# TENSEGRITY

TENSEGRITIES

## Variations with four struts

Characteristics
Most of the tensegrities are enantiomorphic, which means that the tensegrity has a mirror image. In this case it is shown with two variations of a four strut tensegrity. One that turns "right" and one that turns "left'.
In fact there is no real difference between the two. Personally I noticed that I prefer to make right-handed tensegrities. The moment I try to make left-handed ones, my head get mixed up and a moment later also the strings and struts get mixed up.
In some cases this property is used explicitly in the tensegrity. One example is the Needle Tower of Kenneth Snelson.

Variations
Both the left and the right-handed tensegrity have square tops and bottoms. This is because all strings have the same length. But if we vary the lengths of the tendons (see the rectangle at the bottom of the structure below) and we also vary a little with the strut length (it's hard to see but the nearly-horizontal-struts are a little bit longer than the other two) we see that the rectangle shape at the bottom results in a diamond shape at the top (and visa versa). Also when we don't change the lengths of the struts we get a diamond and a rectangle, but in that case the two wouldn't be flat and horizontal.

An entirely different type of tensegrity is the one below, in which three struts, with only two tendons at each strut end, "circle" around the fourth strut.

The construction is quite stable but probably not very strong. In general one could say that strong tensegrities need at least three tendons at each strut end (in comparison with the three space coördinates X, Y and Z). This tensegrity looks quite simple, but if you let approxiametly 50 struts circle around one, you get a nice nearly round structure as can be seen in three fans.

the "left" and "right" version

The Needle Tower, made by Kenneth Snelson. Probably the most famous tensegrity ever built. In fact there are two Needle Towers. The first (1968) stands in the sculpure garden of the Hirshhorn museum in the United States, the second (1969) in (lucky me) Holland in the garden of the Kröller Müller museum. The tower is composed of twenty layers on top of eachother (each one made out of three bars). On each left-handed layer you find a right-handed one and vica versa.

Kenneth Snelson is, by far, the most famous tensegrity builder ever. He has spent a lifetime making these structures. A lot of his work can be seen on his website www.kennethsnelson.net. An absolute must for those interested in tensegrities.

Characteristics and definition
It depends on the definition one uses, but in general one states that struts of a tensegrity shouldn't touch eachother. In this case (right picture) they do so, which means that a lot of people would say that this is not a tensegrity. In any case, it is a structure that deforms itself. In this specific case the strings would form a perfect cube and all four struts would go exactly through the hart of that cube.
The problem of struts touching eachother can be overcome by using bended struts. Two examples are shown below. Although bended struts can have very aesthetic effects, it must be said that the tensegrity loses one of it's typical characteristics: In ideal tensegrities the strings are only submitted to tension forces and the struts are only submitted to compression forces. But in tensegrities with bows or bended struts it is unavoidable that these struts are submitted to tension forces as well. So tension and compression are not totally separated as in ideal tensegrities.

Practice
The problem of struts touching eachother is one of the practical challenges in tensegrity building. Even a experienced tensegrity builder like Adrian Rossiter has difficulties with this phenomena. Describing his own octahemioctahedron tensegrity he mentioned the following: "I wasn't able to get the struts of the four smaller triangles to float. I am not sure if that is due to symmetry, or whether they might miss if I had thinner struts." Adrian speaks of floating struts, like Kenneth Snelson likes to describe his tensegrities as "floating compression" structures. So, compression elements, not touching eachother but "floating on air". Adrian makes beautiful tensegrities with barbecue sticks. More of his tensegrities are shown in www.antiprism.com.

a tensegrity cube, unfortunately the struts touch eachother

The tensegrity below is a special one because it is in terms of Kenneth Snelson "exoskeletal", it has the compression parts at the outside. But as also mentioned by Snelson, regardless the bend struts, the compression forces still are inside the tension network. So, it's more or less a trick, but and here I cite Snelson once more "it's delightful and sophistry".

And finally one other aspect that comes around when bended struts are used: gravity. Normally a tensegrity is a construction that is not influenced by gravity, like, for instance, a conventional brick wall. But the structures on both pictures above do depend on gravity. If you lay these structures "on their side" or put them "up side down" the bended struts will change position.

A wall of struts..

Marcelo Pars