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Re: Tiny wheel
You could use 2" wheels, and have them support the robot. You'd just need more of 'em, most likely.
There are other reasons, though. Like finding a sprocket that small--and adjusting the gearing to compensate for torque/speed. Or even finding a wheel that small.
But how about this one: ground clearance.
Let's assume for a moment that you run 2" wheels on a chain/sprocket or belt/pulley system. You use 1"x1" square tubing as your frame. What's your ground clearance to the bottom of the tubing? How about to the sprocket or pulley? Bonus question: What does FIRST have a nasty habit of putting under the field carpet? (Answers: Assuming the axle is in the center of the tubing vertically, about 0.5". Pulley or sprocket, probably less as it'll be close to the size of the wheel. And the bonus answer: supports for field elements, with some form of ramp/other protective thingy next to it, also under the carpet, often about 0.5" thick counting carpet.) And for an extra bonus, there is a penalty for damaging the field, and there's a higher-than-usual chance that you do that when you're that low.
Not to mention any obstacles to go over.
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Past teams:
2003-2007: FRC0330 BeachBots
2008: FRC1135 Shmoebotics
2012: FRC4046 Schroedinger's Dragons
"Rockets are tricky..."--Elon Musk

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