# What math did you use for your robot?

Hello fellow RoboNerds, what math was used for your robot? Looking at my engineering notebook I came to the realization that we did not use any math for our robot except for math such as 2+2.

You don’t need a lot. But I still wrote about a few cool cases.

I used trig to find out the most ideal plan of mounting two pieces of c channels at a desired angle. I did a table to find the closest estimation of a 135 degree angle.

I also calculated my design’s weight…

ZI method can be counted as math also.

Maybe use the motor’s torque curve and calculate whether your motor can deal with the stress or not. Easier to do on a bar lift. Keep the current under 2A

I attempted to convert encoder clicks to inches. While it is possible to do, its pretty hard to account for wheel slip. I also tried to use trigonometry to find an angle that the robot could go to a designated point on an XY cordinate grid based on encoder counts. If you think hard enough, there is way too much math that you can use to help optimize your robot with. Some immediate ones I remember doing for this season at least:

-Pythagorean theorem to find lift dimensions
-Law of cosines to produce an angle from the skyrise loader to the skyrise base
-related rates between speed and torque to find out what gear ratio I need to lift 6 cubes as quickly as possible with a certain amount of motors. Then used the resulting data to determine how quickly a skyrise would travel up and down under another set of motors and the determined gear ratio (power take off for the win).
-Determining new precision of encoders based off their new placement vs. old placement
-Determining a component’s yield strength based off research of the material specs and design. Then determining whether the structure can withstand the loads i’m placing it through.

more physics oriented
-Dimensional Analysis to predict new lift speeds and loads under different gear ratios based off a prototype I made
-Torque transfer and the affect of gravity on scissor lifts, linkages and linear lifts and different ways to power them (for example, planetary gearing for scissor lifts vs. horizontal linear slides, vs. vertical linear slides)

I mentor middle schoolers, so mostly I present the concepts and not have them actually crank lots of numbers. But here were the concepts I went over that were significantly math related:

Torque = distance x force.

Gear ratios.

The application of the form of equation (y= mx + b) as applied to elastics, Hooke’s law.

The concept of getting the most power out of a motor when you run it somewhat in the middle of the torque-speed curve, since power = speed X torque, and why gearing helps with this. (Kids intuitively try to run their motors at either extreme, not knowing that the extremes don’t provide the most power.)

Work = force X distance = weight X height
Power = Work/time

Most of these are more physics than math, but my team has compared area moments of inertia for bars and c-channels to help choose materials for a scissor lift, derived approximate equations of motion for various parts of the robot, used taylor series to approximate a hooke’s law like equation for the force exerted by a rubber band, and derived an equation that provides a very rough estimate of our robot’s center of gravity as a function of lift height

Please correct me if I’m wrong, but I was under the impression that the torque output of a motor decreased when the width of a pwm signal decreased, so reducing the motor speed would also reduce the power.

Well, reducing motor speed by reducing the amount of electrical power it receives can definitely reduce its power output. But have a look at this graph to understand what I was alluding to:

https://vexforum.com/attachment.php?attachmentid=6427&d=1341809892

For maximizing power output of a motor, there is a peak point where you get the most mechanical power output for a given electrical input, and that peak is not achieved by gearing the motor to run at its top speed (no-load speed) nor is it achieved by gearing the motor to run near its stall torque. That was the point I was trying to make.

If you want to delve into the details of PWM pulses vs. power outputs, etc., then have a look at this amazing analysis done by jpearman:
https://vexforum.com/t/motor-torque-speed-curves-rev2/21868/1

Well this year it’s all about showing how your robot tips over and proving why it did so.

But I love all the other answers so far! More math!!! More real engineering!!!

I completely forgot about that calculation lol. Figuring out how large the base had to be assuming the midpoint between the drive and the raised intake was the center of gravity through trig identities and inverse trig identities. I think I came to the conclusion that you needed like a 36" drive train, so I was like “just stop the tipping before it occurs”

Calculus for pid programming as well as analysis of rate of change of force associated with changing height of lifts and optimization of weight vs strength (probably necessary, we more or less just compared the resistance of the materials to their weight to find the perfect balance). I also used calc to figure out displacement changes as a result of changing acceleration and velocity as the drive accelerates based off of the power input to the motors (using electricity in to calculate work output in ideal system to then figure out how fast the robot will speed up). Trig for Pythagorean theorem, sin, cos and tan function associated with tower struts / structural supports. Basic algebra for torque calculations, force analysis and momentum.

While this sounds like a lot, it doesn’t take that much time and can save you a lot of anger when, for example, your lift is just slightly under-powered to lift three cubes.

We’re by no means done this year (we’re in the middle of our 7th rebuild), but so far we’ve used significant portions of:

• Geometry
• Algebra
• Algebra 2
• Trigonometry
• Precalc

Am I the only one that finds this comment a bit oxy-moronical (is that a term)?

Physics = Math with a purpose

(After reading my comment it sounds a bit pretentious…I mean the above comment in a joking way! Darn unemotional text)