Omni vs Mecanum CoF ?

[gpetilli]

I am looking at the differences between Omni-wheel drive (Killough) and Mecanum drive. I think I understand the cos(45) difference in forward torque and corresponding difference in velocity. I propose that rotating the Omni-wheel could be modeled as a wheel with radius of 1/cos(45) and if this larger wheel Omni-wheel was geared for the same maximum velocity, the available torque would be the same as the original mecanum wheel.

The discussions to date have suggested that there is a relative loss of available traction for the omni-wheel system since the torque of the wheel to the carpet is sqrt(2)/2 larger and will brake traction sooner than the mecanum wheel. Looking at the AndyMark specs for their wheels the Coefficient of Friction for the 6" Omni-wheel is 1.0 where as the CoF for the 6" mecanum is 0.7 F&R - the same sqrt(2)/2 ratio!!! For strafe, the mecanum CoF is only 0.6 which is additional sqrt(2)/2 loss (which I believe is expected).

From a practical standpoint, it would appear that there is no traction advantage for macanum over Omni-wheel drive with the wheels available to FRC. Assuming AndyMark uses the same rubber for both wheels, does this suggest that mecanum drive has the same theoretical loss of traction as Omni-wheel drive? Can anyone explain or dispute these observations? I know that swerve does not suffer from these losses, so lets keep the dialog limited to Omni-drive vs. mecanum drive.

[Chris is me]

I think you're right. In a 45 degree omni drive you can model the wheel as if it were a bigger diameter which explains a lot of the speed and torque phenomena.

Just subjectively it seems like mecanum platforms tend to do a better job of resisting motion, but not by much. I think it's just easier to spin omni drives into a position favorable for pushing.

[Ether]

Originally Posted by gpetilli

[does] mecanum drive [have] the same theoretical loss of traction as Omni-wheel drive

Yes.

Look at Figure1 on Page2 of this document.

You will see that the ratio of forward motive force to traction force is the same for both omni and mec:

mec: (tau/r)/(tau*sqrt(2)/r) = 1/sqrt(2)

omni: (tau/(r*sqrt(2)))/(tau/r) = 1/sqrt(2)

[Oblarg]

One thing to keep in mind is that in the omni-drive, rollers will be turning when you are moving forward or backward. In the mecanum drive, they will not. Whenever the rollers turn, you have non-negligible frictional losses - in fact, if you work out the geometry, you'll see that frictional losses in the spinning of the rollers is the only reason that mecanums strafe slower than their forward/backward movement.

[Ether]

Originally Posted by Oblarg

One thing to keep in mind is that in the omni-drive, rollers will be turning when you are moving forward or backward. In the mecanum drive, they will not.

Assuming "perfect" omni & mec and floor surface, that is true.

However, due to roller axial free play and carpet compliance there will be some motion of the mec rollers, even in the forward direction.

Whenever the rollers turn, you have non-negligible frictional losses - in fact, if you work out the geometry, you'll see that frictional losses in the spinning of the rollers is the only reason that mecanums strafe slower than their forward/backward movement.

In the strafe direction, those frictional forces in the mec rollers require more torque to be applied to the wheel in order to get the same motive torque. This causes increased losses due to carpet stretching, compared to the forward direction. See Page4 of this document.

[gpetilli]

Originally Posted by Oblarg

One thing to keep in mind is that in the omni-drive, rollers will be turning when you are moving forward or backward. In the mecanum drive, they will not. Whenever the rollers turn, you have non-negligible frictional losses - in fact, if you work out the geometry, you'll see that frictional losses in the spinning of the rollers is the only reason that mecanums strafe slower than their forward/backward movement.

Agreed, that does contribute to the forward vs. strafe for mecanum. I don't see the connection to why the mecanum CoF is apparently lower than equivalent Omni in forward.

[Ether]

Originally Posted by gpetilli

Looking at the AndyMark specs for their wheels the Coefficient of Friction for the 6" Omni-wheel is 1.0 where as the CoF for the 6" mecanum is 0.7

Originally Posted by gpetilli

I don't see the connection to why the mecanum CoF is apparently lower than equivalent Omni in forward.

The numbers don't mean anything if you don't know how the tests were conducted.

I suspect the 1.0 number for the omni was tested in the plane of the wheel, not at a 45 degree angle. Someone from AM please correct me if this is not true (I'm sure AM posted their test procedure somewhere but I can't find at right now).

[gpetilli]

Originally Posted by Ether

Yes.

Look at Figure1 on Page2 of this document.

You will see that the ratio of forward motive force to traction force is the same for both omni and mec:

mec: (tau/r)/(tau*sqrt(2)/r) = 1/sqrt(2)

omni: (tau/(r*sqrt(2)))/(tau/r) = 1/sqrt(2)

Okay, so then if I increase the gear ratio by sqrt(2)/2 to increase the available torque for the Omni-wheel drive, it should match the pushing force and traction of the mecanum (minus larger friction loss of rollers for Omni). That leaves the major advantage of mecanum as the mechanical mounting being square. Omni has the advantage of lower weight, cost and complexity.

Do we assume that AndyMark included the sqrt(2)/2 in the CoF specification or is there a difference in materials? IFI reports CoF of 1.1 for Omni-wheels and 1.0 for mecanum - still an difference, but not the magic ratio.

