TENSEGRITY JITTERBUG
The evolution of an idea over time on the mailing list:
This variation of Fuller's jitterbug transformation was invented by Gerald de Jong and his explanation follows the pointers.
a_tnsjt.mov-VE(vector equilibrium) formed from 8
tensejit cells (Quicktime Movie 197k)
This was my first attempt at
animating Gerald's idea. The compression struts rotate 180 degrees then
reverse. Later versions have struts cycling through 360 degrees.
tnsjitve.mov-another version of 8cell (VE) matrix (Quicktime Movie 225k)
tnsjtr.mov-compression struts rotate 360 degrees
(Quicktime Movie 473k)
In this version, all struts rotate clockwise (as
viewed from inside tensejit cells). Because of this, struts in planes of
adjacent cells are rotating in opposite directions causing them to "scissor"
in and out. Gerald wasn't happy with this, so we decided to have left-handed
and right-handed cells (clockwise and counterclockwise rotations) so that
cells could share struts in their adjacent planes
left-right_tensejit movie with octant cells sharing
adjacent struts (Quicktime Movie 410k)
We decided that this was the
most elegant version of the model to date and pondered the parallel strut
phase (middle phase) as compression struts of icosa, but realized that
tension lines connecting struts tips would not form triangles of icosa but
came close .
64cell_tnsjt.MOV- 8 VE of tensegrity
jitterbugs (Quicktime Movie 807k)
Shows the pulsating tensegrity
jitterbug in an all space array. Note how compression struts form linear
waves alternating at 90 degrees. This is a big download but worth the
effort.
64cell1.GIF-VE phase of 64 cell model (GIF 73k)
64cell2.GIF-Octa(duotet)phase of 64 cell model
(GIF 73k)
These two GIFs show phases of 64 cell model in case you can't
download the movie.
duotet.MOV- VE of tensejit cells with 2 tetra in each
cell (Quicktime Movie 290k)
This shows 2 matrices co-extant alternating
VE/doutet. The duotet (or star octahedron) is the central octa with a tetra
on each face which fills the 8 cell cubic domain of the VE
universe-metaphysical model of space -tensegrity
jitterbug VE with transformation to icosahedron ( Quicktime Movie 818k)
Gerald and I and others finally agreed that any metaphysical model must
include the only other prime structure of Universe which the model thus far
was lacking (icosahedron). The Fuller jitterbug model incorporates the icosa
as an "in between phase" as triangles of VE rotate on 4-way axes toward
octaphase. Because the tensegrity jitterbug uses 3-way (cartesian) axes for
tetrahedral transformation, we decided to incorporate the icosa as a phase
transforming from the octa and back to the octa along 4-way axes. Note how
the triangle vertices (strut tips) stay on the tension grid during this
transformation. (RBF said the octa mediates between tetra and icosa).This is
the latest version of this evolving metaphysical model of Universe. As
Gerald points out in his explanation page, this model incorporates the VE
radials and nucleus. There are 7 axes of spin rather than 4.
jitterqt.mov- Fuller's conventional jitterbug
transformation (Quicktime Movie 94k)
... shows the VE transforming through
rotation of 8 triangles along 4-way axes through icosaphase to octa and
back.
jtmatrix.mov-allspace array (IVM) of conventional jitterbugging VEs (Quicktime Movie 347k)
After some three years of thinking and reading about Fuller's Synergetics I became dissatisfied with the images and the explanation of his "jitterbug" transformation. It began as the Vector Equilibrium but strangely enough it had no radial vectors and no nucleus! My feeling was not that Fuller's jitterbug was wrong, just that it was incomplete.
Something else also bothered me about the jitterbug. It consisted of eight twisting triangles, each of them being in some sense solid, which also seemed like only part of the story in view of the elegant separation of tension and compression in Fuller's discussion of Tensegrity. The tension and compression were fused, which, given the insights of tensegrity, began to appear very special-case.
The solution would necessarily involve tensegrity, and must also show a nuclear vertex in the VE phase.
It begins with a tensegrity tetrahedron, with its six compression members and twenty four tension members. Each of the four faces are ringed with tension lines, and each of the tetrahedron's points also has a triangle holding it together. In the tetrahedron phase, the tension and compression member are indistinguishable, but as the transformation progresses, they separate.
If each of the struts are rotated in the same direction on axes that go through the tetrahedron's center, the entire tetrahedron can transform into its brother tetrahedron, with points being replaced by faces and faces being replaced by points. To illustrate this, I built what I call a "tensejit clock" image in the 3DV.EXE DOS viewing program, where 12 o'clock is one tetrahedron and 6 o'clock is its brother. the two ways of transforming appear on the paths via 3 o'clock and 9 o'clock.
This jitterbug can take place without stretching the tension members if the compression members are allowed to compress and re-expand. Not only that, but such a constant-tension-member jitterbug can function in a allspace-filling array! It transforms one tetrahedron to the other within a bounding cube.
We construct eight of these cubes into a big cube with the tetrahedra arranged so that their edges make up a nucleated Vector Equilibrium structure. As the tensegrity jitterbug progresses (*) in each of the sub-cubes, the compression members eventually become parallel to each other and move further to create the alternate form, which is a central octahedron with a tetrahedron on each face - the 'duotet'.
This seemed to me to be a more complete picture of the jitterbug transformation. It began with a nucleated VE, transformed by tidily and temporarily separating tension and compression, and ended as Fuller's jitterbug with an octahedron.
.-.-.-.-.-.
(*) There are two ways to have the transformation take place in the eight-cube array. Either all cubes do clockwise (or counter) in unison, or adjacent cubes jitterbug in opposite directions. The latter seemed to be more elegant, since the former appeared to involve friction.
* gerald_de_jong/rotterdam *
