kaleidocycle aka rotating rings of tetrahedra

by benjamin jenett

Oct 4, 2010

Greetings everyone-

Let me start of by saying that I know GH is not the best for solid based geometry, especially folding origami-esque configurations, but I am determined to make this work.

I am using the "kaleidocycle" as a facade component, and i need to be able to move it through its entire "rotation" in 3d space to understand where and how it is moving. 


this is what it is doing, in general. there are 2 sets of 3 hinges, rotated 180 degrees, making up a hexagonal form. 

here is a rhino model of the form. i used the trigonometric properties of the isoceles triangle to make this model very accurate (63.333, 53.333, 63.333 angles), and now i need to describe the movement. 

It is TOUGH. i think i have it and it just throws me for a loop (no pun intended).

I have a ghx model set up to where it can go through part of the cycle, but the inbetween states are incorrect, and therefore it's not valid, but it shows how something like this could work. The trick is it rotates on multiple axes at different times, and its just very very tricky to figure out what it is rotating around and when.

If anyone has any ideas, or insight, please please let me know. I am working on this in my masters' studies, and I'm pretty screwed if i can't figure this out in grasshopper!

Also, please find attached a research article concerning this form. I haven't been able to apply the geometric findings of theirs, yet. But it shows it can be described mathematically.

THANK YOU!!!!

benjamin

  • up

    benjamin jenett

    oops! forgot the paper!

    Oct 4, 2010

    • up

      Daniel Piker

      I would say work with just one pair of tetrahedra to begin with.
      You know the arrangement has 3-fold symmetry, so you must keep the 2 outer edges of those tetrahedra on 2 vertical planes at 120° to each other.

      I would fix the centre of one of those tetrahedron edges and use its rotation on that plane, about its midpt as the controlling parameter.
      Given the orientation of that one edge of one tetrahedron you need to find the 2 fold angles that will make the opposite edge of the other tetrahedron lie on the neighbouring plane. Finding those 2 angles should just be a case of intersecting some circles.
      Then you array the 2 tetrahedra around the intersection of the 2 planes to get your kaleidocycle.
      1

      Oct 4, 2010