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Prime planetary gear2

ring gear teeth:
R = A053144(n) = A002110(n) - A005867(n).

planet gear teeth:
P = A337022(n) = A002110(n)/2 - A005867(n).

sun gear teeth:
S = A005867(n).

For example for n=4:

R = A053144(4)=A002110(4) - A005867(4)=210-48=162
P = A337022(4)=A002110(4)/2 - A005867(4)=57
S = A005867(4)=48

To create this planetary gear for n=4, the openSCAD from this Thingiverse gear bearing was used.
 CAD



        files and gcode
      for printing this gear.


The planetary gear ratio is given by A038110/A060753 = (1/1, 1/2, 1/3, 4/15, 8/35, 16/77 etc)

Example for the gear ratio: S/(R + S) for S=48, R=162: 48/(162+48)=48/210=8/35=A038110(5)/A060753(5).


Pictures of x rotations of the planetary gear:


 



The planetary gear has a period of x turns of the ring gear when the sun gear is held stationary.

Starting at step1:

Turn the ring gear counterclockwise x.. turns to give step2.

List of the counterclockwise turns of the ring gear with sun gear held stationary:



step1: 0 turns
step2:


Approximate total turns=
Approximate total turns=
Actual total turns=