[Ether]

In the real world of aerospace engineering, systems engineers try to model friction and inefficiency as closely as possible when they are building dynamic models to allow them to build accurate procurement specs for suppliers. So theory does include friction and inefficiency.

Roller bearing friction plays a large and asymmetric role for mecanum wheels. In the fore/aft direction, roller bearing friction is a good thing. It moves the reaction force of the floor closer to the plane of the wheel, so it takes less reaction force for a given forward force. The result is better traction. For a frictionless roller bearing, the reaction force is aligned with the roller axis. As roller bearing friction increases from zero to locked roller, the reaction force moves from being aligned with the roller axis to lying in the plane of the wheel. When the reaction force lies in the plane of the wheel, that's essentially the same as a standard wheel. So, the reason a mecanum wheel doesn't have as much pushing force (in the fore/aft direction) as a standard wheel is not because there's less forward force available, but because the reaction force is larger than it would be for a standard wheel, and therefore the mecanum wheel starts to slip before a standard wheel would.

In the sideways direction, roller bearing friction moves the reaction force toward the plane of the wheel, which reduces the force vector component in the sideways direction. To compensate, the motor must output more torque. This increases the reaction force, which reduces available traction. So in the sideways direction, roller bearing friction is a bad thing. It causes increased motor power consumption (for a given desired force) and it reduces available traction.

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