The Physics Behind BB-8
By: Matthew Winchell
Project Presentation Video
MatthewW.mp4What am I analyzing?
The first thing I calculated was the angular velocity of the ball due to the flywheel mechanism.
Within BB-8, I have a mechanism that allows it to move in place. Using Newton's 2nd Rotational & Conservation of Angular Momentum, I derived the equation to find the angular velocity of the ball from the angular velocity of the flywheel, the motor and the intertia of the flywheel and ball.
The next topic I covered was magnetism. I initially started by calculating the strength of my magnets given a certain distance, but the research involved to find such an answer was too much work.
The easiest solution was instead experimentally finding values. As shown in the graph to the left, Dave & I clamped one magnet in the jaws of a mill while the other magnet was on top of a gram scale. We then decreased the distance between the two magnets and measured the approximate force on the gram scale.
The third thing I calculated was the natural oscillating frequency. Basically, if I were to lock all of BB-8's actuators (the motors, servos and such), tilt the ball and let go, what is the angular velocity of that back and forth rocking? AKA the natural oscillating frequency.
The derivations involved are based on the principle of Newton's 2nd Rotational law, with the added assumption that if my angle is small, then the sine of my angle is going to equal my angle.
Finding the natural oscillating frequency can play a role in my PID loop.
The final thing I calculated was the linear and angular acceleration of the ball.
The purpose of this particular task is to create a simulation of BB-8 in Snap!. The first steps involved deriving the base equations of the x & y components via Newton's 2nd linear and rotational equations.
The second part was more rigorious, as I had to combine several of these derived formulas together and simplify them.
Furthermore, the simplification required me to isolate the variables that I needed to solve for (linear and angular acceleration of the ball)
Once I had the two main equations for both variables, I then went into Snap! and manually rewrote the calculations via Snap!'s block code (which was a pain).
After a lot of tinkering, I finally got the simulation running somewhat smoothly. You can find and mess around with the simulation below.
Snap! Simulation
QUESTIONS?
If you would like to reach out to me, my email can be found on my resume below.
If you would like to see an expanded look at BB-8, I invite you to check out my portfolio website: www.matthewwinchell.com
BB-8 and other projects of mine can be found there.
