paper: Mecanum: we can't even agree on pronunciation?

[lcoreyl]

Thread created automatically to discuss a document in CD-Media.

Mecanum: we can't even agree on pronunciation? by lcoreyl

[lcoreyl]

This paper was worked on during and after LogoMotion, and the intent was to be posted by Dec 2011 so people could read and discuss before the season. we didn't quite finish everything*; however, we've already seen a lot of mecanum debate happening and would rather have this out there now...

now we can have 1 non-game specific thread devoted to heated mecanum debate!!



*Nightmare Robotics is becoming ironic, although we're trying to turn the corner. We'd like to be more like Team HOT, and less Team HOT MESS.

[lcoreyl]

for rev2:

Missed the swedish pronunciation group's interjection on mecanum; I guess Andy Baker loses on this one!

http://www.youtube.com/watch?v=XJ5SDmRpTyU

[StevenB]

Since I've been one of the people apparently spreading misinformation, please help me work through this. The part I have trouble with is this statement:

Originally Posted by Ether

A mecanum wheel generates 41% more driving force than an omni wheel driven by the same torque

Suppose I have robot with four omniwheels mounted diagonally on the corners. To strafe diagonally, two of the wheels drive, and the rollers on the other two spin freely. In this direction, the driving omniwheels act exactly like solid wheels, since motion is parallel to the roller axis. Applying a torque of "1" to these wheels should produce a force on the robot of "1".

If a mecanum drive robot is strafing diagonally, again, two of the wheels drive, and the rollers on the other two spin freely. If the statement above is true, then applying the same torque of "1" will produce a force on the robot of 1.414. This would all make sense if the mecanum wheel had a smaller effective radius (specifically, 1.414 * pi * r). That's precisely what I see in your video with the 8" kit wheel and 8" mecanum, but it's not what I'm reading in your document. What have I missed?

PS - I may have missed something in your document, since I don't have Word and the diagrams are showing up all garbled. Any chance you could post a PDF?

[lcoreyl]

Originally Posted by StevenB

Since I've been one of the people apparently spreading misinformation, please help me work through this.

First off, Kudos for being open to changing your mind. I believe Einstein has a quote about that...

The part I have trouble with is this statement: A mecanum wheel generates 41% more driving force than an omni wheel driven by the same torque

The example you talk about jumps to a more complex application of the statement you quoted. First let's start with a few simpler steps and you can stop me if you disagree with them:

1a) 1 mecanum wheel translates torque to a force 45 degrees from the plane of the wheel
1b) 1 omni wheel translates torque to a force parallel to the plane of the wheel (same as a regular wheel)

2) actually, before step 2 I think I'll get a pdf put up since the wheel pictures are important.

PS - I may have missed something in your document, since I don't have Word and the diagrams are showing up all garbled. Any chance you could post a PDF?

Working on that now...

[lcoreyl]

Originally Posted by StevenB

Any chance you could post a PDF?

Done.

No one should take the timing of completing this request as any sort of indication of future speed

[StevenB]

Originally Posted by lcoreyl

1a) 1 mecanum wheel translates torque to a force 45 degrees from the plane of the wheel
1b) 1 omni wheel translates torque to a force parallel to the plane of the wheel (same as a regular wheel)

Yep, makes sense.

The top half of page 4 makes sense. I get lost on the bold section:

This would imply that a mecanum wheel creates MORE force than the same size regular wheel. You could even put a regular wheel in contact with the mecanum wheel but at a 45 degree angle to increase the amount of torque. Since they are the same diameter wheel you get more torque at the same angular speed which equals more power.

What is the "this" being referenced? Are you proposing that this statement is true or false?

[lcoreyl]

Originally Posted by StevenB

Yep, makes sense.

The top half of page 4 makes sense. I get lost on the bold section:

What is the "this" being referenced? Are you proposing that this statement is true or false?

I'm assuming you are talking about the italic bold part. This was supposed to be interpreted as a 2nd voice that the paper is trying to persuade. After reading your post and re-reading the section I agree it is poorly connected to the previous part (sorry). the "this" you referenced should read:

ThisA force of 10lbs in the plane of the wheel would imply that a mecanum wheel creates MORE force than the same size regular wheel. You could even put a regular wheel in contact with the mecanum wheel but at a 45 degree angle to increase the amount of torque. Since they are the same diameter wheel you get more torque at the same angular speed which equals more power.

Let me try and re-state and see if that helps:
if 2 identical motors put out identical torque to 2 wheels of the same diameter, but 1 is mecanum, then the mecanum wheel translates this identical torque to a larger force than the regular wheel. If you mount them as stated this larger mecanum force would translate to the regular wheel. If the regular wheel is then put in contact with the floor, the REGULAR wheel would now be translating the larger force to the floor.
(so far all correct--here is the incorrect parts in italics)
Since both wheels have the same radius, they will rotate at the same speed. More force at the same speed equals more power

clear as mud now??

***because of these problems I've just updated to rev3 and added another picture

[StevenB]

Ok, I buy that. A mecanum wheel produces more force where the rubber meets the carpet, but at the same total power. 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.

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?

[lcoreyl]

(note that all of the discussion below is assuming the robots are driving forward)

Originally Posted by StevenB

Ok, I buy that. A mecanum wheel produces more force where the rubber meets the carpet, but at the same total power.

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.

(emphasis mine)
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

[lcoreyl]

Originally Posted by StevenB

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?

If you replace the "r" by "r/√2" in the equation for the omni force F shown in the bottom left of Figure2 on Page 3 of this document:

http://www.chiefdelphi.com/media/papers/download/2740

... you get the same force F as shown for the mecanum in the same figure on the bottom right.


Also, if you look at this document:

http://www.chiefdelphi.com/media/papers/download/2731

... and replace "r" with "r/√2" in all the expressions in the "omni" column, you will see that they all match the "mecanum" column.

Who said math isn't fun?

[StevenB]

I get it now. It took a couple hours of staring at Ether's equations and drawing diagrams, but it makes sense. Here was the breakthrough for me: a mecanum drive is identical to a 4-wheel omni killough/kiwi drive with smaller wheels. I've always considered this drive in terms of force, but never thought through it in terms of speed.

Compared to a traditional drive with equal-diameter wheels, an omni drive can only exert between 71% of the force going forward, due to the force vectors cancelling. But it goes 41% faster, since the wheels are moving forward while the rollers slide. The power remains the same. Make the wheels 41% smaller, and now it goes the same speed and has the same force as a traditional drive.


I get it.
Now time to get some sleep - since I don't have a robot to build like the rest of y'all.