Math+and+Robotics

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[] Simple Math Activity Using Robotics Damien Kee

Gary,

 A couple of different thoughts -

 Idea # 1. Turns. Try asking him to figure out the math for making a turn using a point turn or a pivot turn. The middle school teams I mentor are having fun working through the various ratios.

 I've asked them to follow it up with a myBlock to take in a "change of robot heading in degrees" and have the robot turn accordingly. This brings the abstraction and variable manipulation a bit closer to home.

 Idea # 2. Make a Map Another option is to use data logging to record the motor rotations for the robot's movement (like line following around a circle or a track) and ask him to build a map of the track -- Make it easy by telling him there are turns of 90, and 45 degree turns to start with. Using a compass makes this more interesting too.

 The key is... Only show the entrance and exit from the track... obscure the rest of it from easy sight. I've worked up a couple of introductory exercises if you'd like to see how I've started. I'm not satisfied with how well it conveys with my own voluntold children, er, um, the volunteers I live with, but it may spark some ideas.

 Hope this helps, craig

Elwood,

I have found gearing to be quite successful to increase torque or acceleration on robots. We have uphill battles and drag racers every year. I think the difficulty is in using the tri-bot. It's not very well suited to being a drag racer. The challenge in gearing up is in the building. The proper placement of gears so they don't have any backlash or too much friction and building a robot around that so it doesn't fall apart are both great engineering challenges for students.

Ian

br> T�E e Hh ��j y show the entrance and exit from the track... obscure the rest of it from easy sight. I've worked up a couple of introductory exercises if you'd like to see how I've started. I'm not satisfied with how well it conveys with my own voluntold children, er, um, the volunteers I live with, but it may spark some ideas.

Hope this helps,

craig

Another source of ideas for robotics and mathematics activities would be.... []

Rob

Hi Jason,

An interesting way to explore ratios is to explore gear ratios on the NXT. Useful resources include: - [] - [] - and the Modular Test Vehicle (MVT) [] which allows you to easily change gear ratios up and down, see their effect and then calculate the changes you will need to make to programming values.

David

Hi Jason-- Hi Jason-- Your math teachers might be better at what is age appropriate, but what I was aiming at was the idea that from the datalogging you get list of time values and at least one data number ( distance from the ultrasonic sensor, or light level from the light sensor, or acceleration if you have an acceleration sensor) for each time. You can make a graph with the time values along the horizontal and your data along the vertical. Once this is understood and a graph is drawn, you can see visually what your robot sensor was sensing as time goes on. This is a back door way to introduce the idea of an equation by showing visually the relationship between two values first then showing that you can write a formula (or equation) for that relationship. I am a little old school-- I think plain old graph paper is a great tool for understanding relationships…(grin) For example, say you are logging the output of your ultrasonic sensor as your robot approaches a wall. You set the sample rate for once per second and run the robot toward the wall from 50 inches away for 10 seconds. You will get ten times and ten distances. Plot the times across the bottom, the matching distance values above them. Instant graph. If your distance numbers were something nice like 50, 45, 40, 35 etc (not likely in the real world), your plot would be a straight line. You can then ask your student about this relationship—how far does it go every second? In this case, 5 inches. How far in two seconds? (10 inches) how far in X seconds? (5X inches) We write this as something like distance = 5 times the number of seconds ( which is an equation). I hope this helps. Gary

I do apologize for the headache—I forget that not everyone has the background to sort PID out. It is a mindful.

I would recommend datalogging as a good way to get him involved in real world math, and set him about investigating motion. An acceleration/tilt sensor would be a good way to do this. I had been working with one for a while (before it was lost ) and they put out nice data sets. Lots of different experiments with motion—tie it to a rope and swing in a circle, swing it on a pendulum and investigate the relationship of arm length to period, put it on a robot vehicle and track how it starts, stops and turns… Once you get data, you can introduce graphing, formulas and equations.

Another interesting approach to math that I saw years ago involved taking video of an object in changing motion, printing it as a series of frames and plotting the position against time and deriving the speed and acceleration from the graphs. Not robots, but could be adapted.

One more line of investigation is making a PID controller : []. The author says this is targeted to 3rd- 8th grade, but at the third grade you would have to break it up and go at it slowly. Don’t let the word calculus throw you— this is just creating feedback loops for more accurate line following.

I hope I haven’t got too far ahead of your student, just wanted to suggest possibilities.

Gary