This section is from the book "Applied Science For Metal Workers", by William H. Dooley. Also available from Amazon: Applied Science For Metal Workers.

Problems in compound leverage are easily reduced to repeated cases of simple leverage, the force at the end of the first lever being the weight or force applied to the second lever, and so on through any number of levers.

As an example: If the force at W in Fig. 14 is 12 lbs., what is the force at P?

For the first lever the force pushing up at the end of the long arm is: 12 X 3 / 12 = 3 lbs. For the second lever it is: 3 X 3 /12 = 3/4 lb.

While the safest way is always to figure each lever as a simple lever, as just explained, a shorter method of obtaining the answer is as follows:

Multiply the weight by the continued product of the short arms of all the levers, and divide this by the continued product of the long arms of the same levers.

Fig. 14. - Compound Lovers.

Applying this rule to the above problem we have

12 X 3 X 3 / 12 X 12-------------- = 3/4 lb.

The answer is the same as before, and after a little thought it is evident that the two steps in the first case have merely been put together in one expression in the second case. If the weight, 3/4 lb., on the long end of the second lever at P is known (see Fig. 14), and the pressure or weight which would be needed at W is to be found, the same rule will apply but will be expressed in this manner: Multiply the weight by the continued product of the long arms and divide this by the continued product of the short arms:

3 / 4 X 12 X 12 / 3 X 3 = 12 lbs.

Regardless of how many levers there are working together, the rule is applicable. In all leverage problems the first, and the most important, thing is to find and locate the fulcrum, as the fulcrum is the point which determines the moment arms from which the required answer is obtained. The moment arm is always the perpendicular distance from the force or weight to the fulcrum.

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