Per wiki, Killough is the same concept but without using omni wheels.

Killough is the proper name, but I was under the impression that killough was without omniwheels

Mecanum wheels are also known as Ilon wheels after their inventor, not the company he worked for.

Maybe instead of calling them all these incorrect things we should just stop talking about them altogether.

"Meh"canum

Another difference which has not been noted here between Mecanum and what OP refers to as PMM: With the same motors, gearing, and wheel size, Mecanum accelerates 41% better than PMM, while PMM has a 41% higher free speed than Mecanum.

The big advantage of Mecanum over PMM, imho is that (now that both omni and mecanum wheels are available as COTS items), construction of the mecanum chassis is much easier; there is no need for any 45° chassis members. The KoP drivetrain actually has mount points for four TB-micro to support mecanum. You could also build a chassis using versaframe or WCP COTS components without any 45° gussets to be mecanum.

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A wrinkle on PMM I experimented with a couple of years ago is one I called Pakuni Drive†, named after the simian aliens from *Land of the Lost* and their attribute of walking forwards like humans, but running sideways like my little brother Vernon when he was 18 months old. The idea is that I toed in the wheels ~22.5° rather than 45°. (It turns out that the acute angle on a 5-12-13 right triangle is closer to 22.62°, so that’s what I really did.) Anyway, this gives a forward acceleration which is 2.4x better in the forward direction than the lateral (strafe) direction, but a free speed which is 2.4x better in the lateral. My intention was to start the robot accelerating in the “forward” direction, then rotate the robot 90 degrees to “shift” to a speed 2.4x as fast for longer (cross-field) runs. My attempts with an arduino and no gyro or other feedback nor radio input were unsuccessful, so I’m putting the concept out there in case anyone wants to try this with better control systems.

† My earlier name for this before inspiration hit was roto-shifter, as will be explained in later sentences.

If you really want to be accurate with your acronyms, both mecanum and PMM are subclasses of NPP* drive

[*] not participating [in] playoffs

*coughcough1986coughcough*

understandable.

with PMM/ x drive, there is never a point where all motors are running in the same direction, which makes it slower in most cases. Mecanum can have all four motors run forward and backward with it going at its full speed. The frame setup for an x drive is also more complex.

1986 is by no means a normal mecanum, no matter how you slice it.

492 the same year on the other hand…

I’m not sure what you mean by this. To go forward, they all rotate in the forward direction. To go left, they all rotate in the left direction. If you mean direction based on looking at them from the outside (or inside), then they all go in the same direction when rotating in place, same as mecanum and skid steer.

I think he’s trying to point out how, from above, two wheels have to go diagonally left and two diagonally right to drive forward.

^ This. This makes PMM/X drive fundamentally slower and weaker than mecanum in that direction

X drive is weaker, but sqrt(2) times as fast. To picture this, imagine two tank drives moving along the X and y axes away from the origin at 1 m/s. The fourth point of the rectangle formed by these drives and the origin represents the X-drive, which is moving in each direction at 1 m/s and thus has a vector speed of sqrt(2) m/s.

Mecanum is theoretically the same.

Note that the sqrt(2) factor increase in speed leads to a similar reduction in force.

isn’t the speed sqrt2/2? the vector in the direction that the motor is going in is 1, so the x and y axis speeds should be sqrt2/2. and the same applies for mecanum, but only when strafing. the speed going directly forwards and backwards is still 1, since the vectors are all pointing in the same direction. The same idea can be applied to the amount of force, so there is a reduction in force.

Your explanation is paradoxical- if both were divided by a factor of sqrt(2) (which is the same thing as being multiplied by a factor of sqrt(2)/2) then the total power (speed times torque) is reduced by a total factor of 2. Where did this energy go? We are assuming perfect efficiency.

My high school physics teacher had a mantra that continues to carry me through these types of problems. **Perpendicular vectors are independent.**

Let’s consider relative speeds of two drives, each geared at 1 ft/s.

Each pink vector moves at 1 ft/s. On the tank drive, we average these vectors to get the net speed which is 1 ft/s in the direction of the y=x line (45 degrees). Or, <sqrt(2)/2, sqrt(2)/2>

For the x-drive, each wheel spins at 1 ft/s *without impacting the speed of the other wheel*. So when we average these vectors, we get (<1, 0> (top wheel) + <1, 0> (bottom wheel)) / 2 = <1, 0> in the x direction, and similar for the Y direction. So we have a net speed of <1, 1>, or exactly sqrt(2) times the speed of the tank drive in this specific orientation.

Now consider force. Let’s say each wheel of the drivetrain contributes 32.5 lbf of force. We are in a pushing match here. The tank drivetrain has 150 total lbf in the vector direction <-sqrt(2)/2, -sqrt(2)/2> for a vector force of <106, 106>. The x-drive has a total force of 75 lbf in each direction, for a vector force of <75, 75>. The magnitude of this force vector is 106 lbf- exactly sqrt(2)/2 times the magnitude of the tank drive’s force.

And finally, because it’s all really just math until you test it, here is empirical evidence that an x-drive is faster than a tank drive in the robot-forward direction.

Edit: I didn’t cover mecanum, but the math for this is exactly the same as the x-drive, just with fancy wheels. The rollers are the exact same.

I’d like to point out that you can ignore all these computations if you stick to a sensible drive train.

^^ This, as I stated back in post 17 - assuming weaker refers to acceleration, “as fast” refers to free speed, and only left/right/forward/reverse travel are considered.

Given the same motors, same gear ratio, and same wheel diameter, X drive is effectively geared √2 faster than mecanum for forward/reverse/left/right travel. For an apples-to-apples comparison, let us consider wheels of 8 inch diameter (or for simplicity, 25/π inches in diameter which is about 7.96").

Let’s rotate all of the mecanum wheels one rotation in the forward direction. None of the rollers are required to actually roll, and the robot moves forward 25 inches.

Let’s rotate all of the 4WK/X-drive/PMM wheels one rotation in the forward direction. For illustration, I’ll describe what happens to the left front wheel. As the wheel has rollers in the direction parallel to the drive axle, and assuming the robot does not rotate, the position, **based on this one wheel**, is completely indeterminate in the left/front - right/rear (45 degree bias) direction. Just based on this one wheel, we know that the wheel will travel 25 inches in the right/front (45 degree bias) direction, and an indeterminate amount in the left/front - right/rear (45 degree bias) direction.

However, as we have rolled all wheels in the “forward” direction, the robot will (in the ideal case) translate forward with no rotation. This means that each wheel will travel in the forward direction. The only place that the left front wheel can end up and meet both conditions is 25"√2 (~35.35)" forward of its origonal position.

The same logic applies to all four wheels - the X-drive robot will travel √2 times as fast in the forward direction per wheel revolution than the mecanum. Extension to left/right is also not very difficult, and assuming good rollers, it will come out the same.

What is interesting is when you look at travel on the bias. When accelerating or traveling on a 45 degree bias, the same considerations show that the X drive accelerates √2 times faster than the Mecanum, but the Mecanum has a free speed √2 times as fast as the X drive.

Either way, you don’t get something for nothing.

^ I don’t use x drive, used mecanum once, but the computations don’t seem hard, its just I don’t touch them