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Gears and effort force

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A gear is a mechanical device that transmits rotary motion by changing the magnitude and line of action of the effort force.

Gears transmission - force and line of action

The effort force can be expressed as

F = W (r1 r2 .. rn) / (R1 R2 .. Rn)                                     (1)


F = effort force (N, lbf)

W = load force or weight (N, lbf)

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 rn) / (R1 R2 Rn)

  = (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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  • en: gears effort force diameter radius
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