Calculate the mechanical advantage of a 3 gear train system?

[Chocolaty]

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.

 

[Astronuc]

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