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# 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

## Related Topics

• ### Mechanics

Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

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• ### Conn-Rod Mechanism

The connecting rod mechanism.
• ### Efficiency of Small Machine Elements

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• ### Force

Newton's third law - force vs. mass and acceleration.
• ### Force Ratio

The force ratio is the load force versus the effort force.
• ### Gear Reducing Formulas

Output torque, speed and horsepower with gears.
• ### Gear Trains - Bicycle Gearing Calculator

Gear train transmissions - bicycle gearing.
• ### Mass vs. Weight

Mass vs. weight - the Gravity Force.
• ### Toggle Joint

A toggle joint mechanism can be used to multiply force.

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## Citation

• The Engineering ToolBox (2008). Gears. [online] Available at: https://www.engineeringtoolbox.com/gears-d_1307.html [Accessed Day Month Year].

Modify the access date according your visit.

2.19.10