I created the following planetary gear in FreeCAD. planetary gear

I calculated number of teeth using formula R = 2*P+S. In my case R = 75 P = 5 (there are 3 of them) S = 45.

Also all gear have the same pitch of 2.5 mm. However picture has huge gap. I can not figure out what could be wrong. Here is link to FreeCAD file link

  • $\begingroup$ what is the actual problem? ... what is your question? $\endgroup$
    – jsotola
    Nov 5, 2021 at 1:37

2 Answers 2


The following image explains where the formula $R=2P+S$ comes from.

enter image description here

Figure: Planetary gear with 4 planets (https://woodgears.ca/gear/planetary.html)

Although it has 4 planets the spacing will be the same with 2 or more planets. (Three is used for optimal balance and redundancy).

Essentially, the diameter of the Ring $d_R$ should be equal to the Diameter of the sun $d_S$ plus 2 diameters of the planets $d_p$. I.e. :

$$d_R = 2d_P+ d_S \tag{eq:1}$$

However for gears, the diameter of a gear ($d$) and the number of teeth ($z$) are proportional.

  • in the metric system usually the module m is used, $d= m\cdot z$
  • in the US system usually the Diametral Pitch (P) is used, $d= \frac{z}{P}$

In both cases, the equation 1 becomes:

$$z_R = 2z_P + z_S$$

So for $z_R=75$ and $z_S=5$, the correct number for the teeth of sun is $z_S = 75-2*5=65$


You are almost there. Except you need to use $2p=10. \\ not\ \ 2*3*p=30$

You use the number of the gears of one of the middle planetary gears no matter how many are there.

As you can see adding more P gears would not change the ratio, it probably reduces the stress on the gears.

Then you would have

  • R=75
  • S= 65
  • P= 5

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