# Gear Calculations

A project log for MPRT - Modified planetary robotics transmission

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

agp.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 (http://www.efunda.com/DesignStandards/gears/gears_epicyclic_train.cfm).

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:

• R=(1+Nc/Na)/(1-Nc*Nd/Nb/Ne)

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

## Realisation

The gear design has migrated such that the requirement for the two planetary gears to have the same number of teeth is no longer valid.

AlanX

## Discussions

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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