Read here about a leading tensegrity researcher, author and scholar.
Robert Burkhardt is Principal of Tensegrity Solutions, Cambridge, Massachusets. He is a programmer and expert in space frame design and analysis. He is also a college lecturer, instructor, and graduate of U of C Irvine.
An early and energetic tensegrity explorer, he published books, online applications and detailed notes on all his explorations on his website. He also conducted extensive correspondence with Snelson and assisted in the deployment of some Snelson artworks.
Burkhardt's continues to update his site, and his publications online and offline are essential resources.
Approach To Building Tensegrity Structures
Burkhardt wrote to de Jong on his approach to building tensegrity structures
“My design procedure is iterative, but not incremental. I start out with a whole of some sort based a geometry I have in mind. I know enough geometry that I can rough things in pretty well. Then the minimization techniques take over to bring it into a feasible configuration. Or the design may just collapse or go off into some configuration that doesn't look interesting so I have to jiggle some parameters or rethink how I'm connecting things.
“Definitely my design procedure is not Tensegritoy, that is it doesn't involve physical prototyping though certainly experience from previous models I've built is important. When I build, I don't use highly elastic tendons. Braided nylon is about as far as I will go as far as elasticity. My computational procedures are flexible enough that I've never felt the need to use any physical prototyping technique. Certainly I've seen other people come up with some pretty interesting things using prototyping with elastic materials, it's just not my thing. And I think elastic physical prototyping definitely has its limitations. Snelson has an interesting approach using bead chains and slotted struts. That's the only inelastic physical prototyping technique I've seen.
“Once the design is complete and looks feasible, then I think on my materials and draft a realization according to the materials. At this point, I leave the computer for the most part, except I might refer to one of the viewers when I can't quite see how things fall from the 2D snapshot I'm working from, but a carefully chosen 2D snapshot with point labels is fairly adequate for the most part. Most of my realizations involve braided nylon for the tendons (nylon twine for larger structures) and wood of some sort for the struts.
“My method for attaching tendons to the struts varies. For my initial models I almost always used screw eyes screwed into the end of the wooden-dowel struts. Lately I've been favoring single nails driven into each end of the dowel. Splitting of the dowel when driving in the nail has been a problem with this approach, but it seems to allow for slimmer struts and more elegant looking models, at least by my aesthetic standards. For larger-scale outdoor structures I drill holes directly into the garden stakes I use, and I may try this approach at some point for smaller-scale indoor structures.
“My approach to assembly depends on the model. For domes I tend to take a modular approach and build some subassemblies first and then tie the subassemblies together. For prisms I start by assembling one end and work my way to the other end. Same way with masts. It can be very difficult to get the topologies right, and keep track of which tendon should be what length, and more frequently than I would like I find I've tied something wrong and I need to re-tie. Sometimes I use a jig to hold things temporarily, but things have to get pretty confusing for me to resort to such a thing. I try to tie the tendons I know will be tight (according to calculations) as early as possible when things are looser. I try to get all the struts tied in as early as possible.
“It's nice when some tension develops because that's when things start moving from being a shapeless mass to something definite. Of course then I have the problem with having to tie the tendons in a tensed state. That can be a plus and a minus. The minus is that I have to hold the nodes together somehow while I do the tieing. The plus is that many times a knot will stay tied if its always under tension, but may come unraveled in a loose state where it is constantly being jostled. So very often the knot I use depends on whether I'm tieing under tension or not.
“Going for the whole too early can result in a shapeless mess that's hard to deal with. I'm thinking in particular on a torus where I usually proceed as with a mast and it doesn't develop into a complete loop until the last.
“I have to constantly use my imagination to build a tensegrity in the early stages, since it can take awhile for it to start looking how I expect it to, and in the beginning it may diverge quite a bit from the final configuration.
“I don't consider construction my forté. I figure anyone could manage somehow given a design, and putting together accurate specifications was the main hurdle for me when I first started assembling my own tensegrity designs. I probably could have gone far with physical prototyping techniques if making models had been my only interest, but my main interest was engineering large-scale domes, and elastic modeling techniques seemed hopelessly cumbersome and inexact to me, so much so that I didn't even try them.
“Construction technique may be a hurdle in getting tensegrity into the mainstream. I don't think construction is too difficult ex post. With a major project, I think putting together a prototype would teach me a lot. Once the structure is understood, and I know what materials I will be using, a construction sequence can be formulated easily enough.
