I was wondering what is known about hinged quadrilateral panel systems.

If you connect 4 quadrilateral panels, using hinges like this

A|B
- -
C|D

you generally get a "pop-up card" type system, that has one internal
degree of freedom: If you move one hinge, the other hinges all move in a
coupled motion.

If you connect a larger number of quadrilateral panels, you generally
get a rigid surface.
But under some conditions, you get a surfaces with an internal degree of
freedom, like in a "Miura fold":

http://demonstrations.wolfram.com/Mi...gAndUnfolding/

I can build a few other surfaces that are slight generalizations Miura
folds. If the quadrilateral pattern is composed of pairs of strips that
are repeated in 1 direction like this:

ABABABAB...
CDCDCDCD...
EFEFEFEF...
GHGHGHGH...
...........

it will also have 1 internal degree of freedom, giving coupled motion of
all hinges.

My question is:
Is there a general criterion that the quadrilaterals must satisfy to
have 1 internal degree of freedom.

Gerard

On Jul 3, 8:28*am, Gerard Westendorp wrote:
I was wondering what is known about hinged quadrilateral panel systems.


Gerard,

I would suggest looking up 'graph rigidity'. This is a branch of graph
theory but a rectangular panel would have the same rigidity properties
as a ocmplete graph on 4 points.