TENSEGRITY |
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Series
Characteristics
One can treat a tensegrity a little bit like a sculpture. It is possible to make slight adjustments to a basic tensegrity, by changing chords and strut lengths. Compared with chiseling it has the advantage that one can return to the former level if the result didn't turn out as expected.
In the picture one can see slight deviations of a basic 3-strut tensegrity. In the series all chords have the same length, only the strut lengths vary. In the left tensegrity the three struts are all the same, but moving to the right, two struts get shorter and, for compensation, one strut gets longer.
Mathematics
The calculation of the length of the longest strut in each of the tensegrities above, might be a little bit more complex than expected. In the separate section MATHEMATICSon this website one can find an introduction of this topic.
It is just an introduction because tensegrity-mathematics is a study on its own, wich is illustrated by the abstract of the "Review of Form-Finding Methods for Tensegrity Structures" by A.G. Tibert and S. Pellegrino:
"Seven form-finding methods for tensegrity structures are reviewed and classified. The three kinematical methods include an analytical approach, a non-linear optimisation, and a pseudo-dynamic iteration. The four statical methods include an analytical method, the formulation of linear equations of equilibrium in terms of force densities, an energy minimisation, and a search for the equilibrium configurations of the struts of the structure connected by cables whose lengths are to be determined, using a reduced set of equilibrium equations.
It is concluded that the kinematical methods are best suited to obtaining only configuration details of structures that are already essentially known, the force density method is best suited to searching for new configurations, but affords no control over the lengths of the elements of the structure. The reduced coordinates method offers a greater control on elements lengths, but requires more extensive symbolic manipulations."
In the table below you can see the calculated strut lengths of the longest struts according to two tensegrity experts: Bob Burkhardt (who wrote an excellent book "A Practical Guide to Tensegrity Design") and Jan Marcus a Dutch tensegrity friend of mine. Both Burkhardt and Marcus used their own computer program to calculate the strut length. Of course these computer programs can be used to solve more complex tensegrity problems. In this case the tensegrity has only three struts, which makes the problem relatively easy and solvable with the aid of "Pythagoras" equations. A demonstration how the strut lengts can be calculated can be seen indissimilar. But the interesting point here is that as you can see their results differ a little expressing the difficulty in calculating these lengths. The six digits with which Burkhardt expresses his results says something about the accuracy of the man Burkhardt himself.
| long strut lengths according to | ||||
| short strut length | Marcus | Burkhardt | ||
| 300 | 300 | 300 | 299,999949 | |
| 280 | 280 | 335,5 | 335,313337 | |
| 260 | 260 | 363,4 | 363,236890 | |
| 240 | 240 | 386,4 | 385,261993 | |
| 220 | 220 | 401,6 | 401,548012 | |
In the series below, again five tensegrities: going to the reight, two struts shrink while the other two grow. All strings have the same length.
Much easier to calculate is the series below. The picture shows a basic 3-strut tensegrity that undergoes a linear transformation: The original tensegrity at the left is flattened bij an increasing factor and at the same time the tensegrity is stretched in the right direction by that same factor.
Some people might think that there is only a limited number of variations of tensegrities. At least that was what I thought once, till my experience told me different. Each time I built a configuration new variations turned up in my mind till I had so many variations in my head I didn't where to start.
The following pictures show variations on one theme. All tensegrities have an empty truncated terahedron heart surrounded by twelve struts, all equal.
"big nose, jug-ears and a long neck"
Normally I don't appreciate struts touching eachother, but in this case I think the result is quite nice.
