pic: Omni Design Trial

[MrForbes]

No, it's not the end of the story....because I have a mecanum wheel sitting here, and you don't

Originally Posted by George1902

There are no "cases" involved. The wheels behave the same always.

No, they don't. Mecanum wheels behave differently when they move only in the direction of the wheel, than they do when the move any other direction. In the straight ahead case, the rollers do NOT roll relative to the body of the wheel. This is because in this case they CAN NOT roll relative to the body of the wheel, as long as they have full traction. This is a fact, try it and see!

Rolling a wheel and powering a wheel are totally different.

Yes they are...as far as force. No, they are not....as far as velocity.

If you placed a keyed or hex shaft through the wheel and tried to turn it while pressing into the ground, you'd see the wheel would want to walk down the shaft. This is because the wheel produces a vector that isn't straight ahead, but at approximately 45*.

Exactly!!!

But if you constrain the wheel so it cannot move sideways, it still produces the sideways force vector, but the sideways velocity vector is zero.

Ok, let's try changing tack. Assume the mecanum wheels do put 100% of the power forward. We know the gearboxes can't output more than 100%, so there can't be any force sideways. Therefore, the robot could not strafe sideways.

....while the wheels are only rolling straight ahead. There are two different cases, which you seem to be ignoring. The straight ahead movement case is the only one where the motors can transmit all of their motion to the robot. In the strafing case, the motors are not transmitting all of their motion to moving the robot, and the robot goes slower when strafing than it does when going forward, assuming the same average motor speed among the 4 motors in both cases.

However, we know that the robot can strafe sideways. Therefore our assumption is false and the wheels must be producing a sideways force all the time.

No, the wheels are producing a sideways force all the time, but are only producing a sideways motion when strafing! Please try to understand that force does not equal motion.

The mecanum wheels do not put 100% of the power forward. They behave just like regular omnis at 45* angles. You get about 70% power by moving forward, reverse, left, or right.

Nope, with mecanum you get 100% going forward, and less when going sideways or at an angle.

Also, consider the case of omnis vs. mecanum, with all motors turning in such a way that none of the rollers are rolling relative to the wheel bodies. In the case of the mecanum, the robot goes straight along the axis of the wheels. The omni sits and spins in a circle. So, the omni is most efficient when it is not going anywhere!