Design Updates to Tensegrity Blocks Spencer Hunter, 2005 I am placing any unique features mentioned here into the public domain. 8/30/2005 New public-domain pictures of my self-deployable octas are up in the Tensegrity Blocks directory at: http://www.u.arizona.edu/~shunter/cads.html ...or one level up from here. Under "Self-deployable octahedra," here's a description of the models: On the left is the tendon-equator octa, with an elastic band running down the middle to effect self-deployment, consisting of eight hinged struts and four equatorial tendons. It was inspired by Tim Tyler's compression ring, the illustration of which is linked from the Tensegrity Blocks directory. In the middle is my first attempt at Le Ricolais' octahedron, consisting of six struts joined at the center by lashed paper-roll connectors, two inelastic-tendon depolarized triangles, and six elastic tensioning tendons to form a collapsible and self-deployable anti-prism in the spirit of Wang's cable-strut modules. After noticing how similar the strut configuration was to Piņero's pantograph (whose patent illustration is also linked from the Tensegrity Blocks directory), I rebuilt the octa as a pantegrity, shown on the right, consisting of three double-length struts joined at the center by an elastic band, along with the depolarized triangles of inelastic tendons and six elastic tensioning tendons. An effort was made to make the struts in the first two models and the tendons in all three models the same length, with the struts being shorter than the tendons. Under "Close-up, pantegrity octa," I show a closer view of the model on the right, where it can clearly be seen that the struts are double-length and are bound at the center. This is a kind of "poor man's pantograph," since in a real pantograph, the struts would actually be connected to each other. One might even argue that it's a tensegrity, since the structural integrity of the three struts by themselves rely on the tension of the elastic band that binds them together. It has occurred to me that, rather than being the "entirely new hybrid structure" as I had described it, the pantegrity has actually been with us for uncounted centuries. If one looks at Kenneth Snelson's original X-module at: http://www.kennethsnelson.net/new_structure/images/page14_03.jpg ...it can be seen as the tensegrity most of us know as the "diamond kite." If the tensioning kite skin is removed, the remaining struts have no integrity and fall apart. Almost anyone who has built and flown such a kite will quickly attest, though, that an essential component is missing--that the struts are usually lashed together at the center. This has two important effects: first, the connection stabilizes the central node during flight; and second, the connection effectively doubles the strength of each strut, since they mutually support each other at the center. Without the tensioning kite skin, the struts still remain together as they are lashed; i.e., they comprise a crude pantograph. 8/21/2005 While working on the anti-prism octa, I was struck by how terribly similar it was to the basic unit of Emilio Piņero's deployable pantographic dome (U.S. Pat. #3,185,164). In fact, if one thinks about it, the strut configuration of Fuller's tensegrity octa and Piņero's pantograph are identical, only the struts of Piņero's are connected by swivel bolts at the center--as they must be, since there are no tendons in his structure. By combining the very powerful now-public-domain features of both Fuller's and Piņero's developments, we are led to an entirely new revolutionary hybrid structure that is neither purely a pantograph nor a tensegrity: I am calling it a "pantegrity." Like the pantograph, the pantegrity does not rely on tendons for its structural integrity and has a well-defined state during all stages of its deployment. Once fully deployed, it behaves *exactly* like a tensegrity, with the struts bearing only axial compression forces (and they have the strength of half-struts, since they support each other at the center), and the tendons bearing only tensile forces. One could think of the tendons limiting the spread of the pantograph, and as such, they are essential in determining the load-bearing strength of the structure. Piņero himself was on to this when he recognized the benefit of the canopy over his dome limiting the spread, but he saw this only as a side feature and not an essential structural component. Since the mechanism of the pantegrity is basically Piņero's, it almost certainly works around Dr. Lalvani's bothersome current patent on center-node construction. That means the self-deployable pantegrity dome may be manufactured and distributed by anyone, anywhere, and at any time, without legal or financial obligation to anybody. 8/9/2005 A semi-retraction below: an anti-prism octet truss does show up in Fig. C.2 of Appendix C in Wang's book, but all of his di-pyramid trusses have simplex center poles that are perpendicular to the truss plane. A di-pyramid octet truss would have center poles at just over 35-degrees to the truss plane, and that is the omission that I found startling. 8/6/2005 One of the most intriguing structures I have ever seen was a cable-strut octet truss built by the great structural morphologist, Robert Le Ricolais. Each octahedron in his truss consists of six struts radiating from a central node and twelve cable tendons forming the edges of the octa. The struts are joined end-to-end with struts in other octahedra to form a cubic lattice. Using Wang's taxonomy in his book, _Free-Standing Tension Structures_[1], Le Ricolais' octahedron--and his truss built from many copies of it--may be thought of in two ways that make it self-deployable: as an anti-prism and as a di-pyramid. As an anti-prism, the octa is nearly identical to my triangular tensegrity block, only the top and bottom triangles of inelastic tendons are skewed (depolarized) relative to each other, and there are now six elastic tensioning tendons at an angle instead of three vertical tensioning tendons that enable it to be collapsed and stowed. Although heavier and more complex than my triangular block, it is possible that the structure may redeem itself when efficiently coupled with other octahedra in a truss. As a di-pyramid, Wang suggests that two of the struts are fused into one central pole that runs down the middle of the octa. The remaining four struts are attached to a runner on the pole that enables them to fold up. Using a powerful spring mechanism, it can self-deploy in a manner much like many of today's self-deployable umbrellas. Curiously, the deployable or self-deployable octet truss does *not* appear in Wang's book, which is even more remarkable considering that the solid-bar version is the most efficient truss configuration possible. References: 1. Wang Bin Bing, _Free-standing tension structures : from tensegrity systems to cable-strut systems_, London ; New York : Spon Press, 2004 ISBN 0415335957 I previously mentioned that a high-tensile rod can ride along with each elatistic tendon in my blocks to secure them in their deployed state using an attached cone and cylindrical trap. It may be better to replace the cone with a butterfly flange that locks into a wire framework once that framework is penetrated. This would make collapsing the structure easier: one would only have to pinch the flange together to release the rod. 7/23/2005 Inspired by Tim Tyler's compression rings, I posted to the newsgroup bit.listserv.geodesic that one of his rings could be almost half tendons and self-deployable. In his illustration linked from the Tensegrity Blocks directory, only the purple struts need to be struts, and the remaining green and white struts can be tendons; with the vertical tendons acting as tensioning agents. The basic unit is similar to my tensegrity block. It is an octahedron consisting of eight hinged struts and a square equator of tendons. A tensioning tendon running down the middle of the octahedron forces the structure into rigidity. Although I mention that the best approach for deploying these structures might be to develop a powered micro-winch for the pull wires, I have conceived a more low-tech technique. As with my tensegrity blocks, zigzag-strut tensegrity dome, and the above-mentioned octahedron, the tensioning tendons can be elastics that allow the structures to be collapsed and stowed. Riding along with, and perhaps lashed to, each elastic tendon is an inelastic high-tensile rod capable of briefly sustaining minor compressive loads during deployment. A disc screwed onto one end of each rod enables it to compress a hinge. A cone is screwed onto the other end, and during deployment, this cone will penetrate a cylindrical trap that prevents the rod from moving backwards. The cylindrical trap is connected to the opposite hinge and is able to compress it. The configuration of the trap can vary, but it acts in the manner similar to that of a Chinese finger trap. If the midsections of the traps are flexible, they can be individually compressed if need be to release the cones and enable the entire structure to be collapsed again. I presently envision the trap to be as simple as a tube with a slotted plastic end, and once the cone penetrates, the plastic triangles snap in behind the cone and trap it.