Can mecanum wheels operate without sliding?

Question

I am currently learning about robotics, and I have encountered mecanum wheels. I understand their behavior, but there is something that keeps bothering me. It's not difficult for me to understand that the friction forces on the wheels add up and this causes a net force in a certain direction.

But would it be possible for that kind of wheel to work if we assume no sliding is possible? Trying to solve it, I simplified the problem as a wheel rolling making contact with the ground and a wall at a 45-degree angle with respect to the wall's normal, imitating the case in which the robot moves sideways. That way, it seems that movement perpendicular to the wall‘s normal can only be achieved by letting the wheel slide. To sum up, I would like to know if the way I have thought about it is correct, and therefore, mecanum wheels would never work if sliding is impossible.

Answer 1

But would it be possible for that kind of wheel to work if we assume no sliding is possible?

Short answer: yes.

I have borrowed the above image from Wikipedia and added colour coded vectors.

The green arrows indicate unpowered wheels that are free rolling on the roller in contact with ground.

The orange arrows indicate the thrust direction of the powered wheels when the actual direction of the wheel is not aligned with the thrust vector.

The cyan arrows indicate the direction the wheel is moving in when they are aligned with the trust direction.

Taking the wheels with the orange thrust vectors, there would appear to be sliding of the rollers relative to the ground, but I have come to the conclusion that actually there is loss of efficiency, not due to dynamic sliding at the contact points, but due to free rolling of the rollers. Consider the worst case design of rollers on the perimeter having axes that are parallel to the axis of the drive wheel and motor. There would be almost zero efficiency because the torque produced by the motor would not be transferred to the ground due to free rolling of the rollers. As the roller angle is moved away from the wheel axis the efficiency improves up to a maximum when the rollers axes are perpendicular to the wheel axle. The Mecanum design is between these two extremes and about 50% of the input torque is lost due to free rolling of the rollers when the vehicle is travelling straight ahead (a) or sideways (b). When the vehicle is travelling diagonally (c), the vehicle is operating at maximum efficiency as the driven wheels are moving in a direction parallel to the thrust vector and the undriven wheels have a roller in contact with the ground that that is aligned with its natural rolling direction.

Sliding of the contact points does not seem to be significant.

The Wikipedia image is a bit confusing, because on most of the wheels they show the rollers that would be visible at the top of the wheel looking from above, as black diamonds. The rollers that are actually in contact with the ground have the opposite orientation to the top rollers. For the wheels that are free rolling with no input torque (the ones with green arrows) they have greyed out the top rollers and show the free rolling roller that is in contact with the ground as a solid black diamond.

The lack of sliding of the contact points means little damage is done to the ground surface (compared to e.g. a tracked vehicle turning on the spot), but as mentioned above, the Mecanum design is still inherently inefficient compared to a normal wheel when traveling straight ahead, due to the free rolling losses mentioned above. (The most fuel efficient way to travel long distances in a Mecanum vehicle is to travel diagonally as in in diagram c.)

The diagram below shows a design using normal wheels that has all the versatility and manoeuvrability of a Mecanum design:

All the wheels are individually powered and can can indecently go backwards or forwards. (It is also designed so that each wheel can steered independently by plus or minus 90 degrees.) The performance is not the same as the Mecanum design, as in this design there would definitely be sliding and significant loss of efficiency due to friction. There would also be significant wear and tear of the ground surface and the tyres using this design, due to the sliding forces that are not present in the Mecanum design.