My sophomore year I took a Mechanics Based Design class that introduced us to all the basic concepts of common problems that would arise when doing mechanical design. We covered topics relating to, stress and strain, pressure vessels, stress concentrations, failure theories, buckling, bending, shafts, and fasteners.
Our final project was to take these concepts and equations and design a crane that would lift 10 lbs, 1 inch off the floor in 2 minutes. My team was given a servomotor and a small budget to complete the task. The rest was up to us. The beam was not allowed to deflect more than 0.5 inches. From this, we began by finding a suitable beam by calculating the deflection of a cantilever beam for a variety of materials and cross-sections to see which was reasonable and would work. We settled on a rectangular piece of PVC and oriented it with the long side vertical to maximize the moment of inertia, which would directly decrease the deflection. Next, we calculated the gear ratio that would be required to transmit the torque of the motor given to us and lift the 10 lb weight in the time frame. We ended up using a combination of gears, which were laser cut from acrylic to fit with the rest of our design, and pulleys to accomplish this since our original attempt with the gears lifted the weight too slow.