The Reasons of Motive Forces

Of motive forces.

THEOREM XIV.

Vitruvius Marcus Vitruvius Pollio, a Roman architect and engineer whose work was the foundation for Renaissance engineering. makes mention of this kind of machine, called by the Greeks troclearum original: "troclearum" — a Latinized Greek term for a system of pulleys or a block and tackle., which derives its motion by means of pulleys. Let it be constructed as the figure demonstrates, and at the pulley blocks marked D and E, there shall be a pulley in each; and let a rope be passed through the said pulleys, of which one end shall be attached to the upper block, and the other end shall serve to pull the burden, as can be seen in the figure. Therefore, if one pulls the said end of the rope marked G one foot downward, the burden which is attached to the block E will at the same time rise half a foot; and this is because the rope is passed double through the pulleys. Thus, if one pulls 20 feet of rope, the burden will only rise 10 feet. Also, one man will pull as much weight with this machine as two men would if the machine were simple A "simple" machine here refers to a direct pull without the mechanical advantage of a block and tackle.; but the two men would pull twice the height in the same amount of time—namely 20 feet—before the other has pulled more than ten. And if there were two pulleys in the blocks, as in figure M, the force would be quadruple, but the burden would only rise 5 feet for every 20 feet of rope pulled.

A technical illustration of a pulley system. On the right, a tripod or "shears" mechanism supports a block and tackle labeled 'D' and 'E'. A man in period clothing pulls on a rope marked 'G'. To the left, a circular inset labeled 'M' provides a detailed view of a double-pulley block.

THEOREM XV.

Toothed wheels are also made with the same logic as the preceding examples, for by increasing the force, one increases the time proportionally. For example, let there be a machine for lifting burdens, made in such a way that a pinion marked A can turn a large toothed wheel marked B. The said pinion shall have 6 teeth, and the large wheel 48; thus it will be necessary for the said pinion to make 8 turns for every one of the large wheel. Consequently, if one pound original: "liure" — the French livre, a pre-metric unit of weight roughly equal to 489 grams. is hung from axle C, it will be equally balanced by 8 pounds hung from axle E, provided that the said axles are of equal thickness; thus when one wishes to pull 400...

A technical diagram of a gear and axle mechanism for lifting. A man on the right operates a crank handle connected to a small toothed pinion labeled 'A'. This pinion meshes with a larger vertical toothed wheel labeled 'B', which is mounted on a primary axle labeled 'C'. A rope is wound around another axle segment labeled 'E', lifting a weight marked with the number '8'. The mechanism is supported by a sturdy wooden frame.