Gears
Gears effort force vs. load force.
A gear is a mechanical device that transmits rotary motion by changing the magnitude and line of action of the effort force.
The effort force can be expressed as
F = W (r _{ 1 } r _{ 2 } .. r _{ n } ) / (R _{ 1 } R _{ 2 } .. R _{ n } ) (1)
where
F = effort force (N, lb _{ f } )
W = load force or weight (N, lb _{ f } )
r = gear wheel inside diameter (m, in)
R = gear wheel outside diameter (m, in)
Example  Gear Transmission and Effort Force
The effort force in a gear transmission with three wheels:
 wheel 1 : r _{ 1 } = 0.05, R _{ 1 } = 0.12
 wheel 2 : r _{ 2 } = 0.06, R _{ 2 } = 0.13
 wheel 3 : r _{ 3 } = 0.07, R _{ 3 } = 0.14
and a weight load of 1000 N can be calculated as
F = W (r _{ 1 } r _{ 2 } r _{ n } ) / (R _{ 1 } R _{ 2 } R _{ n } )
= (1000 N) ((0.05 m) (0.06 m) (0.07 m)) / ((0.12 m) (0.13 m) (0.14 m))
= 96 N
= 0.1 kN
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