The dynamics of the system were simulated in MATLAB using kinematic relationships, Lagrangian Dynamics, and Euler's method for numerical integration. Results can be seen below:
Slowed-down videos of the forward and backward directions are shown below:
Masses of important components (left gear, right gear, arm, lid, coin) were measured using a scale. The spring constant was calculated by measuring the force of the spring at a known displacement using the scale Each gear's inertia were modeled using the thin disc formula. The arm and lid were treated as slender rods, and the coin as a point mass. Damping components for the gears and the lid were arbitrarily assigned. After some research, the suction cup was modeled simply as a time-delay, as the force imparted by it would not impact the dynamics of the system.
The Potential and Kinetic Energy of the system are shown by the following equations:
After solving the Euler Lagrange equation and substituting the appropriate kinematic relationships between accelerations of the components, the acceleration of the arm is found to be: