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June 18th, 2017, 01:17 PM  #1 
Newbie Joined: Dec 2012 Posts: 10 Thanks: 0  Long Compound Gear Train ratio
Greetings. I am building a board game that utilizes time travel by means of a compound gear train. Each gear will represent a different unit of time, and I would like an idler gear in between so the time gears all move clockwise/counterclockwise at the same time. The units I am using are day (7:1), week (4:1) month (12:1) year (10:1) decade (10:1) century (10:1) millennium (10:1) myriad (10:1) centium (10:1) age (8 teeth). The ratios put together are 7:1, 4:1, 12:1, 10:1, 10:1, 10:1, 10:1, 10:1, 10:1, 8:1 So here is the issue I am having. I don't want to have any of the gears have oddnumbered teeth, and I don't want massivetooth gears (none above 60), and the smallest amount of teeth I want on any gear to be 8. I was trying to avoid having to use pinion gears but it looks like I will have to anyway. What is the best setup for this gear train? What I have for starters is the day to week ratio which will be a compound gear, either 10:20 and 8:28 or 8:20 and 10:28. It gets tricky for me to calculate after that because of the next 4:1 ratio. I also tried started working backwards from the age gear (8 teeth) too but didn't make it very far. Last edited by davidbenjamindix; June 18th, 2017 at 01:32 PM. Reason: mispellings 
June 18th, 2017, 01:53 PM  #2 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 442 Thanks: 36 Math Focus: Elementary Mathematics  Code: (56:8) (32:8) (48:(8:(16:8))) (40:(8:(20:10))) (40:(8:(20:10))) (40:(8:(20:10))) (40:(8:(20:10))) (40:(8:(20:10))) (40:(8:(20:10))) (40:(10:(20:10))) 
June 18th, 2017, 02:38 PM  #3 
Newbie Joined: Dec 2012 Posts: 10 Thanks: 0 
It makes perfect sense! Thanks so much. That's the answer I was looking for. For some reason I hit a mental block while trying to figure it out. Thanks again!

June 18th, 2017, 02:46 PM  #4 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 442 Thanks: 36 Math Focus: Elementary Mathematics  Good to know, that I was of some help. 

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