# Planetary gearbox calculations

I was looking through @jpearman 's robotics pictures when I came across this transmission system.

In the animation, it has a 60T gear and an 18T sprocket as it’s inputs, which results in 1:1 and 4.33:1 output.
I’ve been wondering how to calculate the output ratios if using different input sizes.
Does anyone know how?

Thanks

Just to warn you if you don’t know already no one uses this planetary transmission because the high torque mode doesn’t actually output more torque, because the chain motor is doing more work than the gear motor.

To calculate planetary gear set ratios:
Tr =Turns of the ring gear
Ts = Turns of the sun gear
Tc = Turns of the planetary gear carrier
R = Ring gear teeth
S = Sun gear teeth
P = Planet gear teeth
The ratio formula is:
( R + S ) ×Tc = R × Tr + Ts × S

A good ratio is the same carrier module as jpearman’s animation but with a 12t sprocket input and 36t gear input.
This gives:
torque mode
Tc =100rpm*(36t/60t) = 60rpm. Tr = 100rpm*(12/24) = 50.
(24 + 36) * 60 = 24 * 50 + Ts * 36
Ts = 66.6 rpm
ratio = 0.66 : 1
*
speed mode
Tc =100rpm
(36t/60t)2 = 120rpm. Tr = 100rpm(12/24) = 50.
*2 because ring gear now spins the opposite direction.

(24 + 36) *120 = 24 * 50 + Ts * 36
Ts = 166.7 rpm
ratio = 1.67 : 1

Notes: I used 24 for the ring gear teeth because it is how many teeth a sprocket the diameter of a real ring gear would be.

Ok thanks.
Can you explain with a bit more detail why it won’t output any more torque?
In 9090C’s sack attack reveal, they seem to have enough torque to stall a direct driven drivetrain.

The planetary robot was cheating, because the mecanum robot did not have its front wheels chained to the front, so it is basicly 3/4 as strong as it could be in a pushing match.

I edited my earlier post.
In reality a 0.6:1 ratio on 4 motors is able to stalemate an 8 motor speed drive as I learned in Toss Up.

The planetary robot stalled it because it had 4 motors worth of power, with one doing twice the work. The net force ends up still being 4 motors worth at direct drive.

So in short this doesnt work because there are two inputs, and the two inputs are at different ratios. Real life applicaitons of planetary gear reductions involve one input and locking a combination of Ts, Tr, and Tc.

Correct me if I’m wrong, but are you saying that one motor is providing the pushing force while the other is providing the speed setting?

No, their directions relative to each other determine the speed. I’m saying that one motor is always doing more work than the other because they do not go through the same ratio’s. The sprocket ratio and the gear ratios are different as seen in the different speeds of the carrier and the ring.

Although I am confident in everything I have said so far I must add a disclaimer that I may have innaccuracies so far as I am not an expert but I have researched this in the past.

I worded that badly, that’s what I was trying to say.