Compound lever press and the multiplication of force
Notes reckon a 100-pound, 9-braccia beam with a 1/6 counter-lever raising the load to thousands of pounds.
The sheet studies a compound lever press and calculates the enormous force it can develop. A vertical screw press stands on a timber bench at the left, worked through a long horizontal beam that runs across the top; a lower lever slopes down to the right and ends in a weight hung over a small pulley. The beams are lettered a, b, c and d and annotated with loads in pounds (libbre): the beam weighs 100 pounds and is 9 braccia long with a sixth of a braccio of counter-lever. Reckoning the leverage, every pound applied yields 108 at the fulcrum, so that 100 pounds at the end of the lever and the beam's own weight together amount to some 113 thousand and 400 pounds bearing on the fulcrum.
On this page
Screw press worked by a compound lever
At the left a vertical screw press is mounted on a heavy timber bench. A long horizontal beam runs across the top of the sheet, and a second lever below slopes down to the right to a weight hung over a pulley. The bearing points are lettered a, b, c and d.
Weight of the beam and where it bears
The beam itself weighs 100 pounds, of which 50 bear at b and only 10 reach a. Being 9 braccia long with a sixth of a braccio of counter-lever, it is reckoned to exert 2700 pounds of force by itself, and as much again beyond the fulcrum to stay in balance, so that 5400 pounds rest on the fulcrum.
Counter-lever multiplies the load 108-fold
Because the lever is 54 sixths against one of counter-lever, every pound placed at the end of the lever resists 54 at the counter-lever's end and twice as much again at the fulcrum, which is 108 pounds. So every pound given to the lever yields 108 at the fulcrum of the beam.
Summing the load: 113 thousand and 400 pounds
Giving 100 pounds to the end of the lever makes the fulcrum feel 108 thousand. Joined to the 5400 pounds the beam produces by its own weight, the total on the fulcrum comes to 113 thousand and 400 pounds. The loads 1200, 200, 100 and 50 label the two levers.