To assess whether this was an adequate output torque, we compared it to commercially available mini lathe, which typically have power ratings of 1/3-2/3 hp. At the low end of that range, a 1/3 hp lathe running at 1200 RPM will have an output torque of approximately 2 N*m. Our minimum output torque is comparable and can be increased by downshifting and pedaling faster if necessary.

We are assuming that the rider is applying 200 N on the pedals and pedaling at 60 RPM.  The pedals are 0.175 m from the crank shaft, so the input torque is 35 Nm. So our power input is 220 Watts. To roughly calculate the power at the output, we used an efficiency analysis. We know from class that chain and sprocket systems are 95%-98% efficient and V-belts can peak at 98% efficiency.  However, since our V-belt tension is slightly below the maximum efficiency for a v-belt system, we can assume a safe 90% efficiency. Thus, on the low end the overall system has a 85% efficiency giving us an outlook power of 187 Watts. Commercial mini lathes have an average of 0.33 Hp or 227 watts. This is slightly higher than our lathe but we expect that the built in factor of safety in commercial lathes will mean that this is sufficient. After performing testing we validated that our lathe provided easily enough power to turn soft and hard woods!

For the tailstock block, we are again loading our bolts in shear; however, these bolts are just required to withstand the load that our tailstock undergoes when compressing our workpiece. It would not be possible to load our tailstock with more than 50 lbf due to how small it is. Since our bolts can withstand 150 lbf, as demonstrated with the frame bolts, we are not concerned with this loading condition. 

We decided to use aluminum extrusion (8020) for this project due to its easy of use and overall modularity. We wanted to make a lathe “table” or rail system that the head stock, tail stock, and tool rest could all slide on to accommodate projects of different sizes. Since the machine shop had 8020 available for subsidized purchase it was quite easy to rapidly prototype and build our lathe rail system. Since the shop only had 1 inch x 1 inch 8020 available we used that size. We are not worried about the aluminum extrusion failing or yielding since it is often used in systems that undergo much more mechanical stress and will remain rigid and fixed within our lathe. None of our other subsystems will move along the 8020 rails when the lathe is being used and the entire frame will be bolted to the table underneath. Furthermore, a rubber or foam mat will support the frame and reduce potential oscillations from the head stock. 

We chose steel as our material so that we can easily weld the tool rest together. Additionally, the material is more than sufficient since the tool rest does not generally experience significant loading.

We scavenged an umbrella set screw + knob which is rated for use with an umbrella which is much heavier and experiences larger torques than our tool rest would. Before powering the lathe we verified that the set screw would hold the tool rest by applying over 50lbf to the tool rest and it did not move, thus we confirmed that this would be suitable for the tool rest on our lathe

The bike will not fail in this use case because the loading conditions are significantly lower than typical use of this bike. We are not concerned about any mechanical aspect of the bike failing especially since fixing the original broken derailleur the bike came with.