The Library of Work and Play: Mechanics, Indoors and Out

by Fred. T. Hodgson

In the evening, Mr. Gregg, Jessie, and the boys took a trip, and Mr. Gregg was well pleased with the boat's performance, particularly with the working of the screw. In mentioning this, he awakened the curiosity of George, who reminded his father that he had not yet explained to them about the screw as a mechanical power.

Fig. 33. Theory of screw

That evening George was told to bring his blackboard and equipment into the den, and the father at once began explaining the mechanical qualities of the screw. He told of its great usefulness in the industrial arts. As one of the mechanical powers, it may be considered an inclined plane, wrapped spirally round a solid cylinder. The advantage gained by it depends on the slowness of its forward or backward progress, that is, on the number of turns or threads, as they are called, in a given distance. It is always used in combination with a lever of some sort. When employed as a lifting machine it has great power, and is used to produce compression or to raise or move heavy weights. If a screw is formed on the inside surface of a hollow cylinder, it is called a nut, and used to overcome a resistance; either the screw or the nut may be fixed and the other movable. The acting force is generally applied at the end of a lever or wrench or rim of a wheel. [Fig. 33] represents a screw and nut operated by a lever or length of radius r; p is the pitch of the screw or height of the inclined plane for one revolution of the screw. W is the resistance at the nut and P is the force at the end of the lever r. Remembering that, while the resistance W is raised the distance p the force P revolves around a complete circle and moves a distance 2πν. Let us now apply the condition
Σwork = 0
and we have

P2πν - Wp = 0 or — = P2πν/p (6).

Fig. 34. Worm wheel and screw

The worm gear ([Fig. 34]) is a special case of screw and nut, where the latter is replaced by a toothed wheel called a worm wheel. The teeth work in with the thread of the screw or worm, and thus, as the worm revolves, the worm wheel revolves about its axis. P is the force acting on the worm at a radius r. r´ is the pitch radius of the teeth in the worm wheel and r´´ is the radius of the drum on which W acts. Let K, corresponding to W in equation W P (6), be the force at the pitch circle and worm threads due to the force P; then
K = P2W/p (7).