The Reasons of Motive Forces

Book One,

THEOREM XVII.

A mechanical diagram of a worm gear system. A horizontal screw (labeled B) with a crank handle on the right end is positioned above a large wheel (labeled A). The wheel has four large triangular spokes and a rim with many teeth that mesh with the threads of the screw.

There is also another type of worm gearoriginal: "pignon à vis"; a mechanism where a screw (the worm) meshes with a toothed wheel, allowing for high torque and large gear reductions., as can be seen in the present figure, which causes the force to be multiplied much more significantly; it is also very suitable for certain machines to make them more portable. However, there is a disadvantage: it wears down and is not as durable as the toothed variety, because the screw, while turning, slides along the teeth of the wheel and wears significantly. The other variety with teeth referring to standard spur gears, in turning, pushes the other teeth and does not wear as much. To demonstrate the principle of its force, let there be a wheel of 48 teeth, as shown in the next figure A; and let the worm gear be represented by the letter B, which shall have the spacing of the screw thread of the same width as the spacing of the teeth of the wheel. Thus, in turning the handle one revolution, the said screw will make the wheel A turn by one tooth. It will therefore be necessary to turn the said screw 48 times for the said wheel A to turn once, so that the force will be multiplied in the same proportion as the time—namely, 48 times as much at the axleoriginal: "laxe" (l'axe) of wheel A as at the axle of the screw.

THEOREM XVIII.

A diagram of a vertical screw press. A large vertical screw (labeled C) is threaded through a heavy horizontal crossbeam (labeled A) supported by two pillars. A long horizontal lever (labeled D) is attached to the screw. A man is shown pushing the lever to turn the screw, which exerts downward pressure toward the base (labeled B). The man is positioned at the far end of the lever to maximize mechanical advantage.

The screw press is a machine of great force, which is also similar in principle to the preceding ones; for example, let there be a press marked A B, which will have the screw marked C F, the thread of which screw will be one inch in width. Let the lever of the said screw be marked E D, which shall be 7 feet long from the center of the said screw to the point where the man leans, marked D. Thus, if a man turns the said lever at a distance of 7 feet from the center, according to the method of Archimedesoriginal: "praticque d’Achimedes"; referring to the Archimedean approximation of Pi (22/7) to calculate circumference from diameter., it will be 22 feet in circumference De Caus calculates 22 feet of circumference for a 7-foot lever. Using the Archimedean ratio of 22/7, a radius of 7 feet should result in a circumference of 44 feet; he likely used 7 feet as the diameter for this calculation., which makes 264 inches, which the end D must travel in