# "Gearing for speed" criticism

Top speed is one of the most common metrics used in the FIRST Robotics Competition; yet, the problem is that the great majority of teams design their drive trains considering only the steady-state speed of the system, easily calculated by determining the operating point of the torque-speed curve of the motor (sometimes using a “desired” operating point such as the rule-of-thumb 75% of free speed, seldom using the wheel’s coefficient of friction). Given the power-to-weight ratio we’re allowed by the rules, the time constant of our robots is not negligible and, thus, it is important to consider the dynamics of the system.
From time to time some people do point out to unexperienced designers that “yeah, your final speed is great, but how long does it take to get there?”. This remark only gives a qualitative analysis, though. I propose a different way to look at the problem: How far will your robot travel in x seconds?

Consider a 2012 FRC robot with maximum weight (120 lbs + 15 lbs battery and 15 lbs bumpers) and this configuration:
4 CIM motors driving two CIMple gearboxes, N (N doesn’t really matter as long as they are all powered) HiGrip FIRST Wheels with a 26 tooth sprocket attached. The following graph demonstrates the distance traveled in three seconds by a robot with varying coefficients of friction (from 0.8 to 1.5) and gearbox sprocket (8 - OK, no such thing - to 26 teeth):

https://dl.dropbox.com/u/29016533/graph.png

(distance equal to zero means the gearing is such that the robot cannot overcome friction)

It can be seen that, for each coefficient of friction, there’s an optimal sprocket selection that will make the robot move as far as possible in a given time frame. AndyMark states that the coefficient of friction of the HiGrip wheels is around 0.95-1.0*. Let’s take a look at the distance a robot travels in three seconds using those wheels:

https://dl.dropbox.com/u/29016533/graph_2.png

The gearing selection by AndyMark, with a 12-teeth sprocket, is pretty close to the optimal one, 10-teeth (in a three-second run, that’s about 9 inches you lose in the worst-case). I would love to hear from Andy or Mark if that’s just a fortunate coincidence or if they did in fact take that into account. If so, why choose the 12-tooth over the 10-tooth sprocket?
Another thing that can be readily seen is that if a good-willing but uninformed designer decides to “increase” the speed of his robot by buying a larger sprocket he actually ends up with a robot that covers LESS ground in the same amount of time.

You are quite right in that top speed isn’t that much of an issue. The standard 12.75:1 Toughbox offers a good speed - going above that is usually pointless. In 2011, my team felt that we needed speed very bad, so we built a super fast drive train. Unfortunately, that was the wrong speed - we could go from one end of the field to the other before our arm could lift up to score. Whoops.

Are you assuming that the robot is traction-limited all the time?

Manoel,
I agree that this is a valuable benchmark, and that the majority of users don’t think about optimizing acceleration/top speed for “real field” usage.

I’m curious about more detail of your analysis. Can you share the acceleration model which you’re using for these calculations?

-John

Sounds like your arm was designed incorrectly for your robot’s match rhythm.

Yes it most definitely was. The mechanism that operated it is now on display on our Wall of Shame, such that future generations are not doomed to repeat the mistake.

Manoel, how did you factor the coefficient of friction into your calculations? I’ve never seen a robot slip its wheels when accelerating with the gear ratios discussed here, so traction should not be a concern.

Good discussion, it seems like many teams design for land speed racing instead of drag racing.

Great job with your analysis. We overgeared initially this past year. Modeling currents and time at currents is also a big deal. When geared too fast, you spend a lot of time in the lower half of the motor model which allows for high currents which is difficult on the power system, battery, and motors heating up.

To go along with this should be what is a reasonable top velocity? I see many posts where teams gear for above 10 fps. Can a driver really control a bot at these top ends? How much time per match is max v needed. I know this is game dependent, but I doubt most teams really need above 8 fps. This also ties into joy stick mapping. I submit that lower gearing gives a more precise control of the bot. Question. On a non wide open field and a robot geared to a 6to 8 fps top end, do you really need a 2 speed gear box? Our top end is about 9fps and single speed. We don’t see the need for higher speed in most games and I’ve at times have pushed for a lower top end. I’ll take acceleration and low current draw any day over a high top end.

I see this argument a lot for a reason not to have an excessively fast robot. However, this is where some teams have found a leg up on the competition- figuring out how to control a robot at high(er) speeds.

One example is Cheesy Drive, developed by members of 254. We’ve used the framework for that type of drive control the past 2 seasons on our robots. It is extraordinary how well you can control a robot moving at 18 ft/s (which was the top speed of our 2011 robot). Dipping into the alley (again, 2011) or making a nice fast arc around an opponent are all very easily done once the drive system has been properly tuned.

Manoel- Very nice work! I’m looking forward to seeing some of the discussion that comes out of it.

-Brando