Problem $4$

You want to design a three stage planetary

geartrain. There are a limited number of feasible

gear sizes, including annular gears. The available

sizes go from $=10mm$ to $=40mm$ in increments

of $2$ mm $.$ Annular gears have an additional outward

thickness $t=10mm,$ see the figure to the right. You

need to fit within a certain size constraint. Pictured

above is the side view. Consider the front view.

Your geartrain needs to fit within a circle of

diameter $\frac{O}{80}mm$ in the front view. What is the

max absolute value gear ratio you can achieve?