—_ TOOTHED GEARING 383 
_ of the pitch circle the hypocycloid becomes a point, and no part of the 
tooth lies within the pitch circle. The face of a tooth on a wheel B 
_ which gears with A will be an epicycloid described by the pitch circle of 
- Aasrolling circle. If a rolling circle which describes the face of a tooth 
on A be diminished until it becomes a point no part of the tooth on A 
will lie outside the pitch circle, and as this rolling circle which has 
become a point must be used to describe the flanks of the teeth on B no 
art of a tooth on B will be inside the pitch circle. The teeth on A 
ve thus become mere points, while the teeth on B will have epi- 
eycloidal outlines lying entirely outside the pitch circle. This is shown 
in the left-hand half of Fig. 586. 
It is obvious that practically this 
is an impossible case, but if instead 
_ of mere points, cylindrical pins of 
sensible size be used, as shown in 
the right-hand half of Fig. 586, 
where the outlines of the teeth | \, _---; 
which gear with the pins are curves 
parallel to the epicycloids and at 
a distance from them equal to the 
radius of the pins, then the wheels 
will gear correctly, and either wheel 
will drive the other. — 
The path of contact will be 
either the are Pad or the are Ped.* Fd. 696. 
If the pins are on the follower, contact will take place during recess only, 
and if the pins are on the driver, contact will take place during approach 
only. Since the friction is more serious during approach than during 
recess, it is best to put the pins on the follower. 
Figs. 588 and 589 show wheels gearing internally, one of them having 
DRIVER. 
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the curves of the teeth in the left-hand half of Fig. 588, where the pins 
* For practical purposes this may be taken as true when the pins are small, 
but the exact path of contact is a curve determined as 
shown in Fig. 587, where aPd is the pitch circle of the EP ent ee | ad 
pin wheel, and P the pitch point. Take ¢ any point on ~ 
the arc Ped. Join cP. Make ce’ equal to the radius of 
the pin ; then ec’ is a point on the real path of contact. 
Repeating this construction a sufficient number of 
times and joining the points so obtained, the real path 
of contact Pe'd’ is determined. : 
Fig. 587. 
) pins for teeth. Reasoning as for external contact, it is easy to show that 
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