You are the lead engineer at a production facility, and you have been tasked with designing a machine

consisting of two pulleys, two bearings, and a shaft. The system will be designed to transmit torque from

Pulley A to Pulley C$.$ Pulley A must be located between the two bearings, while Pulley C must be

positioned at the free end of the shaft. Assume the bearings don$$t have any moment resistance $($i$.$e$.,$

simply$-$supported beam$).$

The total length of the shaft cannot exceed $3-$feet, but it should not be smaller than $1-$foot.

As the machine designer, specify a ductile material, and determine the lengths $($L$1,$ L$2,$ and L$3)$ and

diameter $($d$)$ so that the material will not fail with a static factor of safety between $1\mathrm{.}1$ and $4\mathrm{.}0.$

With the dimensions that you have determined, find the deflection at point A $($at the location of the

pulley in between the two bearings$).$

The device will operate at room temperature, and should have $99\mathrm{.}9\%$ reliability. The shaft will be

machined. Using this information, find the shaft$$s endurance strength and find the factor of safety for

infinite life. $($Note $1$: The factor of safety for infinite life can be less than $1).($Note $2$: You can neglect

stress concentrations$).$

Fully document the calculations you used to arrive at these sizes $($L$1,$ L$2,$ and L$3),$ including any

shear$/$moment diagrams you need and which failure theory you employed.