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# Toggle Joint

## A toggle joint mechanism can be used to multiply force.

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)

where

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)

where

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:

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.

F - force (N, kg, lb)

a - length (m, mm, in, ft)

h - height (m, mm, in, ft)

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

## Related Topics

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

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