.2, Section 5.3 and Section 5.4, link in style sheet, misc fixes to get through W3C validator, use id attribute rather than name and don't use it in anchors by itself but put it somewhere else and get rid of the anchor (XHTML/MathML/HTML only).
24Jul06 In this file, Cover, Dedication, Preface, Acknowledgements, List of Figures, List of Tables, Table of Contents, Chapter 1, Section 2.1, Section 2.2, Section 2.3, Section 2.4 and Section 2.5, link in style sheet, misc fixes to get through W3C validator, use id attribute rather than name and don't use it in anchors by itself but put it somewhere else and get rid of the anchor (XHTML/MathML/HTML only).
21Jul06 In References, make it so clicking on external links pops up a new browser window; change link to Wong thesis to conform to MIT spec. (HTML version only). Change format of citation of Val's thesis to conform to existing format used for Wong thesis
20Jul06 In the Acknowledgements, mention Joe Clinton, Val Gómez, Mark Schenk and UCSD. In Section 1.3, in the long footnote on the X-Piece fallout, note that there are two 1949 photos of Fuller holding a mast, and indicate which one Snelson is referring to. Add Val's thesis, Masic et al. article and a cabledome article to References. In Section 1.4, refer to Motro and Hanaor specifically when this is appropriate instead of just as "civil engineers". Note cabledomes and UCSD work. Make some minor edits to Section 1.6. In Section 2.2, say "is obtained" in the footnote rather than "obtains". In Section 2.3, describe the relationship between Figures 2.6 and 2.7. Reorganize the introductory text so it is more coherent. In Section 3.2, tone down description of my partitioning method since I don't know that it yields the best partitioning. Amplify a bit the discussion of total vs. partial pivoting in the footnote. Add missing hyphen to two instances of "conjugate-direction". In caption for Figure 6.10, hypenate "Base-Point" and "Guy-Attachment-Point".
07Jul06 On the Cover, increase the fee for books I print from US$50 to US$70 and decrease my royalty from US$25 to US$15.
05Jul06 In Section 7.2.6, correct typo in formula for ojtilde (XHTML/MathML version only). Extensively revise the Cover to simplify it and make it more accurate, intelligible and useful.
17Mar06 In the link to the VRML models on the Cover, take advantage of the new tag marking the section containing those figures.
27Feb06 In References, link to copy of Fuller's 1961 "Tensegrity" article on R.W. Gray's site and Coplan's 1967 Artforum interview with Snelson on Snelson's site (XHTML version only).
24Feb06 Revisions stemming from conversations with Kenneth Snelson and further tensegrity history studies. In Section 1.3: note Snelson's interest in the Russian constructivists; be more specific about Fuller's 1944 construction (aspension); after the revelation of the X-Piece, until 1959, tensegrity was developed by Fuller and members of his circle which Snelson had left; translate the French word "autotendante" as "prestressed" rather than Emmerich's choice of "self-tensioning"; note Snelson's more specific artistic interest in exploring structure; refer people to first footnote in Section 2.2 for discussion of Snelson's doubts about the reconstruction of Ioganson's structure rather than duplicating the discussion in two places; delete reference to Snelson's work on the atom since it actually doesn't seem that relevant to the tensegrity history discussion; note significance of 1959 MOMA exhibit in that Snelson returned to the tensegrity field. In Section 2.2: note Snelson's skepticism with regard to Gough's claim is mostly related to the credibility of the reconstruction (he actually seems to sometimes think Ioganson did come up with a tensegrity prism or similar structure); give specific patent reference for Emmerich's claim on the prism; correct my incorrect inference that the appearance of the prism in Snelson's patent implied a claim on the invention of the prism -- he just cited it as prior art; use the date of Moelman's work to narrow down the probable time interval in which the prism was developed in the U.S.
