Overview
This group project was one of the first in my undergraduate career, yet it holds a special place as one of the first times I put together all of my skills to investigate and solve a problem.
Inspired by a textbook problem in a classical mechanics class, our group decided to investigate the mechanics of a bead constrained to motion along a loop. The loop is rotating on the axis of the diameter of the loop. Originally, the problem asked for the equations of motion for the loop rotating with a constant angular velocity. This turns out to have a simple solution, in which the bead is attracted to some equilibrium position on the loop determined by a few factors. However, we wanted to expand and investigate the motion given some arbitrary rotation function.
We developed a mathematical model for the problem and ran simulations as a sanity check. We then created a loop with a track by laser-cutting pieces from transparent polycarbonate, and placed a colored bead inside. The whole assembly was then rotated by attaching a magnet and using stirring plate typically used in chemistry experiments.
Slow motion video was taken of the setup, and computer-vision algorithms were used to determine the position of the bead throughout time. We plotted the position over time and compared our results to our theoretical model. For more information, see the writeup here.
Technologies / Skills
MATLAB, Python (openCV, numpy), Laser Cutting, Analytical Modeling
Future Work
A more robust setup with a camera directly attached to the setup for a stable reference frame can helped in analysis of more complicated functions of rotation. A motor with more fine speed control and programmability can also prove very useful.