Figure 14 exhibits the common crank, a simple method of producing rotary motion by hand; while Figure 15 shows the means of producing rotary motion through a treadle by the action of the foot. By the device shown in Figure 16 rotary motion is imparted by one going-wheel to another wheel of the same or of different size by the frictional contact of truly-formed cylindrical surfaces whose axes are parallel, and whose surfaces are held together by a certain constant pressure; the material in contact may be of wood, rubber, leather, rawhide, metal, or any combi nation of these materials.
Liability to slipping is inseparable from all devices which drive by contact. To overcome slipping and to make the imparting of the motion sure and positively proportional to the circumference of the wheels, there are formed upon their peripheries teeth which, being evenly spaced, engage with one another and impart motion and force without loss of velocity. A pair of engaged spur-wheels with external teeth are shown in Figure 17, their shafts turning in opposite directions. In Figure IS the larger wheel has teeth formed on the inner circumference, while the smaller wheel has the teeth on the outer circumference. In this example the shafts turn in the same direction at speeds inversely proportionate to their diameters, and the wheels have more teeth in contact at all times than have those in Fig ure 16. In both cases the motions of the shafts are uniformly circular.
If an irregular motion be required, as when during half the revolution the outgoing movement must be slow and the incoming movement rapid, an arrangement of elliptical cog-wheels (fig. 19) meets this requirement when the shafts are placed in the foci of their ellipses, but the pulsations are doubled per revolution when their shafts are placed in their centres as shown. The cog-wheels in Figure 20, called " rectangular gears," pro duce four waves of motion during each revolution. All gears not truly circular—and their forms arc numerous—are devised only for special purposes.
In all the given examples of gears the shafts of each pair are parallel. When it becomes necessary to drive shafts that lie in the same plane but are at an angle with each other, conical cog-wheels are employed in which all the working lines on the faces of the teeth converge to one common centre, which is coincident with that through which pass the axes of the shafts. Figure 21 (II. 12o) shows gears of this sort, which arc called "mitre-wheels" when both wheels are alike and upon shafts that arc at right angles, and "bevel-wheels" when of different diameters, whatever the inclination of their shafts. The movement shown in Figure 22, to
which the name of " perpetual screw " has been given, consists simply of an ordinary screw that engages with a spur-wheel having teeth set at an angle across its face and conforming somewhat to the screw-thread. The screw in this case may be considered as a cog-wheel of one tooth, which, instead of being parallel with the axis of the wheel, is wound spirally around the screw-hub, and as a consequence the wheel which it drives is advanced only one tooth at each revolution of the screw. The screw may also be applied to propel a rack, as is shown in Figure 23, which is the most ancient form (as early as the fourth century) in which the screw was employed. A superb modern application is that devised by William Sellers Co., in which a screw upon the end of a shaft lying at an angle with the moving bed of a planer drives the bed back and forth. (See p. 121.) The rack and pillion is shown in Figure 24, in this example having skew teeth. In both these examples the motion cannot be contin uous, as in Figure 22, since the length of the rack determines the move men t.
Figurers' 25 and 26 represent ratchet-and-pawl contrivances; the first with lever and pawls for actuating the wheel in a step-by-step intermit tent way, and the second with several forms of "stops" or catches for holding the motion obtained. In Figure 27 the device is given a linkage connection, by which the pawl is automatically raised from the tooth space on the wheel and is lowered into another space by the same motion of the lever that rotates the wheel.
Gears to which the name of "differential " has been given are shown in Figures 2S and 29, the first representing one broad-face spur-pinion gearing into two narrow-face spur-wheels having a different number of teeth—for example, one tooth less in one wheel than in the other. It is evident that when the pinion counts all the teeth of one spnr-wheel it will lack or will exceed one tooth of the other wheel; hence the two spur-wheels have a differential movement. The same result takes place with the move ment shown in the second example: the pinion turns freely upon a hub on the shaft, gearing alike into two internally-toothed rings, one of which has one tooth less than the other. If we fix one ring from turning and permit the other to turn freely upon the common axis, we shall find that when the pinion matches the teeth all around one ring, the other ring will have an advance or a retrograde movement of one tooth per revolution.