Two methods are in use for drawing the form of teeth for racks. The first method is shown in Fig. 268. The pitch line A, addendum line B, and dedendum line C are straight lines located as before described. The teeth and spaces are set off at equal distances on the pitch line A. The sides of the teeth, including face and flank, are composed of straight lines aa inclined at an angle of 14 1/2 degrees from a vertical line or 75 1/2 degrees from the pitch line A. The lower ends of these lines are joined to the dedendum line by small arcs, as previously described. While this form of tooth is not theoretically correct, many racks running with gears having involute teeth are so constructed, and they operate satisfactorily for many kinds of work. However, the second method, Fig. 269, is preferable for accurate work and for carrying heavy loads. The principal lines A, B, and C, and the spacing of the teeth are the same as in Fig. 268. The vertical line DD is erected at the side of one of the teeth. Through the point a of the intersection of this line with the pitch line A is drawn the inclined line EE at an angle of 78 degrees with the vertical line DD, Through the point b of the intersection of this line with the vertical line 3 of the side of the adjacent tooth is drawn the base line F, which locates the centers for the arc with the radius bc, forming the face of the tooth. Through the point d of the intersection of the line EE with the vertical line 2, at the left of the tooth, the base line G is drawn, locating the centers for the arc with the radius de, forming the flank of the tooth. The lower ends of these arcs are joined to the dedendum line C by small arcs, as previously described.

Table X gives the various dimensions of the parts of gear teeth calculated for involute teeth designed upon the diametral-pitch system. It is useful in comparing the different dimensions of the same pitch with one another, and in comparing similar dimensions used in the same pitch; and it will enable the student to avoid making tedious calculations in each instance.

Table X. Involute Gear Tooth Parts

Attention is directed to the following characteristics of these dimensions:

(a) The thickness of the tooth equals one-half the circular pitch.

(b) The addendum equals 1 (one inch), divided by the diametral pitch.

(c) The working depth of the tooth is twice the addendum, as the addendum and dedendum are equal.

(d) The whole depth of the tooth is the working depth plus one-tenth of the thickness of the tooth, which is the clearance. The radius of the clearance arc is one-seventh of the distance between the points of adjacent teeth.

Fig. 270. Bevel Gears at Various Angles.