Can someone please explain this to me mathematically? I still don't get it.
It takes less force to rotate a wheel along the diameter of the turning circle than to scrub it sideways along the same circle. With the omni wheels in the front (right picture),you are basically applying force tangentially to the circle which you turn on, and with the omni wheels on opposing corners, You are waisting a lot of your force going outward from the turning circle, and scrubbing both traction wheels sideways.
Is it just that having the omnis on opposite corners woud decrease the force required to turn the robot, but not as much as the omnis on front of back would do? A little help would be greatly appreciated.