7. Dynamics in 2D

While studying dynamics in the 3D Leonardo grid constructions I also discovered an interesting new way of translating 2D Leonardo grids into dynamic structures. Looking again at the basic grids you will realize that there are two possible interpretations: you can either look at it as a construction built out of rods or as a tiling, a pattern built with a set of tiles. The dividing lines then form the Leonardo grid.
One line in this grid represents the edges of 4 tiles: 2 big tiles and 2 small tiles. So this one gridline can be seen as a set of 4 edges. And because the edges are alternating long-short-long-short, the set of edges can be seen as a collapsed parallelogram. In the original grid the tiles are close to each other so the described has area zero. But what will happen when we 'open' the parallelogram? The set of tiles then turn out to be a dynamic hinged construction. The Leonardo grid lines transform from line to parallelogram to rectangle and back via parallelogram to Leonardo grid line again. And as a result of this process is that a left-hand orientation of the Leonardo grid has changed into a right-hand orientation.
Figure 42: Transformation first stage
Figure 43: Second stage
Figure 44: Third stage
The discovery of this process lead to many designs of Leonardo grid space frames because the process could be applied on all the flat basic patterns. We can also start with a square hole in a pattern. In the same way the flat hexagon is transformed into a skew hexagon, a flat square can be transformed into a skew square. The over a hunderd different patterns that I had drawn as possible designs for the domes can now be transformed to Leonardo grid space frames. In the illustrations you can see some examples of the resulting space frames.
Figure 45: Transformation first stage
Figure 46: Second stage
Figure 47: Third stage
Figure 48: Transformation first stage
Figure 49: Second stage
Figure 50: Third stage
Of course this can be better viewed in animation.