On October 27, 2008, Marcelo Pars contacted me by email looking for help viewing my VRML models. His website reveals him to be quite an innovator in tensegrity. I am particularly fascinated by the structures labeled “de lege stoel” (the empty chair) and “drie waaiers” (three fans — see the photo above). His torus in the “de band” (the tire) section is also interesting and must be based on his two-layer approach shown in the lower photos in “op z'n kop erop” (upside down on top). This latter approach I think I must have seen in Emmerich's work as well, but I am not sure.
There are obviously interesting mathematical techniques, which I am not familiar with, behind his designs in “drie waaiers” and especially “de lege stoel.” In the latter, without such a technique it would be very difficult I think to get such a regular circular base for the structure. Hopefully, I will get a chance to experiment with his technologies myself. I must say I am impressed by the quality of interest in tensegrity shown in Holland.
By November 19, 2008, after some study of “three fans,” I saw a similarity to my studies of girdled prisms (see Concentric Five-fold Prisms and Concentric Five-fold Prisms Revisited). Marcelo's model could be viewed as a girdled prism (Three-fold in his case) where the girdle has many (skew) parallel strands. Just two parallel strands make an incredible and beautiful difference. I plan to call the genre “fan” prisms since Marcelo's label for his study seems very apt. My original concentric prisms represent the first step of a fan prism, but actually neither of the configurations I used seems apt: the best is a configuration where a sequence of side tendons connects one strut to an adjacent one (as in Concentric Five-fold Prisms) but the two prisms should have their struts slanting the same way.
So I took the second step, and was quite impressed by what a difference adding a parallel strand makes for the aesthetic appeal of the structure. The result appears below as Five-fold Fan Prism. It is available for inspection in all the Tensegrity Viewers as “5-Fold Fan Prism.” There the beauty of Marcelo's concept is much easier to appreciate. My realization is designed so all the strut lengths are equal and all the tendon lengths are equal. I think Marcelo must have followed these constraints in his model as well. My design was completed November 20, 2008.
I finally decided to build a three-fold fan prism with a two-strut girdle, for which I have provided a datasheet. This design was completed March 12, 2009. I assembled it on April 21, 2009. It was a pleasure to put it together: it was very easy to assemble and fascinating to watch as it took form. Here is a picture:
|Photo courtesy of Leslie Burkhardt|
|Three-fold Fan Prism|
And perhaps some day I will understand “de lege stoel” as well! In the meantime, Marcelo has allowed me to display it in all the Tensegrity Viewers. Look for “The Empty Chair (Pars).”