A Kapitza pendulum is a rigid pendulum in which the pivot point vibrates in a vertical direction, up and down. It is named after Russian Nobel Prize laureate physicist Pyotr Kapitza, who in 1951 developed a theory which successfully explains some of its unusual properties. 

The unique feature of the Kapitza pendulum is that the vibrating suspension can cause it to balance stably in an inverted position, with the bob above the suspension point. The hybrid component uses discrete switching logic (switch directions of oscillation) based on pendulum position, and is able to stabilize without manual initialization.

For this project, Dr. Poveda requires a physical example to teach advanced hybrid control theory, and needs us to mechanically design a robust pendulum that is able to incorporate this control theory, and implements high frequency oscillations to reach inverted stability without applying direct torque control. The latest design was able to operate for 6 cycles before failure, so for our new design we must achieve the following:

• Operate the pendulum for 100 cycles without mechanical or electrical failure

• Ensure stabilization at inverted position (any starting point) without manual control

• Properly integrate computer vision (closed loop) for accurate pendulum position and movement

• Implement a safety box and damping plate 

One of the most significant changes we'll be implementing onto the Hybrid Robust Kapitza's pendulum is the addition of a timing belt - pulley mechanism.

Said mechanism was designed to reduce strain and torsional stress on the servo motor and its shaft, respectively. It introduces new elements like the servo and shaft pulleys, a timing belt, and idler pulleys, with the latter serving the purpose of increasing wrapping around the pulleys to prevent slipping in the belt from taking place.

Our current design (shown on the video on the left) implements the timing belt, the pulleys and idlers. This is the 2nd design for the timing belt-pulley mechanism, with the 1st only including 2 idlers, and are currently developing a 3rd one with smaller idlers closer to the servo & frame pulleys. 

For MAE 156B, our goal is to optimize our timing belt-pulley mechanism, execute manufacture plans for the finalized aluminum design, and analyze its physical endurance to run the 100 cycles.