Omni wheels work like a powered caster. They rotate when powered like any other wheel and give you flexibility of side movement as well. The rollers are aligned perpendicular to the wheels axis, this allows the wheel to roll on the rollers when a side force is applied.
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Originally Posted by AndyMark.biz
These wheels provide propulsion in the forward and reverse direction, while allowing for easy, smooth-rolling sideways motion.
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Now, when you use one omni wheel like this:
http://andymark.biz/am-0097.html, the rollers do not have a smooth contact to the floor and will shake the robot a little bit. That can be solved for putting two omni wheels together like this
http://andymark.biz/am-0432.html.
You can also use omnis to climb over objects like 6" stairs
http://www.chiefdelphi.com/media/photos/18050.