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Originally Posted by EricH
See the explanations above. A "mecanum" drivetrain is set up like a four wheel drive with each wheel independently powered. You cannot have two wheels powered by the same motor/tranny. If you do, you will lose all sideways ability, and you may as well go with four wheel drive. There are three teams that I know about that have used this setup in competition. Note: If you tried to use them in a "standard" omni drive (Art's left-hand pic), you would go nowhere, or possibly spin out or fry a motor or something else equally bad. (Actually, mecanum drive is a subset of omni drive.)
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actually, in a four wheel omni-drive, if you paired the wheels across from each other together and attached them to a motor, you'd be able to translate freely. unfortunately, this'd mean you would be unable to rotate. i believe you could achieve similar results by pairing the the diagonal wheels on a mecanum drive train together.