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Unread 11-01-2012, 21:56
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AKA: Alex
FRC #4334 (Alberta Tech Alliance)
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Re: The physics of flipping

Quote:
Originally Posted by Ether View Post
Use JVN's mechanical calculator, located here.
I haven't used JVN's calculator in a while, but I' don't think it gives acceleration.

On the other hand I plugged this into wolfram alpha (so I don't have to worry about all that unit conversion):

(21 in-lb / ((12fps / 5310 rpm) / (2*pi (inches/revolution)/inch)))/120lb to m/s^2 * 80%

Getting a max acceleration for my previously stated bot of 5.3 m/s^2. This is approximately half the force of gravity.
Based off that we can have a center of gravity at most ~2x as high as it is far from the front/back of the wheel base (whichever is closer), before you will flip due to accelerating on a flat field.
I would probably suggest keeping it below 1.5x though, for safety.
Quote:
e.x. 37" long robot with a center of mass that is nearly centered on the robot has the following characteristics:
Wheel base = 37 - 2*4
= 37 - 8
= 29"

CoM to edge of wheelbase = 29/2
= 14.5"

Max height of CoM = 1.5 * 14.5"
= ~22"
I ball-parked pretty much every number in this math but it does tell us one thing:
Quote:
If your long-orientation robot has a CoM more than 22" off the ground (or 14" for a wide-bot), you'd better think twice and prototype 10x, because you're in the danger zone!!! NOTE, this doesn't mean that less than those thresholds is safe, it's just that over them is super risky.
Ether, did I overlook anything? If this is reasonably representative for most teams then I'll move it to the top, and hope it helps some people.