being at the pitch point as shown, the 
‘ 
TOOTHED GEARING 379 
If APB and CPD (Fig. 579) be the pitch circles of two wheels with 
teeth in gear with one another, and if ade be the addendum 
- circle of the teeth of the lower wheel, and 
y the addendum circle of the teeth of Drwer. | 
upper wheel, then the rolling circles 
points a and ) where the addendum circles ‘e 
eut the rolling circles are the extreme 0 
points of contact of the teeth, the upper =p pradge-s 
wheel being the driver, and having its ' | ‘ 
motion in the direction of the arrow. At Follower. ‘ 
the point @ a point on the flank of a Fic. 579 
tooth on the driver will come in contact Se 
with the extreme point of the face of a tooth on the follower. As 
the motion proceeds, the flank of the tooth on the driver will slide on 
the face of the tooth on the follower until the point of contact, which 
moves along the arc aP, reaches the point P. The face of the tooth on 
the driver will then slide on the flank of the tooth on the follower until 
the point of contact, which moves along the are Pl, reaches the point b. 
The arc aP is called the path of approach, and the arc Pb the path 
of recess. If the driver move in the opposite direction, the path of 
contact will evidently be the line a’Pd’. 
If man be the flank of a tooth on the upper wheel just coming into 
contact with a tooth on the lower wheel, the point m on the pitch line 
APB will come into contact when it has travelled to P, and the are mP is 
the are of approach. Again, if rbs be the flank of a tooth on the lower 
wheel just going out of contact with a tooth on the upper wheel, the 
point 7 on the pitch line CPD will have travelled over the are Pr since 
being in contact, and the are Pr is the are of recess. If the are Po be 
made equal to the arc Pm, and the are Pt be made equal to the are Pr, 
then either of the arcs oPr or mP¢# is the arc of contact. 
The are of contact may also be defined as that part of the pitch line 
which passes the pitch point during the time of contact of a pair of 
teeth. 
In order that one pair of teeth may always be in contact, the are of 
contact must not be less than the pitch of the teeth. If possible the are 
of contact should not be less than twice the pitch, so as to ensure that at 
least two pairs of teeth are always in contact. Generally the are of 
contact is not less than 1-4 times the pitch. . 
324. Obliquity of Action and Effect of Friction.—Referring to Fig. 
580, if a pair of teeth are in contact at a, and friction is neglected, the 
line of action of the pressure between the teeth is the straight line caP, 
and the angle a which this line makes with the common tangent to the 
pitch circles is the angle of obliquity of action. 
With cycloidal teeth the obliquity of action during approach is 
greatest at the beginning of the path of contact, and diminishes to 
nothing at the pitch point. During recess the obliquity of action is 
nothing at the pitch point, and increases toa maximum at the end of the 
path of recess. 
The effect of friction during approach is to increase the angle of 
obliquity of action by the amount ¢, where ¢ is the angle whose tangent 
e 
