Posted by Dodd Stacy at 1/25/2001 10:27 PM EST
Engineer on team #95, Lebanon Robotics Team, from Lebanon High School and CRREL/CREARE.
In Reply to: Re: Lots of Wheels and F = u x N
Posted by Ernie P on 1/25/2001 5:18 PM EST:
F = u x N is the MAXIMUM force that can be developed between the robot and the floor, parallel to the floor, before the wheels slip. Hook a spring scale to your dead robot and drag it over the carpet, and that tells you what “u” (mu) is, using the entire weight (m x g) of your robot as “N.”
Now, are you able to exploit this MAXIMUM possible horizontal force for propulsion? Depends. Is any of the robot’s weight being supported by wheels which are not powered by the motors? If the answer is yes (eg: 2 wheel drive, 4 wheels on the ground), then the maximum PROPULSION force you can deliver to the ground is limited to F = u x Ndw, where “Ndw” is the weight carried by the drive wheels. Unpowered wheels that help support or balance the robot cannot develop propulsion force. Powering all the wheels that carry the robot’s weight is how you guarantee that you produce as much propulsion force as possible. This is why people use 4 wheel drive.
(This is especially important when robots reach out and pick up a weight, such as lifting a goal off the ground. The robot’s wheels now support the weight of the robot and the goal, and the wheels closer to the goal will bear a lot more weight than the wheels at the other end. (It might even tip over!) The robot has more total weight that it has to drive around or climb up the bridge with. Which wheels are powered? Which ones should be powered? If ALL the wheels are powered, we know that we aren’t wasting any possibility of delivering the maximum PROPULSION force.)
OK, so why have 356,215,492 wheels (actually, I think 6 is the maximum I’ve seen suggested)? Dodd is saying that 4 powered wheels (3, actually) would support any kind of weight (till it tipped over - other physics) and not waste any available PROPULSION force. What’s this 6 stuff? What’s wrong with 4 wheel drive (or 3)?
Errr, sorry, gotta steer. Joe and others (us too!) like to turn the wheels, swerve, swoop, holonomically omni-navigate, etc. You can, too, next year (or later) if you’re masochistic enough (or worse). For now, here’s the deal. Imagine steering the bot as rotating without moving forward or backward. That’s tank steering, skid steering. For reasons not important here, the bot tends to steer/rotate around its center of mass, which is probably near the middle of the bot.
Look at your poor 4 wheel drive bot. You’re driving the right side wheels forward and your left side wheels backwards to turn/rotate left. The two front wheels are sliding directly to the left and the two rear wheels are sliding directly to the right. UNGH (how they DO that?) This is called converting battery power into carpet warmth.
Gee, wouldn’t it be nice if almost all of the bot’s weight were carried by just two wheels side by side with the robot’s center of mass? These two wheels would just roll forward and backward when the robot rotates and wouldn’t have to slip on the carpet at all. AND we would have almost maximum PROPULSION FORCE, because almost all of the weight is being carried on these two driven wheels.
But how to keep the 2 wheeled robot from falling on its face? Talk to Dean about the Ibot. For now, try putting extra wheels at the corners of the bot’s footprint, just to lightly balance the bot if it wants to tip forward or backward. Imagine mounting these 4 wheels 1/8" higher than the middle two. When you turn/rotate, and these “corner” wheels need to skid sideways, they do so easily because there is almost no weight on them. So now we have a 2 wheel drive/6 wheeled platform that steers/rotates easily (because most of the weight is carried on the middle wheels) and has great PROPULSION force capability.
If the robot doesn’t change its weight distribution during the match, you’re done. If it has to go up a bridge/ramp incline and its weight shifts onto the rear wheels, or if it picks up a weight at one end, you better be driving the newly loaded wheels or you’re giving up PROPULSION force capability. That’s why 6 wheel drive.
All of these remarks relate to making sure that normal force (weight) is carried by POWERED wheels and that most of the weight is carried near the middle. Treads are powered along their full length, so they don’t waste any PROPULSION force capability if the loading shifts forward or aft. If they have a bit of “rocker,” then they are also easy to turn/rotate.
…TO BE CONTINUED (too ____ long already)
: Once again my lowly grey matter would be infinitely expanded by your words of superior erudition.
: Thanx, Ernie P
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