21Dec05 Revisions related to recent conversations with Kenneth Snelson: In Chapter 1, footnote 8, substitute information supplied by Snelson for earlier speculations. In References, delete Müller71 reference (Müller, Grégoire, "Kenneth Snelson", Arts Magazine, Vol. 45, No. 7 (May, 1971), pp. 25-27) and relevant paragraph at the end of Section 7.2.2. The excerpt stated
... in Snelson's pieces the degree of tension in the tension elements is directly proportional to the amount of space they occupy -- a practical fact that he has encountered in the making of his sculptures, ...
which implies a minimization of sums of second powers strategy to design. Snelson says ("Re: Snelson sculpture photos", bit.listserv.geodesic news group, December 10, 2005, two messages) that this is a misinterpretation of what he had stated in his interview. The determinants of tendon stresses in his sculptures are many and subtle.
12Dec05 In the XHTML's References, update the link for the Wong thesis.
09Sep05 In Appendix A, fix link to Chapter 5.
08Aug05 On Cover, note existence of versions of some of the book illustrations in VRML Tensegrity Models.
29Jul05 In List of Figures, add omitted word "Sphere" for Figure 6.5 (HTML only). Direct people to Tripod instead of Channel1 for revision history (PDF only).
07Jul05 On Cover, change back link text from "Website Index" to "Tensegrity Solutions Home".
27Jun05 Remove the footnote at the end of Section 3.1.1 and the item in the References citing Roth81 (Roth, B. and W. Whiteley, "Tensegrity Frameworks", Transactions of the American Mathematical Society, Vol. 265, No. 2, 1981, pp. 419-446). Over the years, my recollection confused their axiomatic treatment with the nonlinear programming approach. There must be connections between the two. How do their findings on member forces correlate with mine?
05Apr05 Reformatted the PDF version to 8.5x11 instead of A4. Converted from LaTeX 2.09 to LaTeX2e. The main things that changed were the disappearance of the \footheight parameter and the new placement of picture-environment figures. pdflatex seemed better integrated with LaTeX2e, and all pdflatex-related paths could be removed from tensegenv. It was necessary to put a pdftex.map file in the local directory letting pdflatex know where to find the pfb font files. Took the last one-line paragraph out of the Acknowledgements so the PDF version can get the whole section on two pages. That paragraph read, "In the end, I have no one to blame for all this but myself." Still true, but you'll just have to read it here.
05Apr05 Add an interpretive outline of the book's contents to the Preface. This somewhat parallels Section 1.6, but their different characters persuaded me to leave them both. In the XHTML version of Chapter 3, use HTML '±' symbol as operator instead of constructing it from '+' and '-'.
02Feb05 Reduce price and include more details in offer.
29Jan05 First printing.
27Jan05 Fourth proof of PDF printed.
15Jan05 Minor edits throughout.
14Jan05 Minor edits and clarifications throughout.
13Jan05 Add Figure 6.10 and a line introducing it.
06Jan05 Third proof of PDF printed.
02Jan05 In XHTML version only, correct typo in proof of Section 7.2.6 (left an asterisk off of a μ). In both versions, use a complementary symbol for the second objective function. In Section 8.2.2 and Appendix B, put the reference to Lang in a footnote and mention the other labels for the Schwarz inequality. Minor edits to Section 8.2.4.
31Dec04 Move some parenthetical remarks in the text to footnotes. Complete Section 8.2.4.
30Dec04 Minor edits to Chapter 7. Rethink of logic and notation for proof in Section 7.2.6. Minor edits to Chapter 8, addition of text to Section 8.2.2 motivating that formula a little better and start Section 8.2.4 which will contain an example of angle computation.
29Dec04 Minor edits to Chapters 4, 5 and 6. There was a bad typo in Table 6.6 in which #33's final length was stated to be 1.0 instead of its exceptional value of 1.5.
25Dec04 Tweak the last set of revisions to Section 7.2.4, mainly changing references to "(in)dependent variables" to "(in)dependent coordinates".
