Help finding an equation to relate two folding angles of an origami shape

Grasshopper
1

Hi All,

I’m trying to model a certain type of origami that changes it’s shape when flexed. Please check the first 30 secs of this video which shows the behavior of that shape.

The problem I’m facing now is that between each two tetrahedron there a certain folding angle which somehow relates to the angle between the following one. So if the angle between polygon 1 and polygon 2 is controlled by slider, what would be the equation that relates that to the folding angle between polygon 2 and polygon 3 ? Right now the way I do it is to adjust the second angle manually each time I change the first which is definitely wrong. Please see the attached image and the GH file below. Thanks!

QUESTION.gh (18.4 KB)

QUESTION
QUESTION1140×877 216 KB

1 Like
2

If by “folding angle” you mean Dihedral Angle, try this.
QUESTION-b.gh (30.5 KB)

dihedral
dihedral1381×723 134 KB

https://en.wikipedia.org/wiki/Dihedral_angle

3

Thanks Ethan, unfortunately that didn’t solve it too. It seems that the relation between the two angles is not linear. I tried to keep adjusting manually and then plotting all these numbers in a graph. The curve looks something like that which is a log function.

image
image.png426×567 2.08 KB

I just can’t figure out the exact function yet. I tried log10 in the Expression Function List, which is pretty close but not accurate. Thanks again!