The Brick Bakery: Analysis of Motor Speeds for Geared Motors.

I was having a boring evening - so I decided to test some theories about Lego motors - and at the risk of seeming pedantic - here are my findings:

Myths and Legends?

Several times, people on the Lego Robotics mailing list have asked why their robots don't drive in a straight line - the three most frequently given explanations are:

Mismatched motors - some motors spin at different speeds than others because of age, manufacturing tolerances, etc.
That all electric motors are somehow 'tuned' to run forwards - and hence run slower in reverse. In most simple robots, one motor is running 'forwards' and the other in 'reverse' - this may be done in the RCX software or by plugging the cable on backwards on one of the motors - the effect is the same.
Build technique - it's easy to have Lego wheels, gears or 'collars' more or less tightly held against a stationary part of the robot structure. If one gear train is 'tight' and the other is 'loose' then the robot won't drive straight.

All three explanations sound quite plausible but I was interested to see the magnitude of each effect.

The Experimental Setup:

I hooked up a rotation sensor directly to the output shaft of a motor and wrote a little RCX program to run the motor forwards and backwards for 10 seconds each - many times, displaying the rotation sensor count on the LCD each time. My accompanying document shows that the sensor is quite accurate for 'normal' motor speeds - so this is a good test. Attaching the sensor directly to the motor output gives an almost completely 'unloaded' test - you could probably do better with an interrupter wheel and a light sensor which would add no load at all - but this is quite good enough for our purposes.

I tested all nine of my motors (they are all the modern 'geared' motors such as come with the Mindstorms sets). These motors vary in age between 3 months and a year - and although it's impossible to say which ones have had the most usage over that time, it's probably reasonable to say that these represent a 'typical' set of motors such as most people would have.

I tested the motors first in the order 1,2,3,4,5,6,7,8,9, then again in the order 9,8,7,6,5,4,3,2,1 just to ensure that the batteries on my RCX weren't gradually going flat over the duration of the test and thereby favoring the first motor over the last.

Experimental Error.

The results varied a little from the first run of a motor to the second run of the same motor - and if I keep running the test with the same motor, I can see that the experimental error is in the region of 2% - even between consecutive runs in the same direction with the same motor and with new batteries in the RCX for each run.

All of the motors seem to rotate at about 800 rotation sensor 'clicks' per 10 seconds which is 5 revs per second - or 300 RPM.

How well matched are the motors?

The worst motor out of the nine managed only 788 clicks in 10 seconds and the best did 891. That's an 11% difference. (295 RPM versus 334 RPM) - presumably with a larger set of motors to test, including some really old worn out/corroded ones and some really new ones - we'd find greater variation even than that - so 11% is really the best you can expect and your motors may show still larger variation.

Forward versus Reverse?

"Forwards" is defined here as the result of an "OnFwd" command with the cable connected with it's "tail" pointing away from the IR window on the RCX and running along the slot in the top of the motor at the other end. Reversing the cable drives the motor in reverse.

The theory that motors are optimised for the forward direction does appear to be true - most motors ran slightly slower in reverse than forwards - but generally only by 1 or 2% - which is less than the experimental error...but I didn't find any motor that ever ran faster 'backwards' than 'forwards' when averaged over 5 runs. We may also deduce that the wiring arrangement that I used is indeed the one that was intended to make the motor run in the 'preferred' direction when you tell the RCX to make it go "forwards".

Strange 'memory' Effects.

On a series of five 10 second runs, nearly every motor ran slightly faster on the first of the five runs than on the last. You might say that was due to the batteries being flatter after that time - but I checked that - and motors had the same average speed on the second series of tests with the same set of batteries as on the first - providing I left everything switched off for a couple of minutes between each series of tests.

There are two possibilities that I could think of - the most likely being that the motor had time to cool off between runs and that the friction is somehow higher in a warm motor than in a cool one.

The other possibility (remote - I think) is that there is a known effect in some kinds of battery where the available current drops a few seconds after you start draining it and recovers if you leave it turned off for a while. You can see this with a flashlight that has nearly flat batteries - you turn it on and the bulb glows for a few seconds and then slowly goes out - if you turn off the flashlight, wait 30 seconds and then turn it on again, the bulb glows again for a few seconds before dying. I think that's a long-shot.

Running under Load?

I did some other tests with the motors connected to a long, complex gear chain to provide some loading. This reduced their speed to about a quarter of the unloaded speed - but all the variations I saw in the unloaded case seemed to hold true when the motors were loaded. The motors that were fastest when not loaded were still fastest while driving the gear train - motors that had noticable forward/reverse bias retained that same bias, etc.

Build accuracy?

I dismantled the chain of a dozen or so gearwheels that I used in the load experiment - then reassembled it with exactly the same parts in the same order. I wanted to see if differences in how tightly I clamped the axles and how accurately the gears were aligned would make much difference. I tried not to vary the tightness of fit from one build to another and to build 'nicely' with none of the axles pinching the beams or anything like that.

I was very suprised to see about an 8% variation between the two builds even though I'd taken as much care as I could to build them identically.

This means that even if you carefully measure the performance of your motors to ensure that you pick two very similar ones - then ensure that the robot is designed to make them both run forwards - the mere fact that the two geartrains were assembled differently means that you could see an 8% variation in performance!

Voltage drop along a Lego Cable?

I also tried connecting up all the Lego cables I own (a length of about 10 feet with about 20 connections along the way) to see if the voltage drop would be noticable - and I saw about a 1% drop in speed with a couple of quick tests...nothing terribly significant.

Conclusions.

So - the conclusion is that almost certainly, the reason robots don't go straight is PRIMARILY that Lego motors don't all go at the same speed - and you can expect at least an 11% variation in speed because of that. The forwards versus reverse thing is also a true statement - but it's *FAR* less significant because it only affects the speed by about 1% in most motors.

Most suprising though is that even if you are quite careful, differences in your build technique (how tightly you clamp the axles, etc) can easily make up for an 8% difference in performance between the left and right drive chains of your robot. That huge variation alone is enough to doom efforts to make something go in a straight line without some kind of measurement device. Keeping the drive train simple is probably your best defence against this problem. The fewer gearing stages you have, the fewer sources of variation there are.

We can also say that the speed of motors varies by maybe 1 or 2% over time for who knows what reasons ... temperature, phase-of- the-moon, colour of robot? Cable length doesn't matter much.

However, one myth we can debunk is that the direction the motors run in is super-critical. The 1% to 2% variation due to this effect is really irrelevent compared to build variations and motor selection.

Future Work.

Someone should probably test a bunch of 9volt ungeared Lego motors and some micro-motors to see if the principles outlined here hold for them also. I don't own any of the ungeared motors so I can't test them. Micro-motors are pretty unsuitable to driving robots anyway - so I don't personally think it's really worth the effort to test them.

It would also be interesting to know the force required to stall various motors in the forward and reverse directions and to graph the speed versus torque curve for a collection of motors.

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Steve Baker <steve@sjbaker.org>