# Math Equations

What are some good math equations used to help figure out stuff for robotics? I would like to get more math into our meetings.

Thanks!

(Remember we have 2 middle schoolers, and 4 High Schoolers (most are Freshmen), so keep it, well simpler than college)

Try to be more specific.
Simple equations like circumference =2(3.14)r can help you calculate how far one rotation of your robots wheels will move it. This combined with the amount of ticks per rotation can help you use encoders to go an exact distance. This is good for initial numbers but wheel slippage makes it not as accurate as you would like and trial and error is still necessary.

When talking about comparing different gear ratios what I know a lot of newer teams do is just do it in terms of low strength motors. So an arm with 4 393s in high strength at 1:5 would have 41.65 32 motors of torque. This isn’t in any way perfect but it can definatly get you by for a while.

I have found in the past that for novices working in real units doesn’t work well without a frame of reference so basing calculations off of someone else’s robot is probably the best way to go. If someone’s lift has 4 motors and yours will only have 2 assuming same length arm, gear ratio and equal rubber banding your arm will be able to lift approximantly 1/2 of what their lift can.

Biggest thing is keep it simple and remember the most accurate way to figure it out is to build it not to calculate it.

Using math to convert distance to number of ticks on your encoders. You can find the circumference of your wheels and use that as your single rotation. You then find out how many ticks/rotation, and you’ve got yourself a basic math function.
Using math to convert degrees to number of ticks on your potentiometers. Use known values and degrees and graph it (using Excel, for example)
Using math to convert degrees to distance to ticks on your encoders (to turn a certain degree w/o using gyro). Convert to find measure of arc (geometry topic, won’t go into to much detail), then use same formula as first example.

We have used all of the above equations already.

What about equations for the Lift? What kind of equations do you use?

As far as equations go, I won’t be doing any equations (other than PID, possibly) because our lift is either macro’d or entirely manual control. We would just need to find a handful of values (for ground, trough, high goal, etc.), rather than tell the robot go to 5", 6", etc.

I mean like:

How many motors do you need to life such and such lbs.

How much can you lift with X amount of motors.

You can calculate the in-lbs of torque needed to lift the weight. Then find the in-lbs of torque the vex motor puts out (5.17 I believe). You the multiply that by the torque provided by your gear ratio. You would finally calculate the pivot point deduction by dividing it by the length of the arm. It would look something like this

Arm: 12 in
Weight: 2 lbs
Motors: 1 393 Motor
Gear Ratio: 1:5 (5x Torque)

Torque Needed 6 in-lbs (length of arm/weight)
5.175 (Motor TorqueGear Torque) = 25.85
25.85/12 in (Torque produced/arm length) = 2.15 in-lbs
This means that you would need about 3-4 (4 to be safe 393 motors on this arm to lift the weight.

This is what I used to calculate and so far it has worked.

This is a good tool to use. A ratio for torque is a 5:1 not a 1:5. I always stress this to all the teams I mentor. Saying “a 1:5 for torque” or “a 1:5 for speed” does not sound good in the engineering world. A 1:5 implies speed and a 5:1 implies torque. Other than that, this type of math would save a team quite a bit of frustration and time when it comes to designing and building their robot.

Many places do it differently. I do it 1:5 because the ratio would then be more of a 1/5 speed and the opposite of speed is torque, which would make it 5x torque.

This is just the way I learned it.

The 5.17 in-lb comes from the data here and corresponds to a 393 running at approximately 65 rpm under load based on theoretical data. I’m glad that you are doing these calculations with a reasonable working torque and not the stall torque (14.8 in-lbs) that tended to be used in the past.

“the ratio of the angular velocity of the input gear to the angular velocity of the output gear”

Which would mean small:large would be a “speed ratio” and large:small would be a “torque ratio.” I learned this a couple years back but still don’t say all of my ratios correctly X.X

You can calculate the “mu” value or frictional constant of wheels and other materials on different types of metal, plastic and the field mats. Basically, set it flat, and then raise the sheet you are testing until the other material slips. Measure that angle with a protractor, and the tangent of that angle is this previously mentioned value that can be used in a lot of Physics applications. We used a similar process to determine the necessary angle of our sack storage ramp so the sacks would fall under their own weight, and if we should use lexan or metal for constructing it.

For doing more advanced software work, particularly with PID control, it’s nice to understand basic calculus like integrals and derivatives.

in my experience, using math with vex doesnt always work out we base designs off of

1. experience (1.6:1 on 4" wheels is optimal)
2. what others have done that works (1:7 arm is a safe “noob-proof” arm for first years)
3. common sense (2 motors on drive wont win any pushing battles with robots with 4…)

someone in our club tried to use math once, he was 5 motors off On my previous team (675B) we tried to mathematically model all our mechanical parts. For example: Our initial Gateway arm was going to be powered by 4 269 motors, but we decided to investigate further. We derived some equations based on angular motion and torque to model how our arm will work (time to move to position,torque needed, load on motor). We wrote these equations into a Python script and tested various gear ratios, and motor combinations. We found that we could get away with two 269s on our arm and still keep a competitive speed, and this allowed us to use extra motors on our drive train. We tried to create similar models for the drive train, but it was much more complicated and didn’t work nearly as well as I hoped.

Always build and test if in doubt (we had lots of other problems that we did not anticipate and couldn’t calculate), but don’t be afraid to use math. The results might be surprising (and useful). If anyone is interested I can explain the models we used for our arm and maybe post the Python script we used (if I can find it).

Sorry to drag the discussion back a few posts, but this is important (to me, at least)… Note that the ratio of angular velocity is:
small:large -> speed
large:small -> torque

However, with regards to gear teeth:
smallTeethCt:largeTeethCt -> torque
largeTeethCt:smallTeethCt -> speed

Its always Drive gear (gear attached to power source) : Driven gear (gear attached to object being driven)

Generally we talk in terms of reduction, so when I look up the spec for a motor gearhead it’s written in terms of reduction ratio. Here is a link to a typical datasheet for a Maxon spur gearhead.

http://www.maxonmotorusa.com/medias/sys_master/8801015922718/12_221_EN.pdf

The 15:1 part reduces speed by a factor of 15, so here it’s being shown as input velocity/output velocity and is in line with the definition given by SweetMochi. Another simple way is by using driven(the load) tooth count/driving (the motor) tooth count.

I also found this presentation which may be useful.

http://bowlesphysics.com/images/Robotics_-_Gears_and_Gear_Ratios.pdf

(Hours needed to make robot awesome) = t1.
(Hours currently spent on making robot awesome) = t2.
The equation is:
lim, as t2 approaches infinity: t1 = t2 +1
This holds true for all positive values of t2.
This is known as Geek’s Law.