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two interwoven tensegrity three-fold prisms
(VRML Model)

This is a preparatory study for a bridge which uses tensegrity prisms to join it together. The structure is composed of two three-fold prisms which are Siamese twins. One prism is shown with yellow tendons and the other with red ones. The prisms have two struts in common. These are the two longest struts labeled A and C. (C doesn't appear long due to foreshortening in the view above.) Each prism also has a strut to itself. These are the two parallel shorter struts labeled B1 and B2.

I explored this technique of using prisms to join orthogonally-oriented struts in an earlier page, Tensegrity Prism as Joint. I did the computations for the twins as a single structure, but the result is identical to doing the computations for each prism separately.

As is visible, one of the side tendons of the red prism comes a little too close to a strut (and out of view the same thing happens with a yellow side tendon), but I'll live with that for now. I marvel at how parallel it is with the face of the strut. None of the members go through each other fortunately.

I don't consider this structure a true tensegrity since the tendons of one prism aren't continous with those of the other. But, like the cube I put together at the end of the Tensegrity Prism as Joint study, I think it's kind of interesting.

The bridge consists of two parallel rows of the twins and their reflection. Extended versions of the parallel struts (B1 and B2) are side rails for the bridge. C struts are joined across the width of the bridge to compose a supporting beam for the bed of the bridge. The A struts are poles and can hold lights or something, but they are there mostly to glue everything else together. The four A struts at the ends of the bridge are anchored in two foundations. At these points, single orthogonal prisms are used without their Siamese twin.

side view of bridge
Side View of Bridge (Click on Image for Large Version)

bird's eye view of bridge
Bird's Eye View of Bridge (Click on Image for Large Version)

For the bridge, I changed the A and C struts to 1-inch-diameter cylinders rather than 1-inch-square stock. This made it easier to attach the blue tendons. Some planks or something need to be added to the bed so it's easy to walk on, but I'm neglecting that detail. The Second Datasheet for Three-fold Tensegrity Prism With Orthogonal Struts contains the data for the prisms. Just remember that the relative strut member force should be doubled when two prisms share a strut. When two prisms share a strut, the holes are offset by 2.08293 inches in the direction of the strut and rotated by 90°.

The C struts are 48 inches long. The B struts are 14 inches, and the A struts are 14 + 2.08293 inches. I added the extra blue tendons since I have my doubts about the discontinuous tension. The blue tendons on the side are to help stability in cross winds. The ones on the bottom are to help support any live load crossing the bridge and the weight of the bridge itself. The short blue tendons are 18.91708 inches and the long ones are 23.08292 inches. How much they should be prestressed and how they should be anchored at the ends of the bridge I'm unsure of, and maybe they can be dispensed with.

The design for this structure was completed August 25, 2004. The design for the bridge was completed on August 27. Below are two views of a model I assembled of the twins on October 6. The experience of assembling the model tells me the two prisms aren't as independent as I thought from doing the calculations. I started the model by assembling one prism completely and then adding the second. The first end tendon of the second prism can be added without introducing the B2 strut. When I first put it in, it was taut but very far from its final tension. This tells me that adding the second prism changes the configuration of the struts of the first prism slightly.

The model is the mirror image of the diagram at the top of this page. The yellow prism was done with yellow braided nylon twine and the red prism was done with white twisted nylon twine.

photo of two interwoven tensegrity three-fold prisms
photo of two interwoven tensegrity three-fold prisms
Two Views of a Model of the Twins

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