23Dec04 Expand and revise Section 3.2. The matrix of partials is now referred to as Ψ instead of A. Expansion of this section should have been on my todo list, and I may expand it further to explicitly lay out the matrix algebra of how various derivatives, gradients, etc. are computed. Coordinate and correct the partials example in Section 4.2.3 with the above changes. Coordinate the discussion of the sample calculation in Section 7.2.4 with the above changes and rephrase it so vectors of derivatives are clearly distinguished from vectors of variables or constants. Miscellaneous rephrasings in the above three sections.
20Dec04 Miscellaneous rephrasings in the first three chapters. In Section 2.4, a formula had r'^2 in the denominator when it should have been just r'. The conclusions were still drawn correctly. Bars put over symbols for some of the constants. In Section 3.2, the subscripts of s in the quadratic formula of Step #3 all needed to be incremented by one.
17Dec04 Incorporate results of running spelling checker (ispell). Introduce explicit version number with date.
13Dec04 For Figures 5.6, 5.11 and 7.1, Lighten blue tendons so they show up better and slim down struts (secondary interlayer tendons were merging with them). Improve 600 dpi versions of Figures 7.2 and 7.3. Correct Figure 5.4. Put a bar over all the mu's and the exogenous force vectors to indicate they are fixed. Format math programming problem statement in Section 5.4 better. Correct spelling error in Section 7.2.3. In Section 7.2.5, correct subscripts in PDF version, note what mu is and add mu to the term quoted from the penalty function. In Section 7.3.2, reorder point descriptions and use "hub i" instead of "the ith hub". In Section 7.3.5, reorder and rephrase point descriptions and use "strut envelope i" instead of "the ith strut envelope". Eliminate needless u(ij) in descriptions. In Section 7.3.6, correct verb number ("represents" instead of "represent").
09Dec04 Second proof of PDF printed.
04Dec04 Flip Figures 7.2 and 7.3 horizontally to restore them the way they were. (It turns out if z is used as the "up" parameter in POV-Ray's camera spec, it uses right-handed coordinates without explicitly setting the "right" parameter.) Add a paragraph to Section 5.1 referencing Appendix A and noting the different truss strategies. Tweak formatting of Section 1.3 two-paragraph footnote.
03Dec04 Flip Figures 5.6, 5.11, 7.1, 7.2 and 7.3 horizontally to give them a right-handed coordinate system instead of POV-Ray's default left-handed system. Minor edit to Section 7.3.6. Modify and extend footnote on Snelson's X-Piece in Section 1.3. Minor edits to Appendix A to better give credit.
02Dec04 In Section 4.2, double all derivative and objective function values and forget that stuff about dividing the objective function by 2. Correct typos in the XHTML version where a header in the length tables said "Derivative" rather than "Length". Correct description of A matrix. In Section 4.3, double the objective function value, and note that it is theoretically a tensegrity in the initial configuration, though not assemblable the conventional way since the struts intersect. Move a few words around to try to make the presentation clearer. Minor punctuation change in Chapter 3.
01Dec04 Add Table 4.6. In Section 4.2.3, indicate the value of the objective function for the preliminary solution. Redo Figures 4.8 and 4.11 using right-handed coordinate system for POV-Ray (found out it defaults to left-handed). Figure 4.8 also needed to be redone with the final coordinate values instead of the preliminary ones and so that the omitted tendon location is indicated. In Section 2.4, add a footnote indicating that counter-clockwise obtains when the structure is being viewed from outside.
30Nov04 Minor edits and clarifications to Chapters 1, 2 and 3. Retitle Chapter 1.
29Nov04 On Cover, note printing fees and royalties. Add Skelton97 and Snelson81 to the references section in the PDF version where they were omitted. A few minor stylistic changes. Improve quality of ray-traced renderings for Figures 2.1, 2.8, 4.8, 4.11, 5.6, 5.11, 7.1, 7.2, 7.3, A.1 and A.2.
26Nov04 First proof of PDF printed.
24Nov04 On Cover, note that MathML sections work with Firefox as well.
08Oct04 In Section 1.1, qualify the plant example and note Donald Ingber's work. Add Ingber98 to the References.
