If I have 3 gears meshed with a gear in the center of the 3 gears as shown in the picture. all of those 3 gears are connected to different power sources. They are free to rotate in the same direction and they have different torques and speeds (sometimes zero but never in a different direction). My question is, will the gear at the center has a torque equal to the summation of the other 3 gears? If not is there a certain set-up that can accumulate the torque of multiple gears. Note: my purpose is to generate electrical power using a compact set-up of gears if every gear has a different mechanical power source. I am trying to avoid 3 electrical generators if I can because I don't have too much space.
This problem is very similar to adding balancing resistors to parallel voltage sources in electronics.
What you need is less "stiffness" in the system so that when one gear loads up more than the others, something gives to unload it which serves to increase the load on the other gears.
Something like mounting the drive gears on a torsionally flexible mount would do this for small imbalances but if you want wildly different speeds and torques to combine you're probably out of look without a very complex variable transmission.
The gearing constrains the speed of all the planetary gears to be the same. Whatever that speed change does to the torque of each gear, the torques becomes forces acting on the center gear.
If one gear is connected to a water wheel, another to a windmill, and a third to a bicycle, then they'd all turn together, and perhaps the slow speed of a high-torque waterwheel would slow the windmill, while also spinning up the idle bike.
IOW, it depends on the torque-speed curves of all the components.
(Assuming a direct connection to the motor for the smaller gears), the torque of the larger gear ("sun") will be equal to the sum of the three smaller ones only if the three smaller gears have :
- identical size
- rotate in the same direction
- rotate with exactly the same angular velocity (rpm).
With the direct connection of motor to gear, if the angular velocity even one of the three is different then the assembly will not operate.
There are other types of couplers and gear connection that can be used to allow for different velocities however the torque will not be the sum, but a fraction of it.