# Transmission Design Help

Hi, I’m Joel from team 1155, the Sciborgs, and we are interested in designing a custom transmission in the off season. I’ve looked around the forums and read the other threads regarding transmissions and learned alot but I still have a few questions.

1. How do you calculate the minimum amount of torque needed to spin out the wheels to prevent the breakers from tripping? And how do you calculate the coefficient of friction of your wheels?

2. I’ve noticed in some other threads that a drivetrain efficiency of 81% was used. How was this efficiency calculated?

3. Which maximum RPM value of the motor is used to calculate the maximum output speed of the transmission, the free load, average load, max efficiency, or max power?

4. I know the efficiency of the transmission applies to the maximum RPM, but does it also apply to the maximum torque?

5. What are the pros and cons of using direct drive and using chain reductions?

6. I know that by using smaller wheels, I don’t need as much reduction, but what are the other pro’s and cons of larger and smaller wheels? Specifically 4" and 6" wheels?

7. I’ve made my own spreadsheet over the past few days to calculate things such as max rpm, max torque, and total reduction at various stages of reduction through the transmission, as well as Pitch diameter, center to center distances, total weight, and final speed and torque. Can you direct me to another spreadsheet made by someone more experienced to check mine against?

I hope that isn’t too much to ask, but I’ve only been looking into this subject area for a few days. I’m also a software guy venturing into the hardware world, but I learn quickly :D.

Thanks for any help!!!:):).

to answer the second part of your first question, take a bathroom scale, put it up against a wall, and drive your robot into and keep the joysticks at full throttle for a coupel seconds so you can take a reading from the scale. Then divide the reading by the weight of the robot including battery. That is your COF.

To answer question 6, the advantage of smaller wheels is that you can often direct drive them saving you a couple more chains you have to tension. Also, they save weight and space and give you a longer wheelbase, which is a good thing if you have a wide robot but probably not such a good thing if you have a long robot.

This is dependant on lots of things, rather than explain it all here, I’m going to point you to a presentation I gave with my father last year in Atlanta, which spells it all out.
http://www.team229.org/resources/20/

There is the simple answer, which will generate a lot of debate, and there is the more complicated answer.

The simple answer involves putting a piece of your traction material on a sample piece of FIRST

carpet, and tilting this carpet until the traction material begins to slip. Measure the angle between the ramp and horizontal at the slip point. Take the tangent of this angle to calculate the coeff of friction between these two materials.

This is not TOTALLY true, because it is reliant on the laws of friction as dealing with perfect surfaces (we don’t live in a perfect world). In real life, our wheels will interlock with the floor, and this will vary depending on weight loading and such. For a better estimation, calculate an approximate coefficient of friction for your entire drivetrain. This can be accomplished through the method sanddrag has outlined in the above post. (Though, I typically use a large linear-force scale, and not a bathroom scale.)

You can also just use benchmarks for your calculations. (i.e. if you search this forum, or ask those here, we can give you a good idea of what you’re working with. For instance, skyway wheels measure in the 0.8 range.)

I typically use 81% as my base number when running calculations; I believe this is input as a default in some of the spreadsheets and whitepapers I have posted, because of this I think it is probably my fault that you’re quoting it. 81% is a guestimate, rule-of-thumb, base value I use. I experimentally determined it many years ago during some of my drivetrain experiments on 229.

The type of systems I designed didn’t vary too much from year to year (they all used similar gearboxes, with similar chain setups, with similar wheels, with similar frictional losses, manufactured in similar ways, with similar design methods) so because of all this similarity I continued to use that number. It was usually “in the ballpark” to what I really got, and so it proved to be a good design number.

This efficiency number varies a lot depending on your system. Some people use 90% efficiency per reduction stage as a bench-mark. I usually approximate 81% for the whole drive, and make it turn as smooth as I can, then call it a day. (For more on drivetrain efficiency, search this site. There are lots of methods people swear by.) My favorite method is to add some center-center distance in my gear meshing. This causes them to run a little sloppier, but a whole heck of a lot smoother. How much to use varies from person to person. I think I use .003".

Well, we know the motor won’t run at the free-speed. This is the “perfect-world, no losses” speed of the robot. But there is no such thing as a zero-friction bearing (if you have one, patent it and never work again).

Once again, because I have learned to use some “close enough” approximations in my drivetrain design, rather than do detailed comprehensive modelling of the entire system, I use an 80% of free-speed value. This has always served me well. Again, this value was experimentally determined a million years ago when I wasn’t so lazy or complacent with my gearbox design.

If you calculate for 80% of your free-speed, you’ll probably be in the right place. You can do your own calculations for this if you have a robot similar to the one you are designing. Hand calculate how fast it SHOULD be going (based on free-speed), then experimentally measure how fast it really goes. Compare these two to get your % value.

The non-lazy approach:
Figure out how much parasitic loss is in your system. Experimentally measure the frictional load which will act on the motor during running. Use this value to calculate the load on the motor, and use the speed-torque curves to then calculate the robot speed.

Something to remember:
Motors vary, motor speed varies, and an approximation is probably going to get you close enough.

These two are related. When the motor is running at 0 load, it runs at max speed. If there is some load applied to the motor, it will run at less than max speed. When you are talking about torque applied to the floor, remember that the motor will also need to exert torque to overcome the load caused by friction, BEFORE it ever exerts anything on the floor.

Someone once told me that the chain reductions on my drivetrain account for 80% of my total efficiency loss. While this may be an exageration, it is a valid point. Chain will decrease your efficiency.

However, it also provides an easy means to transmit torque across distance, and it allows for an easy (and forgiving) last reduction. I would rather have a chain break, than a gear or shaft.

If you direct drive, you will need to use a shaft which can handle the torque, which probably means more weight. You will also need additional gear reduction to compensate for your lack of chain reduction (more weight).

