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**Notations of planetary gearing elements for the next table ^[1]**
Name	Number of teeth	Speed
${\color {blue}Driving}\,$	${\color {blue}z}\,$	${\color {blue}n}\,$
${\color {magenta}Auxiliary\ driving}\,$	${\color {magenta}z}\,$	${\color {magenta}n}\,$
${\color {red}Driven}\,$	${\color {red}z}\,$	${\color {red}n}\,$
$Fixed\,$	$z\,$	$n\,$
${\color {green}Planetary}\,$	${\color {green}z}\,$	${\color {green}n}\,$
${\color {cyan}Planetary}\,$	${\color {cyan}z}\,$	${\color {cyan}n}\,$

**Sketch and output speed of planetary gearings**
Output speed	Output speed	Output speed	Output speed
${\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {red}z}})$	${\color {red}n}={\color {blue}n}(1-{\frac {z}{\color {red}z}})$	${\color {red}n}={\color {blue}n}(0+{\frac {z}{\color {red}z}})$	${\color {red}n}={\color {blue}n}(\cos \beta +{\frac {z}{\color {red}z}})$
${\color {red}n}={\color {blue}n}(1+{\frac {{\color {green}z}z}{\color {cyan}z\color {red}z}})$	${\color {red}n}={\color {blue}n}(1+{\frac {{\color {green}z}z}{\color {cyan}z\color {red}z}})$	${\color {red}n}={\color {blue}n}{\frac {1}{(1+{\dfrac {{\color {green}z}z}{\color {cyan}z\color {red}z}})}}$	${\color {red}n}={\color {blue}n}{\frac {1}{(1+{\dfrac {{\color {green}z}z}{\color {cyan}z\color {red}z}})}}$
${\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {red}z}})$	${\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {red}z}})$	${\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {blue}z}})$	${\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {blue}z}})$
${\color {red}n}={\color {blue}n}{\dfrac {{\color {cyan}z}z}{{\color {green}z}{\color {red}z}}}$	${\color {red}n}={\color {blue}n}{\frac {1-{\dfrac {z\color {green}z}{\color {cyan}z\color {red}z}}}{1+{\dfrac {z}{\color {blue}z}}}}$	${\color {red}n}={\color {blue}n}{\frac {1-{\dfrac {z\color {green}z}{\color {cyan}z\color {red}z}}}{1+{\dfrac {z}{\color {blue}z}}}}$	${\color {red}n}={\color {blue}n}{\dfrac {1}{1+{\dfrac {z}{\color {blue}z}}}}$
${\color {red}n}={\color {blue}n}{\dfrac {1}{1-{\dfrac {{\color {cyan}z}z}{{\color {green}z}{\color {blue}z}}}}}$	${\color {red}n}={\color {blue}n}{\dfrac {1}{1-{\dfrac {{\color {cyan}z}z}{{\color {green}z}{\color {blue}z}}}}}$	${\color {red}n}={\color {blue}n}{\frac {1-{\dfrac {z\color {green}z}{\color {cyan}z\color {red}z}}}{1+{\dfrac {z}{\color {blue}z}}}}$	${\color {red}n}={\color {blue}n}(1-{\frac {{\color {green}z}z}{\color {cyan}z\color {red}z}})$
${\color {red}n}={\color {blue}n}\left[1-\left({\frac {\color {magenta}n}{\color {blue}n}}-1\right){\frac {\color {magenta}z}{\color {red}z}}\right]$	${\color {red}n}={\color {blue}n}\left[1-\left({\frac {\color {magenta}n}{\color {blue}n}}-1\right){\frac {\color {magenta}z}{\color {red}z}}\right]$	${\color {red}n}={\color {blue}n}{\frac {1+{\dfrac {\color {magenta}n\color {magenta}z}{\color {blue}n\color {blue}z}}}{1+{\dfrac {\color {magenta}z}{\color {blue}z}}}}$	${\color {red}n}={\color {blue}n}{\frac {1+{\dfrac {\color {magenta}n\color {magenta}z}{\color {blue}n\color {blue}z}}}{1+{\dfrac {\color {magenta}z}{\color {blue}z}}}}$

Reference

^ Pattantyús Gépész- és Villamosmérnökök Kézikönyve 3. tom. Műszaki Könyvkiadó, Budapest, 1961. p.632.

[1] Pattantyús Gépész- és Villamosmérnökök Kézikönyve 3. tom. Műszaki Könyvkiadó, Budapest, 1961. p.632.

[1]

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