(note that all of the discussion below is assuming the robots are driving forward)
Exactly. The same forward force as a regular wheel, but with an extra sideways force that doesn’t contribute to forward motion. More total force, conservation of energy still applies
It’s as if the mecanum wheel had a smaller diameter, which produces more force for the same torque - but at a lower angular velocity.
I think you might mean lower robot linear velocity?
This example is a bit more tricky. I think you are trying to draw the analogy to regular wheel size selection to show a sacrifice is made instead of getting something for nothing. This analogy doesn’t quite hold here in mecanum vs. regular wheel. Mecanum doesn’t need to trade anything because it is not creating more force in the direction of travel. Same input torque & diameter wheels produce the same forward force which results in the same forward velocity.
Mecanum produces more total force for a given torque, but this isn’t a “something for nothing” situation because the total force is not in the direction of travel.
So, is it fair to say that a mecanum drive is equivalent to the 4-wheel orthogonal omni drive I described earlier, if we use smaller omniwheels?
Great question! So, mec vs. 4wheel kilough. Same torque, but omni wheels are a factor of sqrt2 smaller. This would produce the same force in both. The question here would be what happens to the kilough drives velocity?
Note that I am fighting the misconception that mecanum translates a smaller forward component of force as a regular wheel.
In 4 wheel kilough vs regular wheels the analogy would be an omni wheel mounted at a 45 degree angle compared to a regular wheel. The same input torque on both gets you a smaller forward component of force for the omni wheel.
This difference is well illustrated in the figure from the paper you referenced