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Originally Posted by Tristan Lall
Probably because any three points of contact define a plane (e.g. the floor), and the fourth is redundant (in this case, not necessarily touching the ground). So, they leave their front wheels fixed, and let both of the rear wheels pivot so that they effectively have two planes of contact—either rear wheel plus both front wheels.
If you put it on all four, it works, but then the body of the robot becomes (potentially) unstable, because it's now supported on four moving pivots. It's like body roll in a car, only probably quite a bit more pronounced.
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I believe that a mecanum system actually needs every wheel on the ground because the direction is controlled by a different vector from each wheel. If a wheel isn't touching the ground, the robot would drive at the wrong angle because force in one direction is missing, while the bot is programmed to use all four vectors. (Unless the robot was programmed to change its math based on which wheels are touching the ground...)