User:Kaboldy/Something

Notations of planetary gearing elements for the next table

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

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