07Oct04 In Appendix A, give Snelson credit for first examining the double-layer tensegrity truss of Figure A.2. In Sections 1.3 and 2.2, note Snelson's objection to the reconstruction in Gough98 and mention that the claim that Ioganson's sculpture was a tensegrity prism is controversial. In Section 1.3, note Snelson's description of floating compression as an alternative to the term tensegrity. These revisions stem from a personal communication with Snelson on October 6, 2004, which I initiated after reading Val Gómez Jáuregui's Master's thesis, "Tensegrity Structures and their Application to Architecture" (2004, Queen's College, Belfast, Northern Ireland). In Section 1.3, mention Lalvani96 and Wong99 as further resources on the Fuller-Snelson collaboration and controversy. Add Wong99 to the References.
14Sep04 In Chapter 1, substitute Emmerich's French patent number 1,377,291, "Structures Linéaires Autotendants", September 28, 1964, for his French patent number 1,238,308 issued July 4, 1960. The latter just covers space-frame joints and isn't tensegrity related although the joints could be used in a tensegrity space frame. The former covers tensegrity towers.
03Sep04 Strike the last item from the todo list in the Preface:
  • Improve the algorithm for analyzing a tensegrity's response to external forces. The present one doesn't seem to perform very well when Young's modulus gets large. (Omitted. Do it for the 3rd edition? My original idea was to derive a single step formula for the change in member forces for a perfectly rigid tensegrity and use that to initialize things for the Newton iterations. Initial explorations demonstrated to me that I need to study my engineering mechanics a little more than is feasible for the time constraints on the second edition. The present algorithm does OK.)
Rewrite the Preface. Minor rewrites for Chapter 6. Post-adjustment values for problem clearances noted. Augment the links to the Table of Contents for several sections where this had not yet been done (XML only). And that completes the revisions for the second edition!
23Aug04 Continue rewriting the Acknowledgements.
20Aug04 In Section 5.2, reference Cosmography rather than the Fuller letter, and discuss the polylateral concept a bit more. Add a few more links to the HTML version of the Acknowledgements and revise them a bit.
13Aug04 Strike another item from the todo list in the Preface:
  • Add an appendix showing how the octahedral symmetry region used in Section 5.3 and Chapter 6 was derived. (Done, except I put it in Section 5.3 instead of an appendix.)
Update figure numbers in Sections 6.2.1 and 5.4 (XML only).
12Aug04 Rewrite Sections 5.1, 5.2 and 5.3. Remove Figure A.2 to Figure 5.1. Adjust footnote and figure references in Section 5.4 (XML only). Minor revisions to the start of Section 4.2 to better connect it with Section 2.3.
05Aug04 In Section 7.3, redo formulae so signed magnitude of force at hub due to member always coincides with sign for member force, get rid of the inner/outer stuff in the notation and put a bar over ε everywhere. Strike another item from the todo list in the Preface:
  • Improve treatment of units in first exogenous loading example. Add illustration. (Done.)
04Aug04 Adjust column sectioning for tables in Section 4.2, Section 4.3, Section 5.4, Section 6.2.1, Section 6.2.2, Section 6.2.3, Section 6.2.4, Section 6.2.6, Section 7.2, Section 7.3 and Chapter 8 (XML only). Add tag for index links in Section 6.2.5 (XML only).
03Aug04 Adjust column sectioning and asterisk for tables in Section 5.3 (XML only). Make Chapter 6 introductory wording a little less prophetic. Add todo item to Preface. Rewrite Chapter 3 and make corresponding changes to Acknowledgements, Section 6.2.3, Section 7.2 and Section 7.3: determinacy and connector constraints become point and vector constraints respectively, and all w's and W's get written with overline.
29Jul04 At the end of Section 7.2.2, cite Müller71's observations. Put Müller71 in the References.
27Jul04 Conclude Section 7.2.6 by noting that multiple solutions are possible for a given weighted model.
