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The inclined plane constitutes a second broad classification of machine elements. The wedge, the screw, the cam, and the eccentric, all belong to the family of the inclined plane.

FIG. 18.—INCLINED PLANE WITH EFFORT PARALLEL TO THE BASE

A simple form of inclined plane is pictured in Figure 17, which shows a weight W being rolled up an incline. The effort required to carry it to the top of the incline depends, of course, upon the steepness of the incline. The drawing shows a rise of 3 feet on a slope 5 feet long, and the weight of the wheel is, say 20 pounds. To find the effort required, the weight is multiplied by the rise (20 × 3 = 60) and divided by the length of the slope (60/5 = 12) and we find that it takes only 12 pounds to roll the 20-pound wheel to the top of the incline. This holds true when the pull is parallel to the inclined face. If the pull is parallel to the base of the incline, as in Figure 18, we must divide by the length of the base instead of the length of the incline (60/4 = 15) and we find that it takes 15 pounds of effort to pull the weight up the incline. If the pull is exerted at an angle both to the base and the inclined face, we have a problem that is slightly more complicated and we need not go into it here because it involves a bit of trigonometry. In all cases, however, it may be noted that the amount of rope that is taken in, in hauling the weight up the incline, bears a definite relation to the amount of effort required to raise the weight. In Figure 17, 5 feet of rope must be pulled in, in order to raise the weight 3 feet, so that ⅗ of 20 or 12 pounds is all that is required to pull up the weight, while in Figure 18, 4 feet of rope is hauled in for a lift of 3 feet, so that ¾ of 20 or 15 pounds is required to pull up the weight. In this respect the inclined plane is exactly like the lever or the pulley, for the effort multiplied by the distance through which it is exerted is always exactly equal to the weight multiplied by the distance through which it moves. Thus in Figure 17, the effort 12 pounds multiplied by the distance 5 = the weight 20 pounds times the distance 3, and in Figure 18, effort 15 x distance 4 = weight 20 x distance 3. Of course, we are ignoring the weight of the rope and the friction which, in actual practice, are important factors to be reckoned with.

FIG. 19.—ENDLESS SCREW OR WORM GEAR

So far we have considered a fixed inclined plane, but when the inclined plane is moved between the weight and a fixed base it is known as a wedge, and in this case, too, the effort required to move the wedge multiplied by the distance the wedge moves is equal to the weight multiplied by the distance it is lifted.

The commonest form of inclined plane is the screw which is merely an inclined plane bent around a cylinder. A screw engaging a toothed wheel, as in Figure 19, gives a combination known as an “endless screw,” or, more commonly, as a worm gear. The screw or worm is always the driver, and as it must make a complete turn to move the gear through a space of one tooth, the power of this combination is very great. It is practically impossible to turn the worm by using the gear wheel as a driver because the friction developed at the point where the worm and gear contact is very great. For this reason worm gearing is used in the steering gear of automobiles. The shaft of the steering wheel is fitted with a worm which meshes with a worm gear on the parts connected with the wheels. It is very easy to turn the wheels by operating the steering wheel, but if the wheels strike a rut or a stone they are not deflected from their course, because the worm makes it impossible for them to turn the steering wheel.

FIG. 20.—HELICAL OR SPIRAL GEARS

The spiral gear shown in Figure 20 is a cross between a worm gear and spur gear. The teeth are spirals set at an angle of 45 degrees to the axis of the wheel. In this case either gear can be used to drive the other, and the advantage of such a pair is that power is transmitted from one shaft to another in a different plane and at right angles to the first.

FIG. 21.—DRUM CAM

FIG. 22.—PROFILE OR DISK CAM

Cams are usually irregular revolving inclined planes. Figure 21, shows a cylinder or drum cam. A groove is cut in the cylindrical wall of the cam and an arm or lever is provided with a roller which rolls in the groove. When the cam is revolved the lever is constrained to follow all the twists and turns of the groove. A different form of cam is shown in Figure 22. It is formed with an irregular periphery against which the roller is pressed by a spring. As the cam wheel revolves, the roller and the arm to which it is attached must move in and out over all the hills and valleys of the periphery. The cam is one of the most useful elements in modern machinery, for it provides a very simple means of producing the most complicated and irregular motions.

FIG. 23.—ECCENTRIC BY WHICH ROTARY MOTION IS CONVERTED INTO RECTILINEAR MOTION

We cannot attempt to describe all the different types of cams, but reference should be made to the eccentric, which is a form of cam commonly used to operate the valves of a steam engine. The cam in this case is a perfectly circular disk, but the shaft that turns it does not lie at the center of the disk, consequently an object bearing against the periphery must move toward and away from the center as the disk revolves. Instead of using a spring-pressed roller to bear against one side of the disk, the whole disk is encircled with a ring of steel known as an eccentric strap. This strap is bolted to a valve rod and as the eccentric revolves the strap makes the valve rod move back and forth. (See Figure 23.)

A description of all the various combinations of gearing, link motions, ratchets, escapements, clutches, and miscellaneous movements would easily fill the rest of this book, and we must therefore content ourselves with this very brief survey of a few of the more important elements employed in the construction of modern machinery.