28sep2005 - Second Assignment

About one year ago, I met a couple of mathematicians at Cornell University, who had explored hyperbolic surfaces, and had some good fun with it. I had not previously known that there are a number of people all over the world who took up the practice of crocheting hyperbolic surfaces (most notably the lorenz manifold).

Anyway, when presented with this issue of press fit, it occurred to me that a significant factor in designing a system that relies on press fit connections is the utilization of the elasticity of the material (to the extent that plastic deformation can be avoided). Furthermore, card stock materials have good planar rigidity, but start to show this "springy bendiness," parallel to the planar surface, and perpendicular to the cut, when cut to a high enough degree of slenderness. So, I've decided to try making a buckminster-style stick and node set, where rigidity is provided by the tension produced when assembled as hyperbolic surfaces. To do so, one basically connects polygons in such a way that the sum of adjoining polygons at any single vertex possess corner angles that sum to more or less than 360 degrees.

The result is fabulous! (picture below) However, my biggest concern is that the cardboard material will creep, or take on its newly deformed shape, and cease to provide the tension required to hold the joints well. I have determined that it does stay stable for a few hours, at least. We will see if it lasts for the next few days. I would also like to try smaller connector lengths, as the first iteration seems a bit large. Also, I'm thinking of printing words on the elements, like refrigerator poetry, so that one can create little poetry sculptures. I thought that maybe I could restrict the words to palindromes that were composed of symmetrical letters, so that they could be written in but it seems that there are too few of those to make a meaningful poetry set.

I like that we are using cardboard, very much. The resources that are expended when using plastics is indeed relatively tremendous - and, there is an aesthetic to cut corrugated cardboard that is really beautiful.

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30sep2005 - Second Assignment

So, 'kenny's invention kit' does permanently deform, but not enough to make constructions lose enough strength that it is less fun to play with. After a day, it does seem easier to take apart - after a few weeks, it may have deformed enough to be really fragile. But, part of the beauty of it is in its inexpensiveness and the desire to keep playing with it; and if someone wants to keep an item, it is an option to spray coat it with something that will help to bind the joints.

The version with smaller connector pieces works wonderfully well, but loses the gossamer appearance that the longer version has. It is much more practical to work with, anyway.

The poetry version, however, is... sadly... quite contrived. That is the best word that I can find to describe it. I think that there is a lesson here - I tried to modify ('improve') too many aspects of the system at once. The connector pieces are cut with the grain perpendicular to the grain of the previous versions, the connectors are of varying length (to fit the words), and I introduced heptagonal vertices into the system. Some of these aspects simply didn't prove to be functional, such as the grain, which caused problems with fitting the connections. Other changes conflicted with each other, interestingly, and unfortunately to the detriment of the structural function and elegance of the system. For example, the varying connector lengths would probably simply introduce a little chaos into the previous system with triangular connectors, but a system with both heptagonal and triangular connectors requires a level of closure that does not allow connector length discrepancies within the proportional range that I created for the poetry set. Still, it was fun to make, and looks cool (from farther away).

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02oct2005 - kik

My version of GIK consists of two parts - sticks and nodes. The sticks simply hook into the nodes, and this connection gains rigidity through slight twisting of the sticks, as a result of assembly as a hyperbolic surface. An example of the way that this twisting is produced, is by creating a heptagon using nodes that contain only 120 degree connections. The sticks can be of varying length, and the nodes can have varying attachment arrangments. The design of the sticks does depend on the grain of cardboard for proper flexibility and constructibility, and the connector ends were refined with a bit of trial and error. They are longer than the depth of the cardboard to ensure that all edges will contact with the nodes properly, and they are of differing lengths for ease of construction (the long end can be inserted first).

As it turns out, the connector pieces can also be assembled into little maddening puzzles of interlocking pieces, similar to those made from twisted nails.

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