“For a major project, safety is a big consideration since if a tendon lets go, it, or the strut it releases, can pack a big whallop. That's one thing I like about my dome technology is that enough tendons are involved that one doesn't make a big difference. So flying struts are not likely to be a problem. But just a wire cable moving at a good clip can cause quite a bit of damage, so make sure the fasteners you are using can take what you are dishing out and then some. I once tried to quiz Snelson on this and basically what he had to say was ‘it depends on where you're standing.’ Yes. Don't stand in the wrong place.
“Early on I used metal wire for tendons, and attached them by putting the wire tendon through a screw eye and then twisting it to secure it in place. That seems faster than tying the nylon, but the nylon structures are so much more pleasant to have around. Wire can be very handy in assembling a nylon structure as a way to tie two nodes close together so I can get the nylon in place. Once the nylon is in place, the wire can be removed and reused to help tie the next tendon. However, with the split-level prism I just assembled I didn't need wire and just pressed the two nodes together by putting one on a hard surface where it wouldn't slip and pressing the other toward it while I tied the tendon.”
Publications, partial list
Burkhardt's book, A Practical Guide to Tensegrity Design, is available here: http://www.angelfire.com/ma4/bob_wb/tenseg.pdf
His online primer "A Technology for Designing Tensegrity Domes and Spheres" is here: http://bobwb.tripod.com/prospect/prospect.htm
He also published "The Application of Nonlinear Programming to the Design and Validation of Tensegrity Structures with Special Attention to Skew Prisms," Journal of the International Association for Shell and Spatial Structures, v. 47, no. 1 (no. 150, April 2006), pp. 3-15.
Burkhardt shares the coordinates of a large number of tensegrity structures. The coordinates are to be used with his proprietary software. The list of structures he has made available is:
- Aspension Canary
- Aspension Skylon II
- Aspension Tower II
- Concentric Five-fold Prisms
- Concentric Five-fold Prisms Revisited
- Eight-stage Tensegrity Arch
- Eight-stage Tensegrity Torus
- Eight-Stage X-Module Torus
- Eleven-Stage X-Module Arch
- Emmerich's Prism
- First Wheel Based on Gómez Jáuregui Module
- Four-fold Aspension Skylon
- Four-fold Reduced-Symmetry Prism
- Four-fold Tensegrity Obelisk
- Four-stage Tensegrity Torus
- Four-stage X-Module Bean Teepee
- Four-stage X-Module Trellis/Plant Hanger
- Infinite-Stage X-Module Column
- Merger of Three Six-Fold Tensegrity Prisms
- Modified Orthogonal Girdled Six-fold Prism
- Orthogonal Tensegrity Cube
- Perspective Prism
- Second Wheel Based on Gómez Jáuregui Module
- Six-stage Tensegrity Torus
- Skew Eight-Prism
- Skew Four-Prism
- Skew Prism Arch
- Skew Three-Prism
- Split-Level Prism with Equal-Length Struts
- Structure Based on Laminated Skew Prisms
- Ten-stage Tensegrity Torus
- Tensegrity Half Cuboctahedron
- Tensegrity Tetrahedron
- Tensegrity Tetrahedron (2nd version)
- Tensegrity Tetrahedron (Marcelo Pars)
- Tensegrity Tower
- Tensegrity Tulip
- Three-fold Fan Prism (Two-Strut Girdle)
- Three-fold Tensegrity Prism With Orthogonal Struts
- Three-fold Tensegrity Prism With Orthogonal Struts Revisited
- Triangularly Girdled Six-fold Prism
- Twelve-stage Tensegrity Torus
- Two-fold Prism Girdled by Four-fold Prism
- Two-Stage X-Module Column
- Variation on Emmerich's Prism
- Wishbone Tensegrity
- X-Module Tetrahedron
- X-Module Torus 1
- X-Module Torus 2
- X-Module Torus Revisited
- Zig-Zag Tensegrity Cube
Links and References
Main website, http://bobwb.tripod.com/
A Practical Guide To Tensegrity Construction, http://bobwb.tripod.com/tenseg/book/cover.html
Models Burkhardt built as a companion to Synergetics http://bobwb.tripod.com/synergetics/photos/index.html
Email: bobwb -at- juno.com
Postal Service mail to:
Bob Burkhardt, Tensegrity Solutions
Box 426164, Cambridge, MA 02142-0021, USA