A differential movement whose principle is employed in the construction of counting apparatus is shown in Figure 3o (p1. 12o). Two concave-cut wheels are so arranged that a screw will fit into the teeth of both wheels at the same time. If, for example, one of the wheels has one hundred teeth and the other wheel has one hundred and one teeth, then for each hundred revolutions of the screw the hundred-toothed wheel will make one revolution, and the other wheel will lack one degree or one-hundredth of a complete revolution. This differential rotation of the wheels is made visible by fastening to the hub of one wheel and to the axis of the other a hand or pointer; these at starting are so set that the two pointers shall coincide at the zero point: upon the completion of the rotation of the wheels it will be seen that the pointer of one wheel is one division or a degree in advance of the other.
Figure 3r is an application of internal or " epicycloidal " gear to pul ley-blocks or hoisting machines. The toothed ring is connected with the mechanism to be moved; the propelling spur-toothed wheel within is cen tred upon an eccentric-hub on the shaft, but is prevented from revolving by the arm whose slotted extremity slides upon a fixed pin. One revolu tion of the eccentric makes the inner wheel interlock its teeth all around with those of the ring, but as the ring has a greater diameter, and conse quently more teeth, it lacks the difference of circumferences of completing a revolution. In Figure 32 is shown a rotary screen in which a large bevel-toothed ring is secured to the floor; the spindle of the screen rests and revolves in a ball-joint; about midway on the spindle is a bevel-pinion which gears into the teeth of the fixed ring. Turning the spindle imparts not only a rotary motion to the pan or screen, but also a rocking motion.
To obtain an indefinite increase of the power of the screw, without diminishing the strength of the thread, two screws having different pitches (as shown in fig. 33) were proposed by Dr. Hunter, whose con trivance is known as the "differential screw." While the working point is urged forward by the screw that has the greater thread, it is drawn back by the screw that has the lesser thread, so that during each revolution the screw, instead of being advanced through a space equal to the pitch of either of the threads, moves through a space equal to their difference.
For irregular and intermittent motions devices called " cams " are employed. A cam is a projecting part of a wheel or other moving piece, so shaped as to give the desired motion to a piece sliding against or rolling upon it. Figure 34 shows a side-face cam for impart ing one movement at each revolution of the cam; Figure 35 is a cam for giving a succession of lifts and drops to a piece moving vertically, as a stamp; and Figure 36 gives the heart-shaped cam, which imparts a uniform outgoing and incoming motion to the rod jointed to the lever.
Figure 37 is similar to Figure 34, but is double-acting; its opposite face is for making the return !notion certain. Figure 38 illustrates a more com plicated arrangement of cam, lever, and rod. Two cams operate two similar levers and rod-connections. The cams are so shaped that during three-fifths of their revolution the levers will be moved uniformly upward, and of course each will descend during two-fifths of a revolution. If now each rod be attached to a pump-bucket with a valve lifting upward, both rods working in the same pipe, and if the cams be set with their like motions opposite each other, there will result the working principle of the "equable pump" invented by Mr. White prior to 1822, and reinvented many times since.
Figure 39 (pl. 12o) may be classed among cam movements; it represents the barrel-motion of musical instruments, looms, and the like, in which the barrel is provided with pins or staples for lifting their respective levers or parts to which either instantaneous or prolonged motion is to be given.
Mechanical devices arc usually employed for modifying and directing motion; but are also employed for reducing and stopping motion by the application of brakes and friction-pieces. The common brake-block, forced against a wheel by a lever, is shown in Figure 4o; in Figure 41 there is presented a more elaborate device, which consists of a flexible band faced with separated blocks (so as to increase the area of contact and insure its uniformity), which are forced to embrace the wheel by a lever that has a counterweight adapted to relieve the embrace of the band when the pressure is removed. Figure 43 presents an ingenious device, called a " rope-brake," which checks or stops a running rope by the grip of the brake-jaws when the angular distance of their centres becomes less, as it does when the lever end is pressed down. Friction surfaces may be mul tiplied in many ways. In the case of a brake acting as a check to recti lineal moving pieces, compound plates with intermediate friction surfaces are used, as represented in Figure 42. The friction surfaces are all forced into close contact at once by right- and left-hand screw-grip levers operated by a hand-crank or by other means. In various kinds of revolving mech anism driven by a cord, a weight, or a spring, the speed may be reduced, and regulated within certain limits, by the fan-brake (fig. 44), which may be run in the open air or in a liquid enclosed in a box.