I always heard a 4 wheeled drivetrain(using only traction wheels) cannot turn if it is wider then it is long. I also know there’s a 2003 paper explaining the physics behind this but couldn’t find anything. can anyone here explain?
Do you mean “Why can’t a drivetrain turn if it is longer then it is wide?”
For an attempt at explanation:
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Hold your phone in portrait mode and set it down on a table in front of you. Rotate it clockwise. Notice how the 4 corners are dragged sideways more than they advance in the forward-back direction.
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Hold your phone in landscape mode and set it down on the table. Rotate it clockwise. Notice how the 4 corners advance in the forward-back direction more than they are dragged sideways.
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Consider how a wheel would prefer to move in the forward-back direction than to be dragged sideways.
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^What Nate said.
Also, look here. It was one of the original viral white papers on CD, back when that was a thing.
Abstract
Also, this is why drop centers and omni wheels on the corners are things.
Many years ago we made a robot (not for FIRST) that was really long and was only powered at the one end. At the other end we mounted omni wheels for easier turning but because there was so much weight over the omni wheels and not so much weight over the drive wheels, the drive wheels did not have enough friction and would spin. The other problem is that the rollers on the omni wheel also have some friction keeping them from rolling as easily making it harder for the drive wheels to do its job.
Technically you can make a long and narrow robot but you would need to use omni wheels on one side or all sides and the majority of your weight would need to be over your drive wheels. also your motors need enough power to turn it.
I can see how omni wheels help, but how would centerdrop solve this problem?
Center drop means one set of outside wheels have little to no traction. This effectively halves the wheel base making the robot easier to turn.
Fixed that for you Richard.
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halves
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If you want to break it down to a high school physics level, the length of your wheel base increases the moment arm (and thus the torque) of the frictional scrub you have to overcome in order to turn. FRC wheels (generally) have a very high coefficient of friction–compound that with a long moment arm, and you’re going to have to overcome a great deal of force in order to be able to turn…and the forward/backward traction available to overcome that force is limited by the same factor (the weight of the robot on the wheels) that is causing all that sideways friction.
Shorter wheel base = less moment arm for the scrub/friction.
Wider wheel base = larger moment arm for the traction.
Omnis and drop centers are both ways to address this issue, the former by eliminating scrub and the latter by shortening the effective wheel base while turning.
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A quick way to visualize this. An outline of a robot, with 2 wheels in each corner (dimensions 25x35). The circle intersects the middle of each wheel, and represents the path the wheel takes when the robot spins in place.
The dark black line on each robot shows a 45 degree difference. In the case of the robot on the left (a wide robot), this shows that the wheel travels “more forward than sideways” while turning. In the case of the robot on the right (a long robot), this shows that the wheel travels “more sideways than forward” while turning.
There’s no hard and fast rule i’m aware of (it depends a lot on the specific coefficient of friction between the carpet and the chosen wheel), but the more “forward than sideways” the wheel travels, the easier it is for the wheel to overcome the scrub and rotate.
Updated example for a long robot with a drop center below. In the first one, the center of gravity is significantly off-center, resulting in 4 wheels on the ground pretty much all the time. In the second, the center of gravity is centered, allowing the robot to rock back and forth as it turns, essentially letting it spin right on its center wheels. You can see how these circles change the relationship versus the long robot above - the first one has a slight advantage of “more forward than sideways”, while the second has essentially no sideways motion, as it’s tangent to the circle!
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With the center pair of wheels dropped, [at least] two of the wheels aren’t on the carpet at any given time. The wheelbase for turning purposes is therefore the distance between the center and either front or back wheels, not between the front and back wheels.
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FWIW - there’s a product out there called a “Skid Steer” with the configuration you mention. So named as the steering is accomplished by the wheels skidding laterally along the ground.
There is considerable design work to ensure the wheelbase is correctly dimensioned, and the center of mass remains nearly in the center of the wheelbase, even through the loading cycle.
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Center drop primarily solves the problem by changing the relative friction at each wheel. The improvement due to the change in effective wheel base only is secondary.
On a 4 wheel robot that has perfect 50/50 balance all 4 wheels will carry 25% of the weight and thus have equal friction. If the robot is not perfectly balanced say 60% front 40% rear then the front wheels would carry 30% each and the rears 20% each.
If we add the center drop wheel on a robot with 50/50 balance the center wheels will each carry 50% of the weight and the other 4 will carry 0%. Change the balance to 60/40 and now the center wheels will carry 40% each, the front wheels 10% each and the rears 0% each.
With a 60/40 weight distribution and 4 wheels the rears will have 2/3 the friction of the fronts while with a 6 wheel drop center the front will have 1/4 the friction of the center.
That means the frictional loss due to scrub goes way down on those front wheels, which is a good thing because total scrub increases on the front wheels. Meanwhile on the center wheels the frictional loss due to scrub increases but that is ok because the scrub goes down dramatically.
Of course that does not take the effects of acceleration into account which will change the individual wheel loading. Accelerate hard enough and that drop center robot with a forward weight bias will be resting on the center and rear wheels.
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