Expanding Circle - Hoberman - With a core and 4 expansion arms.
8 full segments (16 pieces), so angles are 135 degrees, made into arcs.
Only allows for about 1/2 contraction, core has diameter of 1/3 the outer circle, expansion arms are slightly longer so that they stop just outside the core.

This is the first prototype I made from plastic cardboard and wooden dowels for use in an expanding-gear CVT Transmission idea for human powered vehicles. Here is a link to that project using 3D printed parts:    • CVT Automatic Mechanical (Bicycle) Tr...  

The Inner Pivot Points with the dowels in this example are replaced by pins with small sprockets that connect to a standard bike chain, and on the other end of these pins there are Ratchets so that the Sprockets can lock in the forward moving direction, but spin freely back along the chain (or vice versa) when the expanding circle expands or contracts (oterhwise the chain would lock the pins with the sprockets in place).
This 'expanding circle' would be (most likely) mounted on the front, crank gear of the bicycle, which would be prevented from contracting due to applied torque by resistance spring(s). I played around with various versions of spring resistance ideas, the most recent being a clock spring between the crank arm and the central core disc.

I reached a stopping point on this project in 2022 due to running out of money needed to continue working on this, as I would need to move to metal part production to make sure it works correctly. If anyone is interested in continuing the work on this project let me know. :)

Here is a link to a Google Drive folder with all related project files for the CVT Transmission project idea, including the 3D models (made using Google SketchUp): https://drive.google.com/drive/u/2/fo...