# Formulas Used in VEX Robotics

Hey guys. We are working on putting together a page just for equations. This is what we have so far.

Drive:
[HTML]Stall Point: q = f * r

Revolutions: Ø * π * rev. = Distance
Ø=diameter, π=3.14, rev=desired revolutions
This equation will help find how far your robot will travel with N amount of revolutions. [/HTML]

Lift:
[HTML]Torque: ST * Gear Ratio / length of arm = N lbs Torque per motor
ST=stall torque of motor(s)
This equation is helpful to find your torque (or stall torque) with a given amount of motors.

Stall Point: q = f * r
This equation will help with finding your lift’s stalling point.

Hooke’s Law: f = -k * delta(x)
f=force, k=hooke’s constant, and delta(x)=change in distance
This formula is very useful in finding out how much a couple rubber bands will help your robot lift.[/HTML]

If you can fix/add to the equations if they are not correct, that would be great.

Please add any equation used in robotics. We are trying to make it so there are easier equations for younger students, and more complex equations for HS students.

Thanks!

You may want to show how to calculate RPM using gear ratios. It seems simplistic, but that’s so related to the Power equations you’re using it makes sense to have it available.

Another thing you may want to put up is how rubber bands can be used to “gain” force upon lifting. My understanding of Physics was never what anyone would consider good, but I believe it should use the same equation as springs with a constant I can never remember (.11 is the number in my head, but I could be wrong. Heck, I could be wrong about the entire thing.) Make sure it’s for the #32 Rubber Bands and not the #64 ones, if you do. Only the first are competition legal.
*This is Hooke’s Law. You have it listed. The constant might be nice to have, though.

Does anyone have the frictional coefficients of the different wheels? You need those to properly calculate acceleration. That could come in handy when programming.

Explain why/how an X-Drive works. Vector forces and all that, along with the math.

If I come up with anything else, I’ll say something.

Aura did a good job of explaining that over here.

Yeah, this is what we used earlier in the year to understand it.

How about second moment of area?

A few years back I performed a test to obtain the coefficient of friction for a few different wheels. Here is the post where I explain what I did and give the numbers. Also, here is newer, complete data that I calculated from numbers given in this pull test.

~Jordan

How would this be applied to the robot? I understand from a physics/mathematics perspective what the second area moment of inertia is, but I don’t see an easy application to VEX… (This just goes to show that those college classes are great at teaching a concept, but not necessarily great at teaching how it is applied…)

The second moment of area would be used in selecting the proper materials such as angle vs. channel, etc While I am VERY rusty on this stuff I believe the Parallel axis theorem would be the correct application. My high school team used 5 X 25 hole plate to make 1 X 3 X 1 channel since the 1 X 2 X 1 had too much torsion and 1 X 5 X 1 was too tall. While it is a distant memory there is a correlation between the second moment of area and torsional rigidity. With it having been over 20 years I remember enough to understand the relationship between the two, but not enough to give a detailed explanation.

Thanks to learning trig this year i’ve made a formula for calculating the max height of a 6-bar linkage. This calculates the max and minimum height by calculating when the middle and lower horizontal bars touch. Sometimes in real life they won’t fully be able to touch so leave some room for error.

Here’s the formula (Online calculator if all this is really confusing):

Basically you’re going to calculate the max and min angles, then from there calculate the max and min heights.

min angle = arccos(W/(M-N)) + 90
max angle = 180 - minangle

Where:
W = width of middle horizontal bar (see #3 in diagram below – normal c-channels like in diagram are 1inch)
M = height from ground to axle of middle horizontal bar (see #1 in diagram below)
N = height from ground to axle of lower horizontal bar (see #2 in diagram)

min height = M - (L * sin(minangle - 90))
max height = M + (L * sin(maxangle - 90))

Where:
L = length of middle horizontal bar from axle to axle/pivot (see #4 in diagram)

Robots evolve around the use of physics… quite interesting!