pic: A mechanum wheel that shouldn't bump around at all.

[LLogan]

Originally Posted by exprg:melonhead

so what you are saying is that in order to to drive easily both forward and back, it would be best to have a good 45 degree?

A forty five degree angle makes the vectors of the straight and perpendicular motions equal (this should be obvious if you know basic trigonometry). That is why it is chosen by many teams as the angle for their rollers. It theoretically should make your strafing and forward motions equal. However... I do not think that's the case. There is just too much inefficiency in a mecanum drive system.

Changing the angles will change the vectors of the wheels. A smaller angle (assuming the maximum angle, 90 degrees, is just a roller mounted straight lengthwise) should theoretically give more strafing motion. Vice versa for a larger angle and forward/back motion.

[Ether]

Originally Posted by Formerly Famous

Now yes, yours made sense to. But there is no need to re-explain that which has been explained if it is now understood.

The kinematic matrix transformations were mentioned but not explained. You apparently know all about them but perhaps Justin does not and would be interested in learning.

Justin, if you are interested let me know and I'll start another thread.


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[Hawiian Cadder]

no, if the rollers are at 45 degrees, then the strafe speed is half of what the forward reverse speed is, because going forward, the wheels act like normal wheels, however when they are strafing, they are 2 vectors at 45 degree angles, so only half of the magnitude of the vector is in the direction of the strafe.

[LLogan]

Originally Posted by Hawiian Cadder

no, if the rollers are at 45 degrees, then the strafe speed is half of what the forward reverse speed is, because going forward, the wheels act like normal wheels, however when they are strafing, they are 2 vectors at 45 degree angles, so only half of the magnitude of the vector is in the direction of the strafe.

I do not think so. The resultant of the vectors is in the direction that they roll. There is no way that the magnitude of the vectors would be the forward/reverse vector because then the vectors that composed it would have to be at 45 degrees which would mean strafing motion would be impossible.

This is what the vectors of a mecanum wheel look like.

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

[Rion Atkinson]

Originally Posted by Hawiian Cadder

no, if the rollers are at 45 degrees, then the strafe speed is half of what the forward reverse speed is, because going forward, the wheels act like normal wheels, however when they are strafing, they are 2 vectors at 45 degree angles, so only half of the magnitude of the vector is in the direction of the strafe.

I knew something was sounding off... Thank you for clearing that up. Definitely will keep this in mind.

[Hawiian Cadder]

hmmmm, i know that it is less speedy/ powerful strafing than side to side though.

[AdamHeard]

Originally Posted by Ether

The kinematic matrix transformations were mentioned but not explained. You apparently know all about them but perhaps Justin does not and would be interested in learning.

Justin, if you are interested let me know and I'll start another thread.


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Can you please post your team number and location? You post a lot in a somewhat negative tone, which is easy to do when you have no fear of anyone associating you with a team.

[EricH]

Originally Posted by LLogan

I do not think so. The resultant of the vectors is in the direction that they roll. There is no way that the magnitude of the vectors would be the forward/reverse vector because then the vectors that composed it would have to be at 45 degrees which would mean strafing motion would be impossible.

This is what the vectors of a mecanum wheel look like.

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

Actually, there is a significant observable slowdown when side-to-side is run as compared to front and back. Part of this is due to friction and other inefficiencies (remember, two of the 4 wheels are running backwards); part of it is due to the vectors. I'm not exactly quite sure how that happens off the top of my head; I think Alan Anderson posted an explanation a while back.

Ether, I posted the part I think led Justin "astray"; namely the logical conclusion that if X< than Y, Z is more effective one way and X > Y, Z is more effective another way, therefore if X=Y, Z is optimized for both directions, and that he simply misstated what he meant. It's up to him to correct me if I'm wrong on that. (Also note that I'm in college, and I don't know/don't remember how to do a matrix transformation. I wouldn't be surprised if that reference confused a number of people. Some explanation may be in order, either in here or in another thread, as to a) what they are, b) how to do them, and c) why they apply here.)

[Ether]

A request was made for a more detailed explanation of my earlier post concerning kinematic analysis of a mecanum wheeled-robot, and the derivation of the inverse and forward transformation matrices.

I decided to start a new thread for this discussion in order not to divert the focus away from this thread's OP's intent.

http://www.chiefdelphi.com/forums/sh...51&postcount=1


The analysis answers many of the questions posted here about the effect of roller angle and whether fwd/rev vs strafe should be the same speed etc.



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[Joe Ross]

Originally Posted by AdamHeard

Can you please post your team number and location? You post a lot in a somewhat negative tone, which is easy to do when you have no fear of anyone associating you with a team.

He's from 2474 in Michigan.

[LLogan]

Originally Posted by EricH

Actually, there is a significant observable slowdown when side-to-side is run as compared to front and back. Part of this is due to friction and other inefficiencies (remember, two of the 4 wheels are running backwards); part of it is due to the vectors. I'm not exactly quite sure how that happens off the top of my head; I think Alan Anderson posted an explanation a while back.

