Tensegrity Blocks

[Spencer W Hunter <shunter at U dot Arizona dot EDU>]

Tensegrity Blocks

Spencer Hunter, 2005

(I hope to have accompanying public-domain images under a new
"Tensegrity Blocks" directory in the next couple of weeks at
http://www.u.arizona.edu/~shunter/cads.html .  I'll post an
announcement when they're ready.)

A series of self-deployable tensegrity building blocks or components
are outlined.  These blocks may be deployed on-site and assembled into
complete structures; or, alternatively, they may be factory-assembled
into complete structures that are more-or-less self-deployable.

I do not claim the idea is novel, only that I have developed it
independently.  Unique features, if any, not covered by [1]current
patents are hereby placed into the public domain.

Working on [2]zigzag-strut tensegrities, my intention was to overlap
tetrahedra and dual tetrahedra to form a truss.  In the process of
doing so, I discovered that most of the tendons in the truss interior
were basically unneeded, and the shape that emerged as the basic
building component is what most researchers refer to as the triangular
prism simplex, or what I used to refer to as a "pseudo-octahedron."
The triangular prism simplex is the simplest possible tensegrity,
consisting of three struts that comprise the diagonals of the
rectangular sides of a prism of tendons.  In my [3]self-deployable
parabolic zigzag-strut tensegrity dome, each simplex has three
vertical elastic tendons that enable it to be collapsed and stowed,
which is joined end-to-end with other simplexes in a [4]network.

Heavily influenced by the work of [5]BinBing Wang, I came to realize
that this kind of truss was not necessarily the most efficient, and
was led to design a new configuration with the following
specifications:

a)  Truss depth is maximized
b)  Strut length is minimized
c)  Simplex construction is as simple as possible
d)  Simplexes are collapsible and self-deployable

Returning to my [6]basic tetrahedron, it seemed that whereas the
zigzag-strut tensegrity pulled the
straw-pairs-connected-by-paper-rolls apart, it might be better to
force them back together again at the center.  My problem with the
truss described by Wang made of such "crystal-cell pyramids" was that
it would only be able to resist loads effectively in one direction,
and I wanted it to be bi-directional as zigzag-strut was.

After some unsuccessful experimentation, I came across a simplex
design that does meet all the specifications.  Unlike the basic
triangular prism simplex, my new triangular prism consists of three
tube strut pairs (six struts) with each strut connected by a rolled
connector to another in the pair.  The rolled connectors are lashed
together at the center, and the struts bend out from the center where
they are connected to inelastic ribbon tendons that form triangles at
the top and bottom.  Finally, three elastics comprise the vertical
tensioning side tendons that force the simplex into rigidity.  This
center-node simplex or block is heavier than the three-strut simplex,
but the struts are shorter and the overall strength is greater.  One
problem I came across is that the center node was too flexible, so
that during collapse it would pop outside of the prism and defeat
re-deployability.  Taping toothpicks to the straw struts that pass
through the center node of the model stiffens and stabilizes the node
during collapse.  A similar kind of hinge locking mechanism should
work for blocks of similar configuration.

This same idea of struts radiating from a center node of lashed
flexible hinges works for prisms of greater than three sides as well.
I've built a cubic block that should work for trusses, furniture,
walls, and other structures of the box-obsessed world.  Prisms of five
and six sides could be used for hex-pent geodesic domes.

Of course, collapsibility becomes much more of a liability than an
asset in completed structures.  At that point, adjustable non-elastic
tendons could be swapped for or augment the elastic tendons.  A much
better solution, I think, would be to develop a small
independently-powered winch for ratcheting individual pull-wires to
their desired length and tension.  A system of such winches could be
used to self-deploy antennae in space or domes on Earth or other
worlds.

References

   1. The 1996 U.S. patent #5,505,035 seems to cover single-node
      configurations of irregular polyhedra.
   2. http://www.u.arizona.edu/~shunter/zigzag.html
   3. http://www.u.arizona.edu/~shunter/zdome.html
   4. http://www.u.arizona.edu/~shunter/zfiligree.jpg
   5. Wang, "From Tensegrity Grids to Cable-strut Grids,"
      International Journal of Space Structures, v.16(n.4):279-314
      2001
   6. http://www.u.arizona.edu/~shunter/tetra.jpg

Spencer Hunter, Tucson, AZ
gopher://www.u.arizona.edu:80/hGET%20/%7Eshunter