Gearing Calculations and Cuts

I love to engineer for artists. My friend Yong asked me to help him calculate the gear ratios for his thesis sculpture. I took some time to wrap my head around the system he envisioned.

After my napkin sketch, I set up as an excel spreadsheet to check out a couple of scenarios for possible ratios. The initial drawings he gave me roughly noted the desired ratio between the clock arms and the spinning sculpture. I fixed that ratio on the sheet in yellow. Blue notes inputs from the motor at worst case scenario. From here, I made green all the variables that we could play with. I like making systems what generate themselves from a few inputs. 

I provided Yang with the .DXF's for gears I pulled from solidworks models I made in solidworks. I also provided him with a custom FDM printed worm gear set to translate the motion from gear 4 four to gear 5.