# 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 N *

The force ratio is

*F _{r} = (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).

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