# Parametric Deployable Scissor Structure using Kangaroo2

Hi all, Ive been attempting to to create a workflow that enables domes & Minimal Surfaces to be turned into a Deployable Scissor Structure (Or anything that can be circle packed). I have looked at the Digital design of deployable scissor grids based on circle packing Roovers, Kelvin; De Temmerman, Niels
Roovers_De_Temmerman_2015_IASS15_Digital_design_of_deployable_scissor_grids_based_on_circle_packing_e_version.pdf (1.4 MB)

Still trying to understand the research. Essentially I want to use the same method shown in image two but on a dome or appropriate 3d Structure. (But instead of sphere collide use â€śTangentInCirclesâ€ť). The issue im having trouble solving is making sure that the angles y change proportionally and maintain the structure. If it was planar i would just scale from the base mesh to achieve the shrinking.

7894-Kinetic Scissor Structure Prototyping_GH.gh (12.3 KB)
Dome Base Surface.3dm (227.2 KB)

Still wrapping my head around the paper as well but any help would be appreciated!

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Hi @Noah6

Itâ€™s a nice paper. I remember Iâ€™d been meaning to make an example of this since I first saw it.
The logic is given quite clearly in this figure:

So taking a mesh optimised for tangent incircles we can do this:

edit - moved the mesh generation upstream of the transformations for efficiency:

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Hey Daniel, Amazing help! I played around with the script you have provided to work with circle packing using the vertices as the circle centers and works well however a bit of tolerance is lost as the circle packing is not perfect, Any suggestions on improving/tightening the tolerance (The original circle packing optimisation script can be found in the original post)? Regardless i imagine the joint/connection i design will accommodate such tolerances.

I was originally planning on using a polar method on a 3d mesh as seen here:

The aim would to be to make the structure more compactable compared to the constant angle version which can be calculated by scaling the entire group proportionally. I can manage it in 2 dimensions or â€śArrayedâ€ť systems but I was looking for a similar flexibility to that of the one you provided. Any help is appreciated!

Hi Noah,

Note that it is the incircle packing (in blue below) we need to use to make the linkage.
These can easily be made tangent to a very high degree of accuracy.
You just need to make sure that all other goals are turned off before getting the final geometry out.
(since for example also keeping the vertices exactly on a surface would likely conflict with the tangent incircles property by some amount and make it less accurate. You can use it for the initial shaping, but to strictly enforce tangent incircles turn everything else off)

The red circles on the other hand cannot possibly be perfectly tangent, except in the very specific case of a Koebe polyhedron where the mesh edges are all tangent to a single sphere.
For freeform meshes, when the faces are optimised for tangent incircles, there will be a set of tangent spheres centered at the mesh vertices, but the points of intersection of these spheres with the incircles will not form a circle.

Ah i see, so its not possible unless using Koebe Polyhedrons. Is the same said for using the â€śPolar Methodâ€ť for the scissor structure on a free form mesh, is it simply not possible? Are there any other readings you can suggest for the topic?

Cheers for the help!

To avoid confusion - you donâ€™t need a Koebe polyhedron for this type of free form scissor structure to work precisely, just the tangent incircles.

The geometric mismatch in your images must be from not having the mesh fully optimised for incircles.

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Sorry i meant in regards to this statement. The geometric mismatch is due to me using the â€śRed Circleâ€™sâ€ť Instead.

I will explore using the â€śInCircleâ€ť Method of circle packing as well as explore using the Variable Angle approach.