6WD Chassis Stiffness vs. Maneuverability

[kramarczyk]

A low CG certainly does help you withstand higher turning moments, but it does not help you generate them.

For those that have read Chris Hibner's whitepaper on turning (http://www.chiefdelphi.com/media/papers/1443), which is everybody I hope, it looks at the individual contribution of each wheel to the turning moment, so I suggest we start here. The moment is generated at each wheel by the coefficient of friction (CoF) and normal force (Fn) at each wheel. I think that the CoF is largely understood as demonstrated by the unusual wheel choices cited above. So what changes the Fn at each wheel? Simplifing the frame as a series of beams for discussion we can reference some stock solutions for the beams with 3 supports; based upon a uniform load the 3 moment equations show that the center axle would support 62.5% of the load with 18.75% for the outer axles. A snapshot of this eqn is in a previous post here.

[kramarczyk]

Originally Posted by kramarczyk

A low CG certainly does help you withstand higher turning moments, but it does not help you generate them.

For those that have read Chris Hibner's whitepaper on turning (http://www.chiefdelphi.com/media/papers/1443), which is everybody I hope, it looks at the individual contribution of each wheel to the turning moment, so I suggest we start here. The moment is generated at each wheel by the coefficient of friction (CoF) and normal force (Fn) at each wheel. I think that the CoF is largely understood as demonstrated by the unusual wheel choices cited above. So what changes the Fn at each wheel? Simplifying the frame as a series of beams for discussion we can reference some stock solutions for the beams with 3 supports; based upon a uniform load the 3 moment equations show that the center axle would support 62.5% of the load with 18.75% for the outer axles. A snapshot of this eqn is in a previous post here.

Apparently that got submitted early... whoops. To finish my point...

<theory>
When driving on concrete (or a similar surface) my observations have been that the chassis drives very similarly to how this distribution suggests, however, when we put them on carpet it can be very different. Many attribute this to the CoF change on the carpet, but I think that the Fn also changes as the carpet compresses under the bot like a spring. (See attached spreadsheet.) This is why lowering the center wheels improves the turning of a chassis. Yes, the center wheels can be lowered to the point of rocking, but my 3+ minutes of bot driving time suggest that rocking between 4x4 cg aft and 4x4 forward is not a pleasant experience. A lot of folk do manage it though and they are amazing.

So how does the stiffness of the frame play into this...

Assuming the carpet is spring 'like', the deflection of the frame limits the difference in deflection of the 'springs' under each wheel which eats into the wheel drop. The stiffer the frame, the less wheel drop lost.

In working terms, a stiffer frame requires less wheel drop to move the weight to the center than a less stiff frame. Consequentially a stiffer frame is also more greatly influenced by a change in wheel drop than a less stiff frame. i.e. a more flexible frame is more robust to wheel drop.

</theory>

Unfortunately, the situation is statically indeterminate so I don't have a set of equations to conduct an optimization study with.

[doukjin]

to improve maneuverablilty/decrease turning radius, our team [1002] has moved away from standard wheel setups and gone with 6WD, but with the middle two wheels offset by 1/16th of an inch from the other four wheels

this way at any given time, we have 4 wheels on the ground... usually... and one set of wheels 1/8th inch above the ground

you might not get the best results with this however though [as i said before] it does improve turning radius [and power expenditure for turns] considerably

[=Martin=Taylor=]

I'm not too good with numbers, but I've built a lot of prototypes....

I've discovered one important thing. The closer the traction wheels are oriented into a square the better the robot turns.

This is why 4 WD robots in the "long" configuration turn horribly. Because the wheels are in more of a rectangle than a square.

Many teams have solved this problem by adding another set of wheels in the center to essentially make their robot into two 4WD trains. As the robot tips back and forth the wheels remain in a square (all six are never touching the ground). I believe this is why 254 is so speedy.

Another way to correct this problem is to place two omni wheels on one end of the robot. Since the omni wheels offer no side-friction, the robot will turn just like a 4WD machine with all four wheels in the back of the robot.



We've always built robots with the rocking syle drive train.... and then gone back latter and added omni wheels

[Jonathan Norris]

I totally agree with JVN, ect. that say COG is the most important factor to a smooth driving 6-wheel drive. just try driving only your base drive system, it will drive like a dream, once you lump stuff on top and raise the COG it will never drive the same. comparing your robot this year to 1114, 254, etc. your COG is probably a good amount higher because of your scoring mechanism, thus leading to a tippier rougher driving robot.

[IKE]

Looks like we will have to run an experiment. I will do a tilt test to estimate actual CG height.

I really think that the poster talking about carpet stiffness vs. chassis stiffness is on to something. I think we will build an experimentally stiffened chassis.

NICKE/254? You said that you had to retread wheels daily on your middle and rear wheels. Was the tread-wear even? More on the inside? More on the outside? I do a little amateur racing and you can tell a lot from your tires...

[Cory]

Originally Posted by IKE

NICKE/254? You said that you had to retread wheels daily on your middle and rear wheels. Was the tread-wear even? More on the inside? More on the outside? I do a little amateur racing and you can tell a lot from your tires...

The outside wheels wore down probably 3-4 times faster than the inside, due to the left hand nature of the game.

[IKE]

Originally Posted by Cory

The outside wheels wore down probably 3-4 times faster than the inside, due to the left hand nature of the game.

Very interesting. Our inside traction wheel wore down the fastest. Just an observation.

