I need some math help. I am very good with my hands and building mechanical things, but not-so-good with math calculations. ( I got a D in high school physics but can fix damned near anything...) I would appreciate some help figuring this out.(adsbygoogle = window.adsbygoogle || []).push({});

I have attached a diagram showing what I am trying to calculate, and also some pictures of what I actually built to give the problem some real-life context.

Basically what I have is a large weight that falls and pulls a cable. The cable is wrapped around a drum which is connected to a shaft. The shaft is supposed to spin a series of gear reductions. ( 9 reductions of 5:1 each. 60 tooth sprockets connected to 12-tooth sprockets with heavy duty roller chain ).

The idea is to have an initial shaft speed of .00208 RPM input into the gear reduction system that gets ramped up to 4068 RPMs at the output speed of the final gear. That desired input speed is based on the fact that I want the weight to fall 48 inches in 24 hours- which would mean that the 5 1/4" drum would turn 2.9 revolutions in the specified time period. The circumference of the drum is 16.48 " and therefore if the drum turns 3 times ( rounded to 3 from 2.9 ) in 1440 minutes ( 24 hours ) then that equals .00208 RPMs.

My original thought was to just build the gear reductions and keep adding weight until the darned thing started spinning and the desired output speed was achieved. ( I am so bad at math that I figured it would be easier for me to just experimentally determine the required weight ). However, I seem to have grossly underestimated the required weight / force to move this system.

As I mentioned, I have 9 sets of gear reductions, and I have added 400 pounds of weight so far and it can only move 3 of them! Some of the parts on this contraption I have built are rated up to 900 pounds, which is great, but other parts are going to have to be rebuilt or reinforced to accommodate additional weight. I have a lot of creaking and groaning and sagging of steel going on... The absolute maximum weight I could use is 1200 pounds but that would require a lot of frame reinforcement and before I start re-building this thing I would like to know EXACTLY how much weight is going to be required to move these gears.

In the diagram, "A" is the falling weight. "B" is a pulleys. "C" is a cable attached to the weight and wrapped around a cable drum "D". The drum is connected to the first large gear of the reduction system by way of a shaft. Each set of gear reductions goes from a 60 tooth sprocket to a 12 tooth sprocket. The small sprockets are connected by fixed shafts in pairs to large sprockets- which are then connected by roller chain the next small sprocket in the reduction system and so on. Large sprockets are colored blue in the diagram and small sprockets are colored red. The shafts are colored green. I apologize in advance my terrible art skills.

My question is this- how much weight is required to make the weight fall 48 inches in 24 hours and overcome the mechanical disadvantage of the specified gear reductions and acheive the desired output speed on the last gear? I simply do not know how to determine that without actually building it and adding weight until it moves. I am reticent to proceed because I have underestimated the weight required and the forces involved so far. I am afraid that it is going to require thousands of pounds and i need to know before I build something again that is not up to handling that load.

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# How much weight/force to move gear reduction

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