26Jul04 Rewrite/correct the narrative of Section 8.2.3. Edit the wording at the beginning of Section 8.2 a bit. In Figure A.2, write out "T-Tripod" as "Tensegrity Tripod". Rephrase the necessary condition on a strut by strut basis in Section 7.3.5, and correct a typo and insert a missing sentence in the TeX version. In Section 7.2.3 use vector differences instead of writing out the column of coordinates. In Section 7.3.6, document briefly how many iterations were needed for a solution.
23Jul04 Complete Section 7.3.6. Strike another item from the todo list in the Preface:
  • Introduce "connection constraints" (rigid connections between members). These are necessary for modeling tensegrities where members are not connected exactly at their centerlines. (Done.)
But add another item.
22Jul04 Continue expansion and revision of Section 7.3.6.
21Jul04 Add Figure 7.1 to List of Figures and Section 7.3.6. Correct a misspelling and thank some tensegrity practitioners in the Acknowledgements. Update to note that some illustrations now have been generated using POV-Ray. Don't gripe about missing books at the BPL General Library. In Section 2.2.2, add a missing factor of 2r^2 to one of the equations. In Sections 2.2.2 and 2.2.3 use barred symbols to more explicitly differentiate between variables and fixed parameter values.
16Jul04 Describe meta-iterations in Section 7.3.6. Update List of Tables.
15Jul04 Add metric equivalents to Section 2.2 and label side and end tendons more frequently. In Section 2.2.3, use "u" instead of "a"as the label for the end-tendon length. Start Section 7.3.6. In Section 3.1.4, refer to numerical example with connector constraints in Section 7.3.6.
14Jul04 Add formulas for calculation of strut moment to Section 7.3.5. Change "external" to "exogenous" wherever it occurs in Section 7.3.
09Jul04 Finish Section 7.3.5. Mark start of Section 7.3.6.
02Jul04 Explicitly add vectors to the general statement of the mathematical programming problem in Chapter 3 and indicate how vectors are related to connector constraints. Since I'm starting to rigorously differentiate between vectors and points, in Section 7.3, don't label points as "(vector)". Continue development of Section 7.3.5.
23Jun04 Add Hibbeler98 to the references and cite it in Section 7.3.5. Spell out New Jersey in bibliographical entry for Chajes83.
22Jun04 Correct math typo in Section 7.2.3 (XML version only). Analyze the case of a determinacy constraint. In Sections 2.3, 4.3, 5.2, 7.2 and 7.3 be more specific instead of saying "next" or "previous" section. In Section 7.3.2, use q as a symbol instead of p to avoid confusion with point coordinates. Simplify notation for struts. Note that number of struts is half the number of hubs. Change symbol for external force. Reorder symbol declarations slightly. Just say "point" instead of "coordinates of point". In Section 7.3.3, note that the forces corresponding to the determinacy constraints also get initialized from the results of the endogenous analysis. Use more explicit references instead of "previous sections" and improve wording. Continue Section 7.3.5.
21Jun04 In Chapter 3 and Section 7.2, use lower-case n rather than upper-case N for counts everywhere. Use dot product instead of general format for determinacy constraints in Section 3.1.1. Rewrite Section 3.1.6. Rewrite Sections 7.2.3, 7.2.6 and 7.3 to reflect changes to Section 3.1.1. Rewrite Section 7.3 to segue better into Section 7.3.5 and fix some notational and sign problems.
18Jun04 Section 1.6 footnote: note that "node" is synonymous with "hub". Section 3.1.1: replace "Coordinate values" with list of hub points. Section 3.1.6: mention the coordinate constraint as a frequently-used determinacy constraint. Section 7.2.3: in quoting Newton, use the word "body" instead of "node"; elsewhere, refer to "hub" rather than "node". Section 7.3: refer to "hub" rather than "node". Start Section 7.3.5.
16Jun04 Section 2.2: loose -> lose. Section 7.2: to -> two. Add Section 2.2.4.
14Jun04 Minor revisions to Figure 2.1 (eyes were oriented slightly awry). Shrink Figures 5.4 and 5.9.
