Spinning the Robot with Mecanum Wheels

[craigboez]

Here's a question: if you mount your wheels in a square configuration (ie, your wheelbase = your track), is it possible to rotate your bot about center?

[Alan Anderson]

Originally Posted by craigboez

Here's a question: if you mount your wheels in a square configuration (ie, your wheelbase = your track), is it possible to rotate your bot about center?

Yes. It'll actually work best that way.

(...unless you have your wheels swapped, in which case it won't be able to rotate itself at all.)

[craigboez]

Originally Posted by Alan Anderson

Yes. It'll actually work best that way.

(...unless you have your wheels swapped, in which case it won't be able to rotate itself at all.)

For wheels mounted in the correct configuration, I don't think that it's possible to rotate a bot about center if they are mounted in a square configuration. When summing moments about center they all cancel out when length = width. Only when you have a rectangular bot, where length != width, can you create one pair of moments not offset by the other pair.

This seems to be unconventional thinking, and I can't seem to find anywhere on CD that this has ever been stated. Am I missing something? Would anyone be willing to provide a vector analysis of a square 'bot rotating about center?

(It can be done using four identical wheels, but thats not what I'm after. Two "RH" and two "LH" wheels, mounted in an "O" configuration, cannot seem to create a moment about the center of a square bot).

[Ether]

Originally Posted by craigboez

For wheels mounted in the correct configuration, I don't think that it's possible to rotate a bot about center if they are mounted in a square configuration. When summing moments about center they all cancel out when length = width. Only when you have a rectangular bot, where length != width, can you create one pair of moments not offset by the other pair.

This seems to be unconventional thinking, and I can't seem to find anywhere on CD that this has ever been stated. Am I missing something? Would anyone be willing to provide a vector analysis of a square 'bot rotating about center?

(It can be done using four identical wheels, but thats not what I'm after. Two "RH" and two "LH" wheels, mounted in an "O" configuration, cannot seem to create a moment about the center of a square bot).

Consider a bot with 4 mecanum wheels mounted so that they have the "X" configuration when viewed from the top. Now drive both wheels on the left side forward, and both wheels on the right side backward, all at the same speed.

The front left wheel will be pulling forward and to the right. The rear left wheel will be pulling forward and to the left. The front right wheel will be pulling backward and to the right. The rear right wheel will be pulling backward and to the left. So, all 8 force vectors are pulling CLOCKWISE. The vectors do not cancel, they add. So the bot spins clockwise.


~

[Matt H.]

Specifically, I believe that when you're summing moments (R x F) you are forgetting to include make R negative in one direction.

[Ether]

Originally Posted by Matt H.

Specifically, I believe that when you're summing moments (R x F) you are forgetting to include make R negative in one direction.

Hi Matt,

the pronoun "you" is ambiguous.

which post were you responding to? craigboez or me?



~

[Matt H.]

Originally Posted by Ether

Hi Matt,

the pronoun "you" is ambiguous.

which post were you responding to? craigboez or me?



~

I was responding to craigboez's post.
Sorry about the ambiguity.

[Ether]

Originally Posted by craigboez

Would anyone be willing to provide a vector analysis of a square 'bot rotating about center?

Hi Craig,

Take a look at this PDF:

http://lib.store.yahoo.net/lib/yhst-...lSpecSheet.pdf

It has a force-vector diagram and complete explanation for all three degrees of freedom: fwd/rev, slide left/right, spin CW/CCW

To spin in place clockwise, wheels 1 and 3 should be driven forward while wheels 2 and 4 are being driven backward. If you do this, the force vectors on each of the 4 wheels will produce torque moments about the center of the wheel pattern all in the clockwise direction. They do not cancel, they add.



~

[Ether]

Originally Posted by craigboez

For wheels mounted in the correct configuration, I don't think that it's possible to rotate a bot about center if they are mounted in a square configuration.

Two "RH" and two "LH" wheels, mounted in an "O" configuration, cannot seem to create a moment about the center of a square bot).

The correct configuration is a "X" configuration when viewed from the top of the bot, which is the same as an "O" configuration when viewed from the bottom of the bot. In other words, if you have a bot with the wheels mounted in an "X" configuration when viewed from the top, and you tip the bot on its side and view it from the bottom, it will appear as an "O" configuration.

If your wheel configuration looks like an "O" when viewed from the TOP, it is not the correct configuration, and the bot will not spin properly.


For those of you new to this discussion, here's what we mean by "X" and "O" configurations:

"X" configuration:

\..../
......
......
/....\


"O" configuration:

/....\
.......
.......
\..../




~

[craigboez]

Thanks to all for your input. The fact that the wheels, when viewed from above are different from the wheels when viewed from below was the big aha! moment here. Thanks especially to Ether for the in depth explanation - I have now seen the light.

[Teammax]

Originally Posted by craigboez

Thanks to all for your input. The fact that the wheels, when viewed from above are different from the wheels when viewed from below was the big aha! moment here. Thanks especially to Ether for the in depth explanation - I have now seen the light.

It is kind of funny because now that I understand the problem I see the answer posted in many places.

[Joe Johnson]

Originally Posted by Ether

The correct configuration is a "X" configuration when viewed from the top of the bot, which is the same as an "O" configuration when viewed from the bottom of the bot. In other words, if you have a bot with the wheels mounted in an "X" configuration when viewed from the top, and you tip the bot on its side and view it from the bottom, it will appear as an "O" configuration.

If your wheel configuration looks like an "O" when viewed from the TOP, it is not the correct configuration, and the bot will not spin properly.


For those of you new to this discussion, here's what we mean by "X" and "O" configurations:

"X" configuration:

\..../
......
......
/....\


"O" configuration:

/....\
.......
.......
\..../




~

First off, nice ascii art. Good description of the problem as well.

I have been lurking on this thread for a while, but I kept quiet because I didn't really have anything worth adding... ...until now.

When this issue was first introduced in my mind as a potential problem, I had to think about which way I would orient the wheels if nobody told me the answer and I hadn't yet done the experiment. Sadly, I got it wrong. My first thought was to say that I wanted the wheels on the ground in the X position.

My reasoning went like this: I wanted the small wheels oriented such that it would make it easy to spin the robot about its center. An X seems to provide this feature. And it is true as far as it goes -- if you have the wheels in an X configuration and you lock the main axle of the wheels (i.e. turn the motors off), you should be able to spin the robot about its center fairly easily.

BUT... ...then I thought, "What is going to provide that spinning force?"

Well... ...it is SUPPOSED to be the motors driving the main axles of the wheels, of course.

BUT, the way Mecanums work is that they only apply force to the ground in the direction of the axles of those little wheels (the same can be said for holonomic wheels, by the way).

Now that X configuration is a disaster because all the wheel force vectors go right through the center (or very near the center) of the robot!

Torque is force times moment arm: Small moment arms => small torques.

Even if the wheels are putting out largish traction forces, that force is multiplied by as small moment arm. The net result is a robot that has issues spinning about its center.

So... when it comes to Mecanums the O is the way to go.

Cheers,
Joe J.

[pedro696]

What powerpoint did you use. could you post a link?