Yes, I agree with you that there is a significant difference in the two motions. However, the bolded portion of your text is not entirely relevant to the inefficiencies of a mecanum system. Simple vector analysis shows that the strafing motion is theoretically equal to the forwards and backwards motions. The fact that two wheels are running backwards doesn't matter at all (unless you're talking about motor bias, but I don't think you are.). The forward/backwards vectors all theoretically cancel out and leave only the perpendicular vectors, which are, in magnitude, equal to the forward/backward vectors.

[EricH]

When running front-back, all 4 wheels are contributing "full power" in one direction. When running side-side, all 4 are contributing "full power" in another direction, but two of them have to work against the other two to do it. This will amplify any effects of friction and other inefficiencies that were masked by running all together.

The problem with theory is that it often leaves out reality. This is why engineers use safety factors and try to account for reality wherever they can. Theoretically, there is no friction and no inefficiency, and inefficiency (where it does exist) is uniform any way you look at it. In reality? Not only is there friction and inefficiency, but it's hard to give them a nice, easy number.

[Alan Anderson]

Originally Posted by EricH

When running front-back, all 4 wheels are contributing "full power" in one direction. When running side-side, all 4 are contributing "full power" in another direction, but two of them have to work against the other two to do it.

The left and right wheels are working "against" each other when running front-back, just as much as the front and back wheels are working "against" each other when running side-side.

The issue making the two directions act differently in the real world is the friction of the rollers. It helps in the forward direction, and hurts in the sideways direction. If you use sensors to maintain the same wheel speed, your front-back speed will be the same as your left-right speed. With non-frictionless rollers, though, you have to apply more power to maintain that speed when traveling sideways.

[LLogan]

Originally Posted by EricH

When running front-back, all 4 wheels are contributing "full power" in one direction. When running side-side, all 4 are contributing "full power" in another direction, but two of them have to work against the other two to do it. This will amplify any effects of friction and other inefficiencies that were masked by running all together.

The problem with theory is that it often leaves out reality. This is why engineers use safety factors and try to account for reality wherever they can. Theoretically, there is no friction and no inefficiency, and inefficiency (where it does exist) is uniform any way you look at it. In reality? Not only is there friction and inefficiency, but it's hard to give them a nice, easy number.

I think there has been a misunderstanding. I have never said that the front/back and strafing motions were equal realistically. I actually said the opposite, that the strafing motion is much less efficient than the forwards/backwards motion.

In the backwards/forwards motion, the wheels are still acting against each other. Simple vector analysis tells us that perpendicular components of each force vector cancel each other out. Vector analysis also tells us that the same exact thing happens in the strafing motion, however, this time, the backwards/forwards vectors are the ones that cancel each other out. The two motions have the exact same oppositions, just in different directions.

The only thing that I have been trying to prove is that each component of the force vectors on the wheels are theoretically exactly equal in magnitude. I have only been trying to prove that beliefs like this:

no, if the rollers are at 45 degrees, then the strafe speed is half of what the forward reverse speed is, because going forward, the wheels act like normal wheels, however when they are strafing, they are 2 vectors at 45 degree angles, so only half of the magnitude of the vector is in the direction of the strafe.

are not entirely correct.

Believe me, I understand the fine line between reality theory/inefficiencies. However, I'm just trying to say that the inefficiencies aren't caused by things you described. The only factor at work is the friction of the rollers. If you tighten each roller so that it no longer rolls, you will essentially have four "normal" traction, but you will no longer be able to strafe. This is because the omnidirectionality of mecanum wheels is dependent on the rollers "slipping". However, because there will never be a frictionless roller, the strafing motion will never be equal in force to the forward/backwards motion.

[Ether]

In the real world of aerospace engineering, systems engineers try to model friction and inefficiency as closely as possible when they are building dynamic models to allow them to build accurate procurement specs for suppliers. So theory does include friction and inefficiency.

Roller bearing friction plays a large and asymmetric role for mecanum wheels. In the fore/aft direction, roller bearing friction is a good thing. It moves the reaction force of the floor closer to the plane of the wheel, so it takes less reaction force for a given forward force. The result is better traction. For a frictionless roller bearing, the reaction force is aligned with the roller axis. As roller bearing friction increases from zero to locked roller, the reaction force moves from being aligned with the roller axis to lying in the plane of the wheel. When the reaction force lies in the plane of the wheel, that's essentially the same as a standard wheel. So, the reason a mecanum wheel doesn't have as much pushing force (in the fore/aft direction) as a standard wheel is not because there's less forward force available, but because the reaction force is larger than it would be for a standard wheel, and therefore the mecanum wheel starts to slip before a standard wheel would.

In the sideways direction, roller bearing friction moves the reaction force toward the plane of the wheel, which reduces the force vector component in the sideways direction. To compensate, the motor must output more torque. This increases the reaction force, which reduces available traction. So in the sideways direction, roller bearing friction is a bad thing. It causes increased motor power consumption (for a given desired force) and it reduces available traction.

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