Picture of Planetary Gear
 Intro – planetary gears also refer as epicyclic gearing consisting three elements sun gear, planet gear and ring gear. Sun gear is located at the center that transmits torque to planet gears orbiting around the sun gear. Both systems are located inside the ring gear. In the toothed formation sun and planet gears are externally mesh and ring gear internally meshes. (See Fig. 01)Fig. 01
Planetary gear is found in many variation and arrangements to meet a broad range of speed-ratio in the deign requirements. Planetary gear system is use in varies applications such as, clocks, lunar calendar, car mirror, toys, gearhead motor, turbine engine and many more.
For detail understanding on the planetary gear: Planetary Gear Design
Planetary gear system will no assemble unless the number of teeth in each gear is selected properly.
Planetary spur gear drive ratio 5:1 means the sun gear must make 5 revolutions for each revolution of the output carrier.
Desired number of teeth in the sun gear is 24.
Design requirements:
Ratio   = 5:1
Sun gear  = 24
Module = 1
Since, I am working in the metric unit every dimension will be in mm. Selecting gears in metric unit the gear tooth profile of the spur gear will be in Module.  
M = Module
N = Number of teeth
Nr = Number of teeth on the ring gear
Pd= Pitch Diameter
R = Ratio
PDs=N/M=24/1=24mm  Eq. 01
Pitch diameter of the sun gear is 24.
Calculate the number if teeth required in the ring gear for the ratio 5:1.
R=1+Nr/Pd       Eq. 02
Solve for Nr
Nr=Pd (R-1)=24(5-1)=24(4)=96 teeth

Pitch diameter of the ring gear with 96 teeth and 1 module is.
Pd=Nr/M    Eq. 03  Pd=96/1=96mm
Pitch diameter of the planet gears must be found from.
Number of teeth in the planet gears may now be found from.
PDp=N/M Eq. 04  36mm=N/1  36mm (1)=N  N =36 teeth
R=1+Nr/P_D =1+96/24=1+4=5
The ratio is 5:1, as design was required.
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tplim1 year ago

@KDan, thanks for sharing. Can I run this type of motor 24 hours non-stop? If yes, how long the plastic gear will stand? What I means wear and tear. Please take a look at ebay link

Thank you. Awaiting for your valuable reply before I purchase.

KDan (author) 1 year ago
hanks, plastic gears are standard off-the-shelf and they are machined from Cast Nylon Blanks (strong). ,
bowen931 year ago
hi love all this can i ask how hard the plastic is and are you able to make custom gears and cogs ?
KDan (author)  bowen931 year ago
Thanks, plastic gears are standard off-the-shelf and they are machined from Cast Nylon Blanks (strong). ,
KDan (author) 2 years ago
Thanks, i got these gears from stock drive products SDP A 1C10MYK10096, SDP A 1Z 2MYZ1002408, SDP A 1P 2MYH10036
dr152 years ago
Very cool.
Where did you get the gears?