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Just wondering if this would work. A drive train with 2 mecanum wheels in the center and an omni wheel in each corner. Only the mecanum wheels are powered. If I'm thinking of this correctly you always are crabing with no way to turn your robot. Is this correct? I'm not looking for people telling me how stupid it would be to have a robot that can't turn, i know this, just would this happen?
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You could go forward or backward, and you could do a combination strafe+turn left or right. You couldn't strafe without turning, or turn without strafing.
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the cylinders can be fully extended, fully compacted, but can they be put somewhere in between?
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I think the word you are looking for is "retracted". The simple pneumatic cylinders that came with the 2010 KoP (by request) are force devices, not servos. Operated open-loop, they're not designed to stop halfway and hold that position against an external load. You could, of course, add a position sensor and try to turn the cylinder into a linear servo by doing closed-loop control in software. You'd have a tough time holding the position against a varying load due to the compliance of pneumatics. Getting a robust stable solution would be challenging at best.