Mecanum Wheels - How do they work?

[efoote868]

Originally Posted by Ether

There's no kinematic reason why mec needs to be square in order to rotate properly.

Quickly sketching the vectors on a napkin, it looks like to me that wheels in a square will optimize spinning (maximize total torque on robot) for a particular wheel distance d from center of robot; perhaps you could comment? The other quick example I could think of is if the wheels were in a line. Then the total torque about center is 4*|F||d|*root(2)/2, versus 4*|F||d| with the wheels in a square.