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

 

[quicknote]

To calculate the mechanical advantage of a 3 gear train system, you will need to use a different formula. The general formula for calculating mechanical advantage in a gear train is MA = (N1*N2*N3)/(n1*n2*n3), where N1, N2, and N3 are the number of teeth on the driving gears and n1, n2, and n3 are the number of teeth on the driven gears.

For a 3 gear train system, you will need to know the number of teeth on all three gears. Let's call them gear A, gear B, and gear C. Gear A is the driving gear, gear B is the intermediate gear, and gear C is the driven gear. The mechanical advantage of the entire system will be the ratio of the number of teeth on gear A to the number of teeth on gear C.

To calculate this, you will first need to find the ratio of the number of teeth on gear A to gear B, and then multiply that by the ratio of the number of teeth on gear B to gear C. This can be represented as follows:

MA = (N1/N2) * (N2/N3)

So, if gear A has 10 teeth, gear B has 20 teeth, and gear C has 30 teeth, the mechanical advantage of the 3 gear train system would be:

MA = (10/20) * (20/30) = 0.33 * 0.67 = 0.22

Therefore, the mechanical advantage of this 3 gear train system would be 0.22. It is important to note that this formula only considers the number of teeth on the gears and does not take into account any friction or other losses in the system.