## Mechanical Scales

### Lever Systems

A lever is used to either increase/decrease force or to change force direction. There are three classes of levers as listed below.

- First Class Levers - (multiplying or reducing)
- Second Class Levers - (multiplying)
- Third Class Levers - (reducing)

*Lever Classes*

The ratio of a lever is calculated as (Power Arm)/(Load Arm) or Pa/La

Total multiple of a "lever train" is calculated by multiplying the multiples of each individual lever together.

The ratio of the lever train in the graphic above is 40:1. This is calculated as:

Lever "A" = 40 ÷ 4 = 10 : 1

Lever "B" = 32 ÷ 4 = 8 : 1

Lever "C" = 15 ÷ 30 = 0.5 : 1

Multiply the ratios together give us 10 * 8 * 0.5 = 40:1. Therefore, the ratio of the lever train is 40:1. From this, we can calculate that it will take 6 kilograms on the right pan to balance 240 kg on the left pan (6 kg * 40 = 240 kg or 240 kg ÷ 40 = 6 kg).

Ratios of 1.0:1 or larger are considered multiplying, while ratios below this are considered reducing.

A multiplying lever will allow a large load to be moved with less force, but will require the power arm of the lever to be moved a greater distance, while a reducing lever will require more force than the load to be moved, but the power arm will need to be moved less distance than the load.

- Ratio = Pa / La
- La = (P * Pa) / L
- L = (P * Pa) / La
- Pa = (L * La) / P
- P = (L * La) / Pa

*Formulas for Levers*

- La = Load Arm (length of arm from Fulcrum Pivot to Load Pivot)
- Pa = Power Arm (length of arm from Fulcrum Pivot to Power Pivot)
- L = Load (force applied to lever by scale load)
- P = Power (force counteracting load)
- Lp = Load Pivot (point at which the load is applied to the lever)
- Pp = Power Pivot (point at which power is applied to the lever)
- Fp = Fulcrum Pivot (point around which the lever tends to rotate)

*Where:*

If you were to draw an imaginary line running across the tops of the Lp, Pp and Fp you would have found the "Pivot Line". If you imagine an equal arm balance with the tops of all pivots touching the pivot line and the mass of the lever evenly distributed above and below this line you would have a "Neutral Lever" which is much too sensitive to be useful as a balance.

However, if the mass is slightly heavier below the Fulcrum Pivot or if the Lp and Pp are running below the "Pivot Line" (Open Range), then the lever becomes stable but less sensitive. The heavier this mass, the less sensitive the lever. This effect can be overcome somewhat by adding a "Balance Ball" to the top of the lever. Raising the "Balance Ball" increases the sensitivity of the lever.

If the reverse situation is true, the mass is above the "Pivot Line" (Closed Range), or the Lp and Pp are above the Pivot Line then the lever becomes "super sensitive" or unstable. This type of lever is sometimes used to overcome the effects of lever deflection. As more weight is added to the lever it will tend to deflect, therby lowering the top of the Lp and the Pp. As the beam continues to deflect, it will first become "Neutral" and then "Open Range".