Note: estimated and total degrees of freedom equal 1

Base = 1 in when square​

Ac = (gravity)(base) / (height) = (386.0885in/s^2)(1 in) / (12 in) = 32.1740417 in/s^2

Base = √2 in when diagonal​

Ac = (gravity)(base) / (height) = (386.0885in/s^2)(√2 in) / (12 in) = 45.512 in/s^2

According to the Professor, between a 3 and 4in wheel diameter is ideal.

The bar is placed with a diamond base to allow for greater acceleration. The wheels are 8cm in diameter and .4in width. The wheels are within the wooden base for a lower center of gravity while leaving room at the top for the Arduino and motor. The wheels have many holes in it to lower the weight of the system.

After many test trials, we found our max velocity to be 2 ft/s and max acceleration to be 1 ft/s^2. The code is set up to control the cart’s motion using a trapezoidal velocity profile that smoothly accelerates, cruises, and decelerates over the set distance. It calculates and tracks the velocity and position using encoder feedback to make sure the movement matches the desired acceleration limits. By continuously adjusting the motor’s output, the code maintains a stable speed and achieves the target distance as efficiently as possible.

"Lil Red" consisted of four red 3D printed PLA wheels with a black 3D printed bracket to encase all electronics and wheel axels and a white 3D printed motor bracket. The aluminum bar was set at a 45 degree angle to optimize acceleration and velocity.