Calculate the mechanical advantage of a 3 gear train system?

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SUMMARY

The mechanical advantage (MA) of a three-gear train system can be calculated using the formula MA = n1/n3, where n1 and n3 represent the number of teeth on the first and third gears, respectively. This formula derives from the relationship between the gears, where the outer gears operate based on the central gear. It is crucial to ensure that the gears have the same pitch diameter for accurate calculations. The discussion emphasizes the importance of understanding gear teeth and their sizes when applying this formula.

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Chocolaty
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How do you calculate the mechanical advantage of a 3 gear train system.

The formula I have for gears is only for 2 gears:
MA = number of teeth in the driving gear/number of teeth in the other gear.
 
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If the two outer gears are running of the same central gear, there is a one to one correspondence to between both outer gears, or if n1, n2 and n3 are the number of teeth on each of three gears, and the input is from 1 to 2 to 3, then the ideal MA (excluding friction) is just

MA = n1/ n2 * n2/n3 = n1/ n3.

The number of teeth relates to the diameter of the gear, so one has to be careful in applying the number of teeth, which is only valid if the teeth are the same size (same pitch diameter).

See these references - http://selland.boisestate.edu/jbrennan/physics/notes/Force/simple_machines.htm

http://www.maelabs.ucsd.edu/mae_guides/machine_design/machine_design_basics/Mech_Ad/mech_ad.htm

http://download.micron.com/pdf/education/lessonplans/machinesextension.pdf
 
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