404 APPLIED MECHANICS 
of this line to the axis of the cam. A line C,CC, parallel to B,P’ deter- 
mines the section of the screw surface by a plane containing the axis of 
the cam. 
The roller may be turned in an ordinary lathe if the point of the 
cutting tool is set at a distance below the lathe centres equal to OP’, ~ 
while the top slide rest is set at an angle to the axis of the lathe equal to 
the angle B,P’B,. In practice the distance OP’ and the size of the 
roller compared with the outside diameter of the cam will generally be 
much smaller than shown in Fig. 650. 
If the follower is to be driven positively by the cam in both direc- 
tions, a second roller, shown by the dotted circles at O,, will be 
necessary. 
It should be pointed out that in the roller designed as just described 
there is an end thrust which is taken by a collar on the pin carrying the 
roller, and the friction and wear of the roller on this collar may more 
than neutralise the saving of friction and wear due to pure rolling 
between the roller and the cam. 
339. Interference in Cams.—In designing a cam to fulfil certain 
conditions, it may happen that the formation of one part may cut away 
a part already formed. For 
example, in Fig. 652, let ABC 
be a part of the pitch line of 
a cam to work against a roller. 
As the axis of the roller 
moves along AB the envelope 
DLE is the corresponding 
part of the outline of the 
cam, and as the axis of the 
roller moves along BC the steeds mentee: 
envelope FLH is the corresponding part of the outline of the cam. It 
will be seen that the parts DLE and FLH interfere with one another, 
and the possible outline for the cam is DLH. The axis of the roller — 
will therefore move along the path AKC instead of along ABC, the 
dotted part at K being an arc of a circle whose centre is L. The amount 
of interference in this case will evidently be greater the more acute 
the angle between AB and BC at B is, and also the larger the roller is. 
Interference may also occur in other cases, as, for instance, when the part 
of the follower which works against the cam is a flat plate. Fig. 653 
shows such a case, the required outline of cam being the envelope of the 
lines A, B, C, etc. It will be seen that the fair curve which touches 
the lines A, B, D, ete., will not touch the line C. In a case like this all 
that can be done is to make a compromise by drawing a curve to more 
nearly approach C and cut the adjacent lines at acute angles, as shown 
by the dotted curve. 
340. Velocity Ratio of Follower and Cam.—In Figs. 654, 655, and 
656 EPF is part of the pitch line of a cam, RPT is the tangent, and 
CPD is the normal to EPF at P. In the position shown the follower is 
in contact with the cam at P. The point P on the cam has a velocity 
v, =PA in the direction PA, and the point P on the follower has a velocity 
v) = PB in the direction PB. If the velocities v, and v, be resolved along 
and perpendicular to the normal CPD, the components along the normal 
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