Pasting from the other thread:
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You may be correct, but from what I have observed from the ball differential it should work. The omni wheels will be attached to the shaft that is attached to the disc holding the balls. The balls will be pressed on each side by the sprockets. If the sprockets are going the same direction than the wheels must be moving the same speed. If the sprockets are going in opposite directions (equal full speed) than the omni should be stationary. Correct? Now if one sprocket is not moving while the other is moving at full speed than the omni wheel should be moving one direction at half speed. Thus allowing for a 45% angle run of the robot. Any other difference should be also of the same ratio. On paper the ratios work out but in practice I may be wrong. We will be building a test system this fall to find out.
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The problem lies in the direction of the force vectors that the omni wheels add when they spin. When you're trying to lateral at 45 degrees off of forward motion, I see now that the omni will only spin at half speed. However, the omni wheel still spins
forward therefore your 45 degree angle of velocity is cut down to (ideal physics here...) 45/2 or 22.5 degrees.
You should be able to account for this in code by adding a
small backspin to the front mecanum wheel, yet there may be a bit of tweaking to make it smooth from zero to 90 degrees in each quadrant. Good luck and keep us posted!