I'm interested in printing a working two degree of freedom planetary gear set. I searched around and found a paper from University of Maryland in 1988 (source). I am having difficulty translating the information into a real-world model.

The goal is to make a system that allows two independent inputs to affect the speed and torque of a single output. As the paper points out, a differential system doesn't quite make this possible.

Although mechanical systems with multiple inputs or multiple outputs have existed for many years, generally, they have been used as a series of one-DOF devices rather than as true multi-DOF mechanisms. For example, the automotive bevel-gear differential, a two-DOF mechanism with one input and two outputs, is made-up of a one-DOF gear train in series with its gear box.

I tried analyzing a standard differential system but I don't believe you can alter it to use two independent inputs. The six link systems described in the paper seem to be the right direction, and so I would like to understand the graph.

Here is the figure from the paper:

Excerpt from paper

And here is my attempt to interpret graph 6-1-1:

enter image description here

I think this is clearly incorrect because elements 5 and 6 have no effect on the system. Could anyone help me interpret the graph?


2 Answers 2


Your model looks mostly accurate, your gap between gears 5 and 6 isn't large enough though. What are you treating as your inputs and your outputs? If you start your analysis like that I think you'll see the effect 5 and 6 have on the system.

Machinery's Handbook has some basic examples of epicyclic systems with 2 inputs.

  • $\begingroup$ That's definitely the question I'm asking myself, what are the inputs and outputs here. Can I ask: since the two inputs are independent, it should be possible to allow one to free-wheel with no load while driving the system entirely through the other input? Meaning that there is no reaction force required from one input to help the other drive the output? I will look at the handbook as well, thank you! I'll mark your answer after I do some research $\endgroup$
    – daDib
    Commented Mar 30, 2020 at 16:58
  • $\begingroup$ It would make sense to use 5 and 6 as the independent inputs since there are fixed to each other through linkage 4. These means 2 would be your output. Rotating 5 drives 1 which drives 2. Rotating 6 drives 3 which rotates carrier A, which will drive 2 as well. You can analyze the reactions from there. $\endgroup$
    – jko
    Commented Mar 30, 2020 at 18:08
  • $\begingroup$ That's what I was thinking. But realistically to get the output at 2 to do any work outside the system I would need something like a large ring gear to collect both the revolving and orbital motions of element 2? $\endgroup$
    – daDib
    Commented Mar 30, 2020 at 20:39
  • $\begingroup$ So essentially this is a schematic to independently drive the sun and carrier of a normal planetary set? $\endgroup$
    – daDib
    Commented Mar 30, 2020 at 20:40
  • $\begingroup$ Needing a ring gear to effectively get work out of this was my understanding as well. Not sure what real world application would be driven by this but there's probably something out there. So yes, this is just a schematic of suns and a carrier (the way I interpret it). $\endgroup$
    – jko
    Commented Mar 31, 2020 at 12:50

After help from jko I was able to put together a working model for a six link epicyclic gear system. It is essentially three standard planetary gear mechanisms tied together, each with a sun, four planets on a carrier, and a ring gear. I color coded the important interconnections:

1) Blue: The left and right planet arrangements share a common carrier. This double-sided carrier is also the main axis of rotation. The two parts making up this carrier mesh and their rotation is coupled.

2) Yellow: The middle and right planet arrangements share a common sun gear.

3) Red: The left sun gear is also the middle carrier.

6 Link Mechanism


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