SOMETHING BIG
SUMMARY:
Our project for this week was to MAKE SOMETHING BIG. At the moment, our fab lab does not have a shop bot. However, there are machines in the area that can cut 4 x 8 sheets of plywood, which gives us the needed opportunity.
I found the following link which had a nice animated gif file, which ideally portrays 15 rotating gears arranged along the path of a mobius strip. I wanted to see if I could make something similar, realizing that my gears would not rotate, but still wanting to explore how gear shaped elements would interlock to make a mobius strip.
PROTOTYPING AN INFINITE GEAR TRAIN LOOP
I began by making some cardboard elements on the laser cutter. These pieces are a little under 4 inches. I ultimately chose an outer 11 toothed gear with an inner 13 toothed gear to support the individual elements. A slit was cut between the inner and outer surfaces so the elements could be assembled into an interlocking sculpture
WOOD PATTERN, EVEN NUMBER OF ELEMENTS (18 TOTAL), ARRANGED IN A CIRCLE
I then cut a few dozen out of quarter inch plywood, and painted the 2 sides different colors. Unlike the gif image, I needed more pieces to assemble a circular display. 18 is about the minimum given the geometry of my element. More might be better. The ideal gears would seem to have some curvature to them, which is not readily obtainable with laser cut plywood.
WOOD PATTERN, ODD NUMBER OF ELEMENTS (17 TOTAL), TWISTED INTO MOBIUS STRIP
Turns out you need an odd number of pieces to make the mobius gear train. You also need to put in half a twist, much the same as if you were making a mobius strip with a piece of paper. It also turns out that two hands are not enough when you go to assemble this, as by the time you have one side properly arranged, the other side rotates out of alignment! The scaled up version should allow for some judicious pruning to assemble properly
CLOSE UP OF THE CROSSOVER SHOWING NATURE OF MOBIUS GEAR TRAIN
Here is a close up of the crossover, which shows where the gears make the turn and roll into eachother, creating an infinite gear train
DISCUSSION
Looking forward to the scaled up version! My plan is to scale up times four, from an element of about 4 inches to one of about 16 inches. This will result in a sculpture approximately 16 inches tall and 40 inches wide. I will need about 1-1/3 sheets of 11/32" or 1/2" 4'x8' plywood, and a bit of paint to get this done. If time and money were no object, it could be scaled up to an installation sized piece, in my case hammered out of steel to achieve the needed flexures, and welded together for stability.
I think more work could also be done in choosing the appropriate number of gear teeth given the size and number of elements needed to form the infinite loop. I used intuition in lieu of mathematics which should give a reasonable approximation in conjunction with a sharp saw.