Can a planetary gear be a CVT?

A planetary gear has 2 inputs. When they are spun full speed in the same direction, one gear ratio is achieved, and when they are spun full speed in opposite directions, another gear ratio is achieved. However, what happens if only one input is spun? What if one input is spun full speed, and the other is spun half speed? As there are an infinite number of way to spin these inputs between the 2 endpoints, are there also an infinite number of gear ratios between these points?

If so, could you explain the math behind determining the gear ratio to me? If not, could you explain where my reasoning was derailed?

Here’s an older thread:

Thanks! I have a question, though.

For @Stanley Shi(2R) 's hypothetical transmission, running the carrier at half speed in the same direction as the ring results in 16.6rpm. On a direct drive, this would be a 6:1 (torque) gear ratio. Will this have that much torque? How much torque does it have?

@puzzler7 I am not sure I understand fully in the first post.

Are you saying you have a 12 tooth gear at North South East and West positions on a 60 tooth gear. Example is to run North and South at half power and East West at full power?

The results in that case will be to whatever resultant force on the big gear wins and you are creating a drag with the less powered motors as they get pulled along. So somewhere in between what you want but I do not think it would be great for the slower motors useful life I think.

I meant that in this transmission, the inputs are shown at full speed in the same and opposite directions, along with their resulting gear ratios. However, what is the resulting gear ratio, speed, and torque if one of the inputs is run at half speed, or not run?

Didn’t you ask this same question years ago, @puzzler7 ?

I did, but I didn’t get an answer regarding the equations for gear ratio, speed, or torque. I figured I’d ask again rather than necroposting.

Ah, alright.
In short, yes. There are infinitely many gear ratios between two endpoints. I’ll have to think a bit for the math, but it’s fairly simple once you understand it.

However, torques don’t… torque. If you check out the thread relating to my differential transmission concept, you’ll begin to understand. This is because the planetary transmission it, in some ways, a cousin of the differential.

One more thing: as @DracoTheDragon said ages ago:

Can you point me in the direction of this math? I’m pretty good at math, I just don’t know where/how to start.

How would I go about measuring torque, to verify/in lieu of calculations?

Not sure about the math. As for measuring torque, I recommend using a rubber band setup to test stall torque of motors. Imagine a cam being held back by rubber bands. As the cam turns, the rubber bands react with increasing force. The distance traveled is the stall torque. Try once with a normal motor for control, then once on the planetary’s low gear, and once on the high gear. Barring friction, you’ll find the torque does not follow the gear ratio.

That’s odd… Intuitively, a speed ratio should have a lower torque than a 1:1 direct drive.

Okay, yeah. I made a mistake there! I’ll edit that out.
My point was that regardless of gear ratios, you’ll only have torque of one motor.

What if my ring and/or carrier gear has 2 motors, while the other only has one?

I believe you’ll only have the torque of one motor. Once the output starts to stall, the ring gear will start to back drive the planets.
Not sure though; I’m far from an expert.

Also, would the torque be equivalent to one motor for every gear ratio in between the endpoints?

Ah. If I get some time, I’ll do some tests.

I see the problem in my explanation. In all of these situations, the output will have the impulse (Torque / Speed) from one motor, not the torque. Think of it a bit like if you geared it back down to 1:1 with a solid gear drive, and then took the torque. THAT will be the same.

That’s what I meant. So if I used this, I would essentially have a CVT, but for a 2 motor drive?

EDIT: That is, assuming I had 2 motors on either side of the drive.