pic: Omni Design Trial

[MrForbes]

This is hard to visualize! but easy to demonstrate if you have a mecanum wheel to play with. Unfortunately they're hard to find....and hard to make....and expensive....

The rollers act as "tread" when the weel is going straight ahead. To be able to roll relative to the wheel, there must be sideways motion. If there is no sideways motion, the roller in contact with the floor cannot roll, it can only "go along for the ride" as the wheel turns.

(I am assuming the rollers get good traction on the floor)