Gears

Gears and effort force

A gear is a mechanical device that can transmit rotary motion and change both the magnitude and the line of action of an effort force.

The effort force can be expressed as

F = W (r₁ r₂ .. r_n) / (R₁ R₂ .. R_n)         (1)

where

F = effort force (N, lb)

W = load force or weight (N, lb)

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 : r₁ = 0.05, R₁ = 0.12
• wheel 2 : r₂ = 0.06, R₂ = 0.13
• wheel 3 : r₃ = 0.07, R₃ = 0.14

and a weight load of 1000 N can be calculated as

F = W (r₁ r₂ .. r_n) / (R₁ R₂ .. R_n)

= (1000 N) ((0.05 m) (0.06 m) (0.07 m)) / ((0.12 m) (0.13 m) (0.14 m))

= 96 N

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