There are people who swear by both methods. I swear by chain reductions.
(Along with non-driven wheel axles, but that is another debate for another time.)

Search Chief, and you will likely find more pros/cons for each side.

Smaller wheels can be further out towards the outside of your robot. (i.e. the center of a 6" wheels MUST be 3" from the envelope of your robot, but a 4" wheel only needs to be 2" from the envelope of your robot.) This means that if used correctly, smaller wheels will result in a larger footprint, and increased robot stability.

Larger wheels can climb over obstacles better. Larger wheels make it easier to increase robot ground clearance.

Some people believe larger wheels increase robot traction, but I still haven’t seen any logical reason why this is true. I’m not convinced.

I like small wheels - lighter, more stability, lighter, lighter.

This is GREAT. I’m glad you’ve taken this step.
Here is mine: http://www.chiefdelphi.com/media/papers/1469
Which has seen a lot of use. I am still overdue for an update. Hopefully before kickoff this year.

Also,
http://www.usfirst.org/robotics/2006/cmp_conference.htm
If you’re going to be in Atlanta this year, on Thursday at 12-12:45 Ken Patton and Paul Copioli are giong to be giving a drivetrain presentation. This is a must-see thing. Ken & Paul have both taught me INCREDIBLE amounts about drivetrain, and they’re both “experts”.

Good Luck, and welcome to the wonderful world of robot drivetrain design.

There is a lot of good stuff on Chief you can read to help you along the way. I am mostly “self-taught”, simply by reading posts from guys like Ken Patton, Paul Copioli, Andy Baker, Joe Johnson, and others.
Feel free to ask questions, and you will certainly get help.

-JV

PS - Why would I do my real work, when I can spend 30 minutes posting about drivetrains? Yeah, I’m a sucker for gears.

Thanks A LOT John!!

I viewed the presentation you linked to a few days ago and the only problem I had was how to obtain the coeff. of friction(or what that was actually, things are a bit harder when you’re only a sophmore in HS who hasnt taken physics yet :().

You’ve cleared up alot of things and the rest of the design process shouldn’t be too hard from here and once again thank you very much :).

I’ve heard that too and I wasn’t able to figure out any possible reason why someone might think that until just the other day. I won’t be convinced until someone throws the scientific method at it but here’s why larger wheels might have the potential of increasing traction.

Neither the tread surface nor the carpet is a rigid surface; they are both quite deformable and interlock with each other. If the tread was a rigid surface, and the carpet was a rigid surface, the place where the two meet would be a line. However, this is not the case. Since each can deform, the interface between then is actually something like a small plane, allowing for more bite. Now, take a wheel. Take a very narrow slice out of it, like a slice of pie or pizza. Look at the curvature of the “crust” (tread surface). A larger diameter pizza/pie/wheel will have less curvature than a smaller diameter pizza/pie/wheel. You could say that the slice with less curvature is “flatter” on the crust/tread and that this “flatness” gives it a larger interface plane with which to interlock with the carpet. See, as diameter approaches infinity, curvature approaches zero (flatness).

I have no idea if any of the above is true, but it sounds probable.

Wouldn’t the width of the wheel have a much greater effect on its traction rather than the diameter? Perhaps by saying a “bigger” wheel they are referring to the width of the wheel. And if you look at it using basic kit wheels, the bigger wheel, the pneumatic wheel would be thicker, have a larger diameter, and have greater traction due to its tread, than the smaller, smoother skyway wheels.

Width DOES play a role in traction, but not a major one.
Again, because we are dealing with non-perfect surfaces the Frictional Model of F=mu*N doesn’t quite work. As a result of this, surface area does affect traction.

How much does it affect traction?
I don’t really know. This is something you should play with, and get some experimental data for. When it doubt, test it.

So JVN, if you don’t believe it plays a huge role, why did you use 1.5" wide wheels on some of your robots?
Well, here is why:
Assuming a wheel has a known force that is going to be transferred to the carpet (has a set Normal force applied to it, with a set torque, set coefficient of friction) a wider wheel will disburse that load over a larger area. As a result of this disbursement, tread will wear slower (so you won’t have to replace wheels as frequently) and it will be less likely to cause carpet damage.

Also, because I don’t totally know the nature of “how much traction increase will a wide wheel give you” I hedge my bets, and go with a medium width wheel. Yes, I’m a cop-out.

Other factors to consider?
The wider wheels will likely cause increased turning scrub. This must be taken into account when designing the wheel-base layout.

-JV

You’ll have a greater sideload so it may wear your wheels down a bit more when turning, but that also means that you have a lot of sideload traction that will help you stay planted so teams will have a harder time trying to push you from the side. Say, if have two robots with the exact same transmissions, but one has 1" wide wheels and the other has 2" wide wheels, the one with 2" wide wheels will be a lot harder and sometimes impossible to push sideways, while the robot with 1" wide wheels, you can actually push around. So I would say that width this year plays an important role. If you can shoot and not get pushed around so easily, from any angle, you would be a force to be reckoned with. That’s just what we noticed this year going with the 2" wide wheels.

But then your robot has to overcome that resistance to turn, causing the jerky, flexy bam-bam-bam driving we all hate. The ideal is finding a middle ground. Pop casters are a good solution, six wheel drive have great foward traction, but at the expense of “plantability.” The required characteristics depend on the game. This year six wheel drives seem to be the class of the field. (barring swerve drives, since they are in such small numbers) It is just like speed/torque, you sacrifice turning for planting, but could get around that through trickery like swerve drives and mecanum, whose parrallel in transmissions would be the shifter/CVT. Personally, I love the driveability of a 50/50 or 55/45 TW/WB (trackwidth/wheelbase) four wheel drive design, or a six wheel drive if that is not practical.