10Jun04 Try linking to U.S. Patent Office patent images for U.S. patent references in Chapter 1. Note other independent originators of the prism in Section 2.2. Back out of links to patents since they expire after a short time.
08Jun04 Elaborate the discussion of connector constraints in Section 3.1.4. Revise Chapter 1 to reflect my more recent research. In Section 6.2.3, mention Kenner76's "self-sufficiency" terminology as an alternative to Wang98's "self-supporting" term. Minor edits to Section 7.1. Strike another item from the todo list in the Preface:
  • Update the introductory chapter with special attention to Haresh Lalvani, ed., "Origins of Tensegrity: Views of Emmerich, Fuller and Snelson", International Journal of Space Structures, Vol. 11 (1996), Nos. 1 & 2, pp. 27-55. (Done.)
Mention Emmerich in Appendix A and reduce the sizes of Figures A.1 and A.3.
26May04 Revise graphic for Figure 2.1. Add note to Section 7.1 about usefulness of force analysis to developing an assembly strategy, and add qualification regarding detailed analysis of tensegrities. Other minor edits. Clarifying edits to Section 7.2. In Section 6.2.3 note that fixing the base points of the dome results in a structure that, strictly speaking, is not a tensegrity. Describe Bin-Bing Wang's definition of tensegrity in a footnote. In Chapter 1, note the presence of Wang's definition. Add Wang to References. Increment footnotes in Section 6.2.6. Strike a few items from the todo list in the Preface. Either I've done them, I'm going to leave them to the Synergetics Gallery, or I'm going to omit them as far as 2nd edition is concerned (I'm way behind):
  • Add a chapter or appendix on tensegrity prisms. This would generalize Hugh Kenner's analysis to handle the case where side tendons skip one or more struts instead of connecting adjacent struts. It would also compare the result on tendon forces for this special case to Ian Stern's analysis. (Leave to the Synergetics Gallery.)
  • Illustrate things a little more profusely and better. (Done, but I may do more.)
  • Add a chapter on designing very-high-frequency domes including asymptotic behavior of double-layer trusses (planar double-layer tensegrity arrays). (Omit, though results of this analysis were used in the illustrations for Appendix A.)
  • Add an appendix describing an ad hoc (for simplicity's sake in lieu of connection constraints) approach for deriving tendon lengths for the construction of dowel-and-fishing-line tensegrities. For the reader's convenience it would include cookbook plans for several popular tensegrities and other details on the construction methods for this type of tensegrity. (Leave to the Synergetics Gallery.)
  • Add an appendix on doing calculations for M. Schrogin's tensegrity arches which would cover Snelson's towers as a preliminary. (Omit.)
Add gaps between adjacent figures in Sections 4.2 and 4.3.
20May04 Add note about the ‡ marker in the tables to the text explaining the external loading example. Substitute correct "t-icosahedron" for "t-octahedron" in the first paragraph of Section 2.4. (TeX/PDF version was OK.) In Table 4.10, the second column should be labeled "Length" rather than "Derivative". (TeX/PDF version was OK.) Flip Figure 2.1 so its sense coincides with the rest of the examples. Fix link to Figure 4.2 in Section 5.4. Add Figures 4.8, 4.11, 5.4 and 5.9 with minor edits to accompanying text to reference them. Add labels to entries in Contents so chapters can back link to their section of the list.
12May04 Add Figure 2.1 and slightly revise text for Section 2.2 to refer to it. Substitute new graphics for Figure 2.8. Substitute new graphics for Figures A.1 and A.3 and eliminate text that interpreted shortcomings of the previous graphics.
03Mar04 Add and/or reposition back links to revision history.
19Feb04 In the Cover, note that, while Microsoft's Internet Explorer 6.0 and perhaps some earlier versions work with MathML, I haven't got the math pages here working for that browser yet.
20Jan04 In the Cover refer people to the Synergetics Gallery for more tensegrity examples.
14Jan04 Mention the Boston Public Library in the Acknowledgements.
06Jan04 Provide a more exact reference to Ioganson's prism in footnote 1 of Section 2.2.
