This section is from the book "Practical Mechanics For Boys", by James Slough Zerbe. Also available from Amazon: Practical Mechanics for Boys.

The technical name for gears, the manner of measuring them, their pitch and like terms, are most confusing to the novice. As an aid to the understanding on this subject, the wheels are illustrated, showing the application of these terms.

When a gear is ordered a specification is necessary. The manufacturer will know what you mean if you use the proper terms, and you should learn the distinctions between spur and pinion, and why a bevel differs from a miter gear.

If the gears on two parallel shafts mesh with each other, they both may be of the same diameter, or one may be larger than the other. In the latter case, the small one is the pinion, and the larger one the spur wheel.

Some manufacturers use the word "gear" for "pinion," so that, in ordering, they call them *gear* and *pinion*, in speaking of the large and small wheels.

The first thing to specify would be the diameter. Now a spur gear, as well as a pinion, has three diameters; one measure across the outer extremities of the teeth; one measure across the wheel from the base of the teeth; and the distance across the wheel at a point midway between the base and end of the teeth.

These three measurements are called, respectively, "outside diameter," "inside diameter," and "pitch diameter." When the word *diameter* is used, as applied to a gear wheel, it is always understood to mean the "pitch diameter."

This term is the most difficult to understand. When two gears of equal size mesh together, the pitch line, or the *pitch circle*, as it is also called, is exactly midway between the centers of the two wheels.

Now the number of teeth in a gear is calculated on the pitch line, and this is called:

To illustrate: If a gear has 40 teeth, and the pitch diameter of the wheel is 4 inches, there are 10 teeth to each inch of the pitch diameter, and the gear is then 10 *diametral pitch*.

Now the term "circular pitch" grows out of the necessity of getting the measurement of the distance from the center of one tooth to the center of the next, and it is measured along the pitch line.

Supposing you wanted to know the number of teeth in a gear where the pitch diameter and the diametral pitch are given. You would proceed as follows: Let the diameter of the pitch circle be 10 inches, and the diameter of the diametral pitch be 4 inches. Multiplying these together the product is 40, thus giving the number of teeth.

Fig. 123. Bevel Gears.It will thus be seen that if you have an idea of the diametral pitch and circular pitch, you can pretty fairly judge of the size that the teeth will be, and thus enable you to determine about what kind of teeth you should order

In proceeding to order, therefore, you may give the pitch, or the diameter of the pitch circle, in which latter case the manufacturer of the gear will understand how to determine the number of the teeth. In case the intermeshing gears are of different diameters, state the number of teeth in the gear and also in the pinion, or indicate what the relative speed shall be.

Fig. 124. Miter Gears.This should be followed by the diameter of the hole in the gear and also in the pinion; the backing of both gear and pinion; the width of the face; the diameter of the gear hub; diameter of the pinion hub; and, finally, whether the gears are to be fastened to the shafts by key-ways or set-screws.

Fig. 122 shows a sample pair of miter gears, with the measurements to indicate how to make the drawings. Fig. 123 shows the bevel gears.

When two intermeshing gears are on shafts which are at right angles to each other, they may be equal diametrically, or of different sizes. If both are of the same diameter, they are called bevel gears; if of different diameters, miter gears.

Fig. 125. Sprocket Wheel.It is, in ordering gears of this character, that the novice finds it most difficult to know just what to do. In this case it is necessary to get the proper relation of speed between the two gears, and, for convenience, we shall, in the drawing, make the gears in the relation of 2 to 1.

Draw two lines at right angles, Fig. 124, as 1 and 2, marking off the sizes of the two wheels at the points 3, 4. Then draw a vertical line (A) midway between the marks of the line 2, and this will be the center of the main pinion.

Also draw a horizontal line (B) midway between the marks on the vertical line (1), and this will represent the center of the small gear. These two cross lines (A, B) constitute the intersecting axes of the two wheels, and a line (5), drawn from the mark (3 to 4), and another line (6), from the axes to the intersecting points of the lines (1, 2), will give the pitch line angles of the two wheels.

For sprocket wheels the pitch line passes centrally through the rollers (A) of the chain, as shown in Fig. 125, and the pitch of the chain is that distance between the centers of two adjacent rollers. In this case the cut of the teeth is determined by the chain

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