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Toggle Joint

A toggle joint mechanism can be used to multiply force.

Toggle joint mechanism

The toggle mechanism is made of two arms linked together. Point 1 is fixed, point 3 can move horizontally (as indicated in this principal drawing). The effort force acts vertically in point 2. 

The horizontal force acting in point 3 can be calculated for arms with equal or unequal lengths.

Arms with equal lengths

P = F a / 2 h                            (1)


P = horizontal force in point 3 (N, lb)

F = effort force (N, lb)

a = length (m, ft)

h = height (m, ft)

Arms with unequal lengths

P = F a / b                             (2)


b = length (m, ft)

Example - An Improvised Press for Replacing Car Bushings

A press to remove/refit bushings in car linkage arms can be improvised with two pieces of lumber:

toggle joint - improvised bush press

The effort force acting on the toggle joint (in point 2) with a person with weight 90 kg can be calculated as

F = (90 kg) (9.81 m/s2)

  = 883 N

The force acting on the bush (in point 3) can be calculated as

P = F a / 2 h

   = (883 N) (1983 mm) / (2 (258 mm))

   = 3393

The force ratio is 

 Fr = (3393 N) / (883 N)

    = 3.8

- the initial effort force is amplified near four times

Toggle Joint Calculator

This calculator can be used to calculate the resulting force in a toggle joint with arms with equal lengths. The calculator can be used for imperial and metric units as long as the use of units are consistent.

Note that kg is the SI unit of mass - check the difference between mass and weight (force).

Related Topics

  • Mechanics

    The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

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