384 APPLIED MECHANICS 
are mere points, and the dotted curves on the right must be hypocycloids 
described by the pitch circle of the pin wheel rolling inside the pitch 
circle of the other. The corresponding curves in Fig. 589 are epicycloids 
described by the pitch circle of the pin wheel rolling on the pitch circle 
of the other, the latter being inside the former. 
An interesting case of the internal gearing shown in Fig. 588, is 
where the pitch circle of the pin wheel has a diameter equal to the radius 
of the pitch circle of the other. The faces of the teeth on the outside 
wheel now become the sides of parallel slots, the centre lines of which 
are radial lines of the larger pitch circle. Two examples of this case are 
shown in Figs. 590 and 591. In Fig. 590 the pin wheel has two teeth, 
while in Fig. 591 the pin 
wheel has four teeth. A 
peculiarity of this gearing 
is that the path of contact 
between a pair of teeth is 
the circumference of the 
pitch circle of the pin wheel 
excepting a small are in the 
neighbourhood of the centre 
of the larger wheel. When 
a pin is in the neighbour- 
hod of the sentee at the baat het ae 
larger wheel the obliquity of action is approaching a right angle and the 
driving effort is approaching zero, but when there are two or more pins 
on the pin wheel, only one pin will be in a disadvantageous position at a 
time. The path of approach is equal in length to 
the path of recess, and it is therefore immaterial Up 
which of the two wheels is the driver, except in the AG 
case where the pin wheel has only one tooth. When am 
the pin wheel has only one tooth it must be the PAEY 
driver, otherwise motion of the follower would ZB -% 
cease when the pin reached the centre of the 
larger wheel, unless it was carried past this dead 
centre by the inertia of the follower or the parts 
moving with it. Contact in the neighbourhood of 
the centre of the larger wheel can be insured, and larger bearing surfaces 
secured by making the slots wider and placing blocks on the pins, as 
shown in Fig. 592. 
328. Bevel Wheels.—The pitch surfaces of bevel wheels in gear are 
frusta of cones whose vertices coincide, the axes of the cones being the 
axes of the wheels. Fig. 593 
shows the pitch surfaces of 
two bevel wheels in gear, the pe 
one cone being external to sZ = 
the other. In this case the lf 
wheels are said to have ex- 
ternal contact. Fig. 594 
shows the pitch surfaces of Si areas» 
two bevel wheels having internal contact, one cone being inside the other. 
A mitre wheel is a bevel wheel whose pitch cone has a base angle of 45°. 
