Gear Calculations

A project log for MPRT - Modified planetary robotics transmission

The reduction of strain-wave, but using a 'single' stage planetary gearset.

agp.cooperagp.cooper 04/19/2019 at 09:141 Comment

Gear Calculations

I could not be bothered tying to work this out, someone has done it before, I just have to find it.

On my search journey I found the gear system we are using are call Epicyclic gears.

Anyway I did find a website that published the equation for this specific gear system (

If the gear train is Na/Nb/Nc and Nd/Ne (i.e. Sun1/Planet1/Ring1 and Planet2/Ring2) where Ring1 (Nc) is fixed ,and the planets (Nb and Nd) are locked the the reduction ratio is:

Here is the worked example from the website:

Gear Train – Worked Example
NA 21 Sun 1 Driven
NB 61 Planet 1 Locked to Planet 2
NC 141 Ring 1 Fixed
ND 41 Planet 2 Locked to Planet 1
NE 121 Ring 2 Output

Gearing 1 7.7143 Check

Gearing 2 0.2168 Check

Gearing 0.0281 Check

Reduction 35.5870

Here is Daren's design:

Gear Train – Daren
NA 18 Sun 1 Driven
NB 21 Planet 1 Locked to Planet 2
NC 60 Ring 1 Fixed
ND 21 Planet 2 Locked to Planet 1
NE 57 Ring 2 Output

Gearing 1 4.3333

Gearing 2 -0.0526

Gearing -0.0121

Reduction -82.3333

Note the sign change in the reduction ratio, this appear to be correct.

And here is my five planet version:

Gear Train – Alan v2
NA 25 Sun 1 Driven
NB 20 Planet 1 Locked to Planet 2
NC 65 Ring 1 Fixed
ND 20 Planet 2 Locked to Planet 1
NE 60 Ring 2 Output

Gearing 1 3.6000

Gearing 2 -0.0833

Gearing -0.0231

Reduction -43.2000


The gear design has migrated such that the requirement for the two planetary gears to have the same number of teeth is no longer valid.



Daren Schwenke wrote 04/19/2019 at 14:28 point

First stage is 3.3~:1 for mine, not 4.3:1.

Yes, the negative sign is correct.  It switches directions depending on if the output has more teeth than the input or vice versa.

33:1 is a more workable ratio than the original.  Good job.

Also, at this point you have contributed more to the project than 90% of all contributors I have had for projects.  @Morning.Star is still winning in that regard, but the two of you may just change my mind about contributors...  :)

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