Rigid Spiral from Thingiverse Parts

Hi,

Late last year, I made some construction kit parts available on Thingiverse.

By putting together rings and spiral in particular ways, they can be made more rigid and in the blurb, I came up with an explanation for rigidity in the rings. Coincident ring edges have conflicting geometries, and this conflict forces parts and edge materials to rub against each other.

Now a few weeks ago I wrote to a designer who contributes to the Bridges conference in Europe, and he was encouraging of my work, and so I got to thinking about it a bit more.  The blurb has my ideas about how ring stacks become rigid, but what about the spirals?

This kept me awake one night last week, and my thoughts led me to fractional polygons, that is polygons with 4 1/2 sides (or similar whole no. plus fraction) per revolution, and 2 or more revolutions to close. Fortunately I didn't have to suffer in my jocks for too long, and a web search revealed fractional polygons are actually a thing, as this site reveals.

So anyway, I went into excel, and worked out how to plot some fractional polygons in 2d in excel. For a 4 1/2 sided polygon, you can calculate 360 / 4.5 and that will be the angle between all the points on the polygon. So you "set a clock hand going" and draw lines between all the stops at multiples of 360/4.5 or 80 degrees. To move things into 3d, I moved to a separate sheet and used the maths to calculate coordinates of 2 3d spirals.  This was done by adding in a Z column (increase Z by a fixed amount each time) to the X and Y already calculated. The coordinates can be copied to a text file to make a script which can be run in AutoCad or Draftsight to represent a couple of 3d lines.

The lines represent shapes that rows of tiles each side of an edge want to force on the edge.  Neither shape can be made and the resulting conflict between parts makes the spiral rigid.  The spreadsheet and pdf blurb can be downloaded here.

And here are a few screen grabs of the plots, enjoy!

Regards

Steve Nurse

2d fractional polygon from excel.

End of a script run in Draftsight which produced the spiral.

3d view of spiral

Side View

Top view has no perspective and looks just like 2d.