Polar Vortex went 1-2 at RoboGames 2017, scoring one knockout.

Having done my area qualification on genetic algorithms for my master's degree, I wanted to know if I could design a single-tooth disc using less computing power.

By starting with the intersection of two offset circles, one can make a disc with a single tooth. You can divide the resulting shape into six different geometric shapes, each with a simple algebraic formula for its center of gravity. By putting these into a spreadsheet, you can define the disc by six parameters. Since the shape is symmetric about the X axis, you only need to adjust these parameters to center the mass on the Y axis. You can use simple "bisection search" to find a solution with a center of gravity at <0,0>. This search can be done by hand and the error can be reduced to less than one part in a million in about two dozen iterations.

To demonstrate the proof of concept, we sent the file off to Big Blue Saw to be water jet cut from a plate of half-inch 6061 aluminum. For a real weapon you'd want to use a hard steel, and a thicker plate, but for testing balance a piece of aluminum is more economical to start with.

The math gives us an outer profile that is balanced around the center, but to make a real weapon you must add a keyed bore, in this case for a 2 inch shaft with a 1/2 inch keyway. We also added "e;lightening holes"e; to reduce the weight near the center. The effectiveness of a kinetic spinner depends on its angular moment, not just its weight, so the more mass located farther from the center, the more rotational energy the disc can store. As long as the holes are symmetric around the bore, they do not affect the cener of gravity.

For purely stylistic team tradition we used five-way symmetry with holes every 72 degrees.

The photo on the left shows the actual drawing file sent off to the water jet cutter, and the right shows the test rig we used to spin the aluminum disc to 6,000 rpm.

The method chosen was to simulate an Aristotelian spiral using four separate quarter-ellipses. Including the fillet region, there are only six parameters to specify the shape, including the small red area for the fillet.

Since the shape is not symmetric about either axis, you must use "hill climbing search" to optimize the center error. Basically you can alternate reducing one axis to zero using bisection search, then optimize the other axis. Again the process approaches one part in a million after only two dozen calculations on the spread sheet, and can be done in few minutes on a laptop computer.

Confident after our first test with the aluminum disc, we ordered our production weapon discs out of S7 tool steel, heat treated to Rockwell C50 hardness. We ordered two discs each of three thicknesses, 1.5 inch, 1.75 inch, and 2 inches thick. That gave use options to choose based on the actual weight of the robot, since the discs had to be ordered two months before the robobt itself could be built and weighed.

Last updated 10-Jun-2019 Lazy Toad Ranch Web Site contents Copyright © 2000-2019 Michael L. Mauldin