Toggle Joint

Overview

Engineering reference data for Toggle Joint in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Example: Improvised Press for Car Bushings

An improvised press to remove or refit bushings in car linkage arms can be created using two pieces of lumber, forming a toggle joint. The effort force is applied vertically at point 2 by a person's weight.

Given:

• Weight of person: $m = 90 \, \text{kg}$
• Acceleration due to gravity: $g = 9.81 \, \text{m/s}^2$
• Arm length: $a = 1983 \, \text{mm}$
• Height: $h = 258 \, \text{mm}$

The effort force $F$ is calculated as:

$$F = m \cdot g = (90 \, \text{kg}) \cdot (9.81 \, \text{m/s}^2) = 883 \, \text{N}$$

Using the formula for toggle joints with equal arm lengths:

$$P = \frac{F a}{2 h}$$

where $P$ is the horizontal force at point 3.

Substituting the values:

$$P = \frac{(883 \, \text{N}) \cdot (1983 \, \text{mm})}{2 \cdot (258 \, \text{mm})} = 3393 \, \text{N}$$

The force ratio $F_r$ is:

$$F_r = \frac{P}{F} = \frac{3393 \, \text{N}}{883 \, \text{N}} = 3.8$$

This shows that the toggle joint amplifies the initial effort force by nearly four times.

Toggle Joint Calculator

A calculator is available to compute the resulting force in a toggle joint with arms of equal lengths. It supports both imperial and metric units, provided that the units are used consistently.

Input parameters:

• $F$: effort force (N, kg, lb)
• $a$: length of arms (m, mm, in, ft)
• $h$: height (m, mm, in, ft)

Note: When using kg for force, it is the SI unit of mass. Ensure to convert mass to force by multiplying by gravity if necessary, as the calculator assumes $F$ is in force units (N or lb).

This calculator simplifies the calculation by applying the formula $P = \frac{F a}{2 h}$.

References

• Original Source