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: http://en.wikipedia.org/wiki/Epicyclic_gearing 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.
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
The ratio is 5:1, as design was required.