31Dec03 Change label of the t-octahedron of Section 2.3 to t-icosahedron and don't state that it's the only one exhibiting mirror symmetry. Note discoverers of the simple tensegrities. Mention Pugh76 as a resource for model building information in Section 2.2. Minor edits.
09Dec03 In Section 2.2.2, make Figure 2.3 and the text consistent with Figure 2.2. Correct minimize equation for final mathematical form and another nearby typo in the XHTML version. Correct Table 2.2 in the XHTML version. Thanks to Zeke Cummings for prompting me to spot these problems. Put subject in email link.
11Jul03 In Chapter 3, give all constraints explicit constraint parameters. Rename iterator symbols and explicitly define ranges. In Section 7.2, synchronize notation with new notation in Chapter 3, add a second, more general, justification for the method of computing member forces.
02Jul03 Add connector constraints to the general model of Chapter 3. Systematize the naming of constants and indexes a little better to avoid so much alphabet soup.
24Jun03 Correct meta description tags for Chapters 5 and 6. Make sure all pages have meta description tags. Redo terminology in Chapter 7 (internal and external stress analysis become endogenous and exogenous force analysis). Correct typos. Fix minor inconsistencies in headings between the LaTeX and HTML versions.
20Jun03 Redo links on Cover.
27May03 Add more revision ideas to the Preface and revise its wording to indicate the plan for future releases. Reposition footnote 6 in Chapter 3 slightly. Characterize alternative to email as "Postal Service mail" on the Cover.
23Apr03 Added a line about prerequisites in the Preface. Adjusted the margins of the PDF version (per suggestion by Joe Moore) and made page numbers correspond to PDF pages.
15Apr03 More revisions to the Preface and Acknowledgements.
14Apr03 Make PDF file of the Guide available instead of using Postscript format. Thanks to Chris Fearnley for suggesting this and pdflatex for making it feasible. PDF file now includes Preface and Acknowledgements. Minor revisions to Preface, Acknowledgements and Table of Contents. Touch up T-Prism array graphic in Appendix A
04Apr03 Make Zip file of the Guide in Postscript format available. Refer to LaTeX instead of TeX.
02Apr03 Add sample calculation to Section 7.3. Add Preface and Acknowledgements. This completes the first internet release of the guide.
26Mar03 Add Section 7.3 (except for sample calculation). Systematize References a little better and add Vilnay90 and links where known.
25Mar03 Add Sections 6.2.5 and 6.2.6. Note μ penalty value everywhere and suggest better way of selecting clearance thresholds in Section 8.2.3.
18Mar03 Add Section 6.2.4. Tidy up or compact scanned graphics. Minor edits.
12Mar03 Revise Section 6.2.3 to use a more general technique. Plug more general numbers into Table 6.16.
11Mar03 Complete Section 6.2.3. Minor edits to Section 6.2.2.
10Mar03 Complete Section 6.2.2. Minor edits.
04Mar03 Complete Section 6.2.1. Minor edits.
03Mar03 Start Section 6.2. Minor edits.
28Feb03 Add Dedication and slots for Acknowledgements and Preface in the Table of Contents. Add more keywords, correct editing gaffe and capitalize Envelope Theorem in Section 7.2.
25Feb03 Add Section 7.2.
18Feb03 Add Chapter 8.
14Feb03 Add Section 6.1 and Section 7.1. Complete Table of Contents. Substitute chap7_1.html for chap7.xml links.
11Feb03 Fill in Section 5.4. Add omitted table to Section 5.3.
05Feb03 Add Section 5.3 and two figures for Section 5.4.
30Jan03 Add first two sections of Chapter 5.
29Jan03 Label triangles in Chapter 4 figures.
28Jan03 Minor revisions to figures and text in Chapters 1 to 4.
27Jan03 Fill out Appendix B.
19Jan03 First release in HTML/XHTML/MathML format (first four chapters and Appendix A). Originally published using LaTeX in 1994 in spiral-bound format.

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