[Mr. Lim]

I'd love to pick the brains of someone familiar with team 25s 6WD. If I recall correctly, they ran an extremely maneuverable 6WD totally chainless setup with no centre wheel drop whatsoever for a number of years. I'd bet someone there could tell us whether the secret to achieving this was through superior chassis stiffness.

[IKE]

25 was a 8WD chassis. They had a good article in the 1st Behind the Design book. I just read through the one for their 2007 chassis (2nd book), and it was limited but did remind me that they turn down the treads on their wheels and then carve a specific pattern. I would love to hear more if anyone from 25 is offereing up adivce/opinions.

kramarczyk-
Thanks again for posting that paper. It is a really good example and applies really well to a drop-center or rocker style 6WD. This paper really should be included in the KOP. While the overarll results seem more like common sense to most vetrans, many rookies don't have their machines running until someone helps them program it at their first competition. That is a horrible time to learn taht you have a dynamics issue.

[kramarczyk]

Originally Posted by IKE

kramarczyk-
Thanks again for posting that paper. It is a really good example and applies really well to a drop-center or rocker style 6WD. This paper really should be included in the KOP. While the overarll results seem more like common sense to most vetrans, many rookies don't have their machines running until someone helps them program it at their first competition. That is a horrible time to learn taht you have a dynamics issue.

I swear, that white paper is one of the best kept secrets out there. I did a spreadsheet to save some of the 4x4 users from the minutia of the math. http://www.chiefdelphi.com/media/papers/1917 I've got a beta version for 6x6, but got stuck on some of the issues we're discussing here.

[JesseK]

Originally Posted by kramarczyk

I swear, that white paper is one of the best kept secrets out there. I did a spreadsheet to save some of the 4x4 users from the minutia of the math. http://www.chiefdelphi.com/media/papers/1917 I've got a beta version for 6x6, but got stuck on some of the issues we're discussing here.

This is a good spreadsheet, but it assumes the center of mass, center of area, and all forces of the wheels are perfectly coplanar and are at a height of zero. It also assumes the center of mass is right/left centered on the bot, which sometimes isn't the case. Also, for a 6WD rocking chassis to rock, the CoM must break the vertical plane of the middle axle, which inherently assumes a CoM above the axles.

Since the act of rocking helps a turn anyways, perhaps the first iteration of an improvement to the spreadsheet could simply be to account for a three-dimensional CoM? Even turning in place, a CoM that isn't centered will cause each wheel to contribute a different turning moment. Then we could split the 6WD rocking chassis into two separate 4x4 arrangements with different CoM heights based upon the "default" and "rocked" states.

Of course, early in the build season we would have to estimate CoM height based upon desired manipulators (elevators, arms, etc), but later in the season for tweaking it can really help determine the best placement for mount points and heavy-component placement.

[IKE]

Here are some "tilt table" pics. By balancing the robot, the CG appears to be about 12 inches off of the floor centered side to side and for-aft. I measured this with the Ball in which adds about 7 lbs. 26 inches off of ground-line thus moving the CG up and forward a bit.

The math on this is pretty simple trig. Balancing the robot on various edges will give you planes that the CG is along. The intersections of these planes will then show where you CG is. The assumption there is that the "robot" is a rigid body and there are no large shifts in weight (i.e. fluids in a tank, or arms that flop around).

[Billfred]

In 2006, when I was still with 1293, we used the kitbot--stock ratios and all--feeding one IFI wheel in the center and Skyways on the corners. The videos I've seen all show us whipping around pretty hard, and we were quick enough to do our job (defense) effectively. It didn't get us into eliminations, but it was good enough to be the best finish the team has ever achieved in qualification rounds (before or since).

In 2007, I took the concept with me to 1618. This time, we used skinned-and-roughtopped AndyMark FIRST wheels, driven by a Gen2 AM Shifter using the big and small CIMs. We used the second speed to blitz across the field, important when stopping folks on the far side of the rack. Observation from off-season testing and Brunswick Eruption showed that this design was a little harder to turn. It doesn't like to turn in place, though it'll do it when you push it hard enough (as I found when one of the pre-rookies on 2458 about spun the numbers off of it at Brunswick Eruption).

This year, we switched to the AM Super Shifter with two CIMs per side for lack of the large CIMs. (And, truthfully, we would only have used other motors on drive if we really needed a CIM elsewhere.) Instead of roughtop, we used wedgetop cut with the long diamonds going around the wheel (as opposed to how IFI cuts theirs) for a little less CoF since we were flirting with the upper limits of current draw if we stalled a motor. (That was before we never got to a manipulator and weighed in south of 75 pounds.)

The more revolutionary change for us was riveting the frame together instead of using bolts. The result was the tightest frame I've ever had a hand in (well, excluding Bob in 2004 where we sent out the 2x4 aluminum of that year's kit to get welded together). The weight was slightly skewed towards the rear, with virtually nothing more than a foot off the ground. When driving both, I've found Speedy Debris to be a little easier to turn than Uppercut before it, though it may be a function of the 30-pound weight difference. An apples-to-apples comparison of bolted frames against riveted frames would be interesting.

[AdamHeard]

294's base for 2007 and 2008 (along with the 2007 summer prototype) were all extremely stiff by the nature of their design. All had 3/16" of center wheel drop, and were all very maneuverable (in the hands of a good driver; I didn't make the 2007 base look great). I hope this provides some anecdotal evidence for you.

I think your idea of stiffness changing the manueverability makes a great deal of sense.