# Gear train system (3 gears)

## Main Question or Discussion Point

I have a gear train system where i have 3 gears meshing with each other (different sizes) gear A, B and C. Gear B is my input/driver and gears A and C are my output/driven. If i know the input RPM and input torque for gear B, what are the gear ratios/the amount of torque transmitted to gear A and C. I doubt that i can say that ratio between A and B = ratio between B and C.

Also, would it be correct to say TA + TC = TB since gears A and C are in a sense parallel to each other. Use N for rpm and T for torque please. I would highly appreciate it if you just refrained from posting comments such "Google is a savior" and the sort.

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OldEngr63
Gold Member
If I have understood you correctly, you actually have two simple trains,
B→A, and
B→C
that share the common input gear B.

The basic kinematic relation for rolling at the pitch point is
rb θb = ra θ a= rc θc
where the r's are pitch radii and the θ's are the angles turned by the respective gears.

The respective train ratios are then
θ ab = rb/ra = nb/na
θ cb = rb/rc = nb/nc

The last equality follows because the tooth numbers are proportional to the pitch radii.

With this much given to you, let me suggest that you think a bit about the static equilibrium problem for this system in order to get the torque relations.