The Golden Ratio Project - Phyllotaxis on a Laser Cutter
In my Geometry Honors class last year, we completed a PBL on the Golden Ratio. In the intoduction to the project, I showed my students different examples of the Golden Ratio. One of the most popular examples was the Helicone by PlayableArt and based on the work of John Edmark. Around the same time, I had also produced a spinner using 22mm bearings. These two ideas seemed to have synergy so I started out on a project to produce a larger Helicone based on bearings that could be robust and interactive - ideally strong enough for student use at an all-boys K-9 school.
I went through multiple prototypes, some of which neared completion before determining that the mechanism or materials were not strong enough. I also had to flip the rotating mechanism so that the input would be from the base and not from the top of the helicone. Early iterations used rivets and slots to trigger and limit the rotation but these ended up bending or getting ripped from the wood after continued use.
Prototype 1 - Plywood, Rivets and Tapered Branch Lengths
This seemed like the most obvious method when I started this project. I found hollow brass rivets on Amazon and designed the mechanism with the pin poking through the top layer of each. The golden angle was relatively easy to calculate and designs were made on Inkscape to have a slot on the bottom of each layer to create a helix and a golden ratio "rush". I designed many, many files so that each layer could be cut separately.
Problems discovered: Wood layers will warp when using wood glue. Warped layers consequently interrupt the smooth operation of the helicone. Also, the helicone seemed to worked best when engaged from the top layer which seemed a bit akward.
Prototype 2 - Acrylic, Rivets and Tapered Branch Lengths
Acrylic took care of the warping issue but rivets did not fit perfectly and would still get ripped out when the helicone was spun at high speeds. Acrylic is also much more expensive and requires the use of hazardous materials to fuse together. On the plus sides, the look of the material both the color and rastering results is impressive (may do another of these in the future).
Prototype 3 - MDF, Rivets and Tapered Branch Lengths
MDF is hard to find but I finally found a supplier through Etsy. Great material to work with but the edges are not particularly strong (weaker than plywood) and it became clear that rivets were not going to be the right mechanism. I made about 12 layers with MDF before punting on this idea and almost quitting on the project.
Prototype 4 - Plywood, Bow-Tie Mechanism, Uniform Branch Lengths
I considered an idea of using wood itself for the mechanism after seeing an example of a helicone made on a 3D printer. The benefit of this "bow-tie" design is that the mechanism has better symmetry and distributes the forces on each side of spinner. I also liked that it did not require special order rivets and only required screws (#4 x 3/8") for construction. During this last prototype, I also learned more about the use of adhesives. Spray adhesive works well for large flat layers and provides a fast even coating with adequate attachment. For the more critical pieces, such as the bow tie and pedal connectors, I still use wood glue and allow time for setting.
During this prototype I also decided to streamline the constructions process and files. I made one file for printing 6 spinner mechanisms but did not include the pedals. This allowed me to fine tune the design for checking the mechanism and also used the sheets of material more efficiently. The pedals for each layer are cut separately and attached with wood glue and take advantage of a "puzzle piece" connector. I also think this design results in less warping as each layer uses multiple pieces of wood rather than long pieces from one piece.
After finding success with this last design, I focused on how to make it interactive. I spent some time cutting sprockets from both wood and HDF but it became clear that bike chains exert tremendous force on the material and require the use of metal sprockets. A quick visit to the Harris Cyclery in West Newton (and $20) and I had the front and rear sprocket as well as a matching chain. I cut some additional plywood pieces on the laser cutter to match these sprockets and added the same 22mm bearing to allow for smooth actuation. I also learned how to break a chain and use a connecting link to adjust the chain to the proper length.
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Step 1: Materials Needed
8x22x7 Bearings (40) (link) $30
#4 x 3/8" Screws (100) (link) $10
1/8" Plywood 12"x24" (approx 15 sheets) (link) $50
Small bike sprockets (front & rear) and chain $20 (sourced from local bike shop)
8mm x 500mm steel rod (link) $15
Rod collar (2) (link) $10
Spray adhesive (1) (link) $8
Washers 8mm (link) $7
Total cost $150
and of course an Epilog 40 watt laser cutter.
Step 2: Cut the Spinner Mechanism
6 spinners will be cut per sheet of plywood (12"x24"). 30 or 36 spinners total depending on your rod length. Color mapping makes life much easier.
Step 3: Glue the Bow Ties
I glue the bow tie to the back of the bottom layer using wood glue. Line up the bow tie piece by using the rastered out bottom of the bottom layer. Let this glue set for about an hour.
While that glue is setting, assemble the other layers using spray adhesive.
Step 4: Top Layer
Spray this side and immediately attach to layer 2.
Step 5: Glue Together Layers 1,2 & 3.
Top layer is the cut out that stops the bow tie mechanism during operation. The 2nd layer is the abuts the top of the bearing. Layer 3 holds the bearing in place (along with the layer attached to the bow tie). Make sure the alignments are accurate.
Step 6: Insert Bearing and Attach Bottom Layer
The bow-tie should hold pretty well with the wood glue, but I hold it in place by inserting the two #4x3/8" screws. I countersink the screws (using the philips head driver in the screw gun). I also add a screw to the space on the side to secure all layers together.
Step 7: Final Assembly of Spinner Mechanism.
Screws holding in bow tie and also one securing the layers together.
Step 8: Assemble the Petals
Spray adhesive works well to laminate the layers. Binder clips work great to guarantee strong even adhesion..
Step 9: Glue Petals to the Spinner
I use wood glue to attach them to the spinner mechanisms