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=8, R=22:
      8/(22+8)=8/30=4/15=A038110(4)/A060753(4).

      

      Pictures of 105 rotations of the planetary gear: (step label step5
      was accidentally skipped)

      

      

       

      

      

      

      

      The planetary gear has a period of 105 turns of the ring gear when
      the sun gear is held stationary.

      

      Starting at step1:

      

      Turn the ring gear counterclockwise 105/11=9.5454.. turns to give
      step2.

      

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

      

      (step5 label is corrected in the below list)

      

      step1: 0 turns

      step2: 105/11=9.5454.. turns

      step3: 105/11=9.5454.. turns 

      step4: approx 7.2 turns

      step5: approx 2.3 turns

      step6: 105/11=9.5454.. turns 

      step7: 105/11=9.5454.. turns 

      step8: approx 4.75 turns

      step9: approx 4.75 turns

      step10: 105/11=9.5454.. turns 

      step11: 105/11=9.5454.. turns 

      step12: approx 2.3 turns 

      step13: approx 7.2 turns 

      step14: 105/11=9.5454.. turns 

      step15: 105/11=9.5454.. turns 

      

      Approximate total turns= ((105/11)*8)+(7.2*2)+(2.3*2)+(4.75*2)

      https://www.wolframalpha.com/input/?i=%28%28105%2F11%29*8%29%2B%287.2*2%29%2B%282.3*2%29%2B%284.75*2%29

      Approximate total turns=104.863636...

      Actual total turns=105.

      

      When the sun gear is fixed, the 105 ring gear rotations, gives 60
      planet rotations, and 105*(4/15)=28 planet carrier rotations.

       

      error in above I think: should be 60*11/4=165 planet rotations and 28*11/4=77 planet carrier rotations.

      

      correction1: for fixed sun gear, when the ring gear rotates 105/11=9.54.. 


the planet gear rotates 15, this ratio is (105/11)/15=7/11=0.63636..


so if the ring gear rotates 105 times then the planet gear should rotate


105*(11/7)=165 times.



correction2: for fixed sun gear, when the ring gear rotates 105/11=9.54.. 

the planet gear rotates 15 times, and the planet carrier rotates 7 times. 

this gear ratio for the ring to planet carrier is (105/11)/7=15/11=1.3636.. 

so if the ring gear rotates 105 times, then the planet carrier should rotate

105*(11/15)=77 times.

The gear ratio of the planet carrier to planet gear is 165/77=15/7=2.1428..



      

      More gear ratios:

      

      S=8 #teeth on sun

      R=22 #teeth on ring

      P=(R-S)/2 #teeth on planet

      Pc=planet carrier

      

      input: Pc

      output: S

      fixed: R

      gear ratio=1+R/S=(R+S)/S=A060753/A038110=15/4

      

      input: S

      output: Pc

      fixed: R

      gear ratio=1/(1+R/S)=S/(S+R)=A038110/A060753=4/15

      

      input: R

      output: S

      fixed: Pc

      gear ratio=-S/R=-A038110/A161527=-4/11

      

      input: S

      output: R

      fixed: Pc

      gear ratio=-R/S=-A161527/A038110=-11/4

      

      input: Pc

      output: R

      fixed: S

      gear ratio=1+S/R=(R+S)/R=A060753/A161527=15/11

      

      input: R

      output: Pc

      fixed: S

      gear ratio=1/(1+S/R)=R/(R+S)=A161527/A060753=11/15

      

      

      Formula for gear ratio=1/(1+S/R)=A161527/A060753=11/15:

      A161527(n)=(1/(1+A005867(n)/A053144(n)))*A060753(n+1).

      ie: for n=5:
      A161527(5)=(1/(1+A005867(5)/A053144(5)))*A060753(5+1).

      61=(1/(1+480/1830))*77.

      formula simplifies to:

      A161527(n)=(A053144(n)*A060753(n+1))/A002110(n)

      ie. 61=(1830*77)/2310.