Gears

Gears and effort force

A gear is a mechanical device that can increase the magnitude 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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