Levers

The effort and the load are on the same side of the fulcrum, applied in opposite directions.
The load lies between the effort and the fulcrum.
The effort force is smaller than the load force.
The effort moves a greater distance than the load.
Functions as a force magnifier.

Third-Order Lever

The effort lies between the load and the fulcrum.
The effort force is greater than the load force.
The load moves a greater distance than the effort.
Functions as a distance magnifier.

When a lever is subject to multiple load forces, the principle of moments is extended. The generic equation for the effort force ( $F_e$ ) required to balance multiple loads ( $F_{lA}, F_{lB}, ..., F_{lN}$ ) is:

F_e = \frac{F_{lA} d_{lA} + F_{lB} d_{lB} + \dots + F_{lN} d_{lN}}{d_e}

Where $d_{lA}, d_{lB}, ...$ are the respective distances from each load force to the fulcrum.

Example: A lever is subjected to three loads: $F_{lA} = 1\ \text{lb}$ at $d_{lA} = 1\ \text{ft}$ , $F_{lB} = 2\ \text{lb}$ at $d_{lB} = 2\ \text{ft}$ , and $F_{lC} = 3\ \text{lb}$ at $d_{lC} = 3\ \text{ft}$ . The required effort force at an effort arm distance $d_e = 2\ \text{ft}$ is:

F_e = \frac{(1\ \text{lb} \cdot 1\ \text{ft}) + (2\ \text{lb} \cdot 2\ \text{ft}) + (3\ \text{lb} \cdot 3\ \text{ft})}{2\ \text{ft}} = 7\ \text{lb}

References

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