# teaching math trough robots

any curricula for trigs, matrices, derivative, integrals, differential equations?
thank you.

Go take calculus 1 and 2, vector calculus, and differential equations at your nearest local community college…

(or if you think you can teach yourself, buy the \$500+ worth of textbooks for those 4 classes…)

I really forgot to say: teaching all those subjects Through robots!!
Thank you again uncle Joe!!

OH! You should have said so…

A good calculus textbook actually might not be a bad idea… Your library should have several of these, and you can learn the principles behind everything.

Carnegie Mellon has put together some very good curricula for teaching just general programming applications, and that uses a lot of math…

If you want to apply the math through the building of the robot, I’d recommend loaning a statics/dynamics book, and make yourself comfortable with vectors, forces, accelerations, kinematic equations, Bernoulli’s Principle, and all that fun stuff… I know I have found that I can apply almost all my college classes to robotics.

On a side note: what are you using differential equations in a robot for??

Thank you. I am in touch with the academy and believe me is not so much what you can find to teach the math I am talking about.
I want you to know that I am very familiar with statics and dynamics but no matter what, to introduce all those concepts in 16 weeks class where you need to cover what you need to cover is dificult.
The idea is uncle Joe to find out any experiences in this matter.
Thank you again.
If you want you can write me at [email protected]

I don’t know of any formal curricula – perhaps you’ll have to assemble one yourself. If you find a good curriculum, please share it here, as I’d be interested in it.

One robotics concept that uses trigonometry is back-pressure on a lift arm. Suppose you have a simple hinge lift (an example is the Animal Grabber project in this document). When you lift the arm using the remote control then release the button, it flops down due to the torque caused by the weight of the load. There are a number of ways to get the arm to stay in place when you let go including:

1. using elastics on the back of the torque arm
2. using a counterweight on the back of the torque arm
3. using back-pressure through programming

To use # 3, since torque = r X F = r F sin(theta)

you need to measure the angle, theta, which can be done using the potentiometer. You would then program the motor to run at the speed you calculated from the torque equation, and this would provide just enough pressure to keep the arm from flopping down, but not enough pressure to make the arm move of its own accord (without further input from the user).

An important robotics concept that uses calculus is PID (Proportional, Integral, Differential) control, which measures the rate of change of distance & speed in order to optimize the positioning of a robot and minimize overshoot. For example, when you want to approach a target, it makes sense to race toward it when you are far away, but to gradually slow down as you near the target, allowing both speed and precision. An example of code that uses this technique has been posted by Team 1103 at this link.

You could also do some power calculations by using integration to find the area under curves like this one. Taking the derivative of these curves, you could also find the time values for which the curve is nearly flat (within a certain tolerance) to get the range of best stability of voltage.

Honestly, there is math at every level tied into robotics. I frequently use gear ratios (switch the gearing from 1:5 to 5:1 to speed up/slow down a robot) and simple formulas like C = pi X diameter with my 5th grade students, Pythagoras for my algebra students (what length arm can you use and still fit inside an 18" X 18" X 18" cube), and on up through trig and calculus.