That said, I have one extra design variable available with Omni-wheels because I am not locked into 45deg mounting by the wheel manufactures. If I build an asymmetric Killough with wheels at 30deg, I get 22% more forward torque and traction (0.866 vs. 0.707) than can be achieved with mecanum. Am I missing something here? Of course this comes at a price, I get 0.5 vs. 0.707 = 30% less side torque and traction. More forward traction is highly desirable for better forward acceleration. Having even poor staffing capability has benefits over KOP 6-wheel tank drive, if the other tradeoffs can be managed.

[gpetilli]

Originally Posted by Ether

The numbers don't mean anything if you don't know how the tests were conducted.

I suspect the 1.0 number for the omni was tested in the plane of the wheel, not at a 45 degree angle. Someone from AM please correct me if this is not true (I'm sure AM posted their test procedure somewhere but I can't find at right now).

AndyMark is good about posting forward vs. side for their wheels, so I believe that the CoF comparison is valid (never expected it tested at 45deg). What I was less sure of is that the CoF measurement would have exhibited the sqrt(2)/2, but I believe your diagram predicts that it would. IFI does not report forward vs. side for their mecanum and given the similarity in CoF to the Omni, I am highly suspicious that they are reporting the CoF for the roller material, not the wheel assembly.

[Ether]

Originally Posted by gpetilli

Okay, so then if I increase the gear ratio by sqrt(2)/2 to increase the available torque for the Omni-wheel drive, it should match the pushing force and traction of the mecanum

To a first approximation. Keep in mind that friction in the rollers reduces the available forward pushing force of omni, but increases the available forward pushing force of mec: roller friction causes an omni to lose traction but causes a mec to gain traction (in the forward direction). See the second-to-last paragraph on Page3 of this document.

If I build an asymmetric Killough with wheels at 30deg, I get 22% more forward torque and traction (0.866 vs. 0.707)

Decreasing the toe-in angle of omni indeed increases the forward force (for a given wheel torque), and the available traction.

[Oblarg]

Originally Posted by gpetilli

More forward traction is highly desirable for better forward acceleration.

I believe free acceleration (i.e. not pushing against another robot) is almost never traction-limited in FRC; you'll pretty much only ever slip your wheels if you gun it from a dead-stop, and only for a few fractions of a second.

I did some crude calculations recently, and found that for a 150lb, 4-CIM robot with a wheel CoF of about 1, you are traction-limited at a dead-stop for any gearing below ~12 feet/second.

So, if we have a mecanum geared for 12 feet/second, then, which is a pretty standard gearing, we'll only be traction-limited until our motor torque drops to ~70% of stall torque, which corresponds to ~30% of top speed.

With this in mind, I don't think you're going to see all that much practical change in your acceleration with increased CoF.

[JVN]

Originally Posted by gpetilli

AndyMark is good about posting forward vs. side for their wheels, so I believe that the CoF comparison is valid (never expected it tested at 45deg). What I was less sure of is that the CoF measurement would have exhibited the sqrt(2)/2, but I believe your diagram predicts that it would. IFI does not report forward vs. side for their mecanum and given the similarity in CoF to the Omni, I am highly suspicious that they are reporting the CoF for the roller material, not the wheel assembly.

We report CoF for an overall drive assembly, weighted to 150 lbs (120 lb robot + 14 lb battery + 20 lb bumpers = 154 lbs). In this way, we are reporting the average CoF of a drive train "in application."

These tests were done with locked wheels (not locked rollers) using the tilted incline method (which we believe allows for greater accuracy than the pull test method).

[gpetilli]

Originally Posted by JVN

We report CoF for an overall drive assembly, weighted to 150 lbs (120 lb robot + 14 lb battery + 20 lb bumpers = 154 lbs). In this way, we are reporting the average CoF of a drive train "in application."

These tests were done with locked wheels (not locked rollers) using the tilted incline method (which we believe allows for greater accuracy than the pull test method).

Thanks John for the quick reply. That helps clarify things, and I agree that incline method is best.

Would I be possible to update the specifications with the side CoF for your wheels? It would help greatly with part selection verses other vendors. Is there a good way for measuring dynamic CoF? I am simply assuming 85% of static.

BTW: we just received shipment of 4 VEXpro 6" Omnis and we were very impressed with the design and build quality. Assuming the 2014 game is appropriate, we intend to use them for an asymmetric Killough drive.

[Ether]

Originally Posted by Oblarg

I did some crude calculations recently, and found that for a 150lb, 4-CIM robot with a wheel CoF of about 1, you are traction-limited at a dead-stop for any gearing below ~12 feet/second.

Would you mind posting your calculation please?

[JVN]

Originally Posted by gpetilli

Thanks John for the quick reply. That helps clarify things, and I agree that incline method is best.

Would I be possible to update the specifications with the side CoF for your wheels? It would help greatly with part selection verses other vendors. Is there a good way for measuring dynamic CoF? I am simply assuming 85% of static.

BTW: we just received shipment of 4 VEXpro 6" Omnis and we were very impressed with the design and build quality. Assuming the 2014 game is appropriate, we intend to use them for an asymmetric Killough drive.

I will look into posting the sideways CoF. I don't believe we tested that when we did our experimentation last year.

Our omni directional wheels should have very very low CoF Side-Side, since we're pretty happy with how freely the rollers spin.

Unless I'm missing something, using the locked-wheel test, shouldn't the Mecanum Side-Side be identical to front-back? (Isn't that the simplifying virtue of a 45-degree angle?)

Regarding a method to measure dynamic CoF -- one method I've used in the past is:
Get the robot sliding, using the incline test. Slowly reduce the amount of tilt until it stops moving. Measure the angle and calculate like normal.

Out of curiosity -- what sort of design are you doing for FRC which requires dynamic CoF?