MISCELLANEOUS MECHANISMS 405 
- must each be equal tov= PC. aand f are the inclinations of RPT to 
PA and PB respectively. 
For a sliding cam (Fig. 654), in which the direction of the motion of 
Fria. 656. 
the cam is perpendicular to the direction of the motion of the follower, 
~? — tan a=cot B. 
% 
For a cylindrical cam, of which Fig. 654 is the development, if R, is 
the radius of the cylinder and o its angular velocity, then 
m%=Ro, and ?=R, tana=R, cot B. 
For a plane cam rotating about O, and a follower having rectilinear 
* . i OD . . 
motion (Fig. 656), 3 inB™ OP* If w is the angular velocity of the 
eam, then w= ro , and therefore “2 OD, where OD is perpendicular 
to the line of stroke of the follower. 
For a plane cam rotating about O, and a follower swinging about O, 
(Fig. 656), if , is the angular velocity of the cam and , is the angular 
velocity of the follower, then in the position shown, 
Sid lee ODM Ga oe one 
A, 8. a EN 
where O,M and O,N are perpendicular to CPD. Join O,O,, and produce 
iti 2. v , v _OM_O,D 
it if necessary to meet CPD at D, then ,O,N * OM ON O,D* 
341. Hooke’s Joint or Universal Coupling.—By means of a Hooke’s 
joint a motion of continuous rotation may be transmitted from one shaft 
to another when the axes of the shafts intersect, but are not in the same 
line. This joint is frequently used when the axes of the shafts are 
nominally in the same line, but through a lack of rigidity in the frame 
carrying the bearings of the shafts the axes may get slightly out of line 
several times during a revolution. The Hooke’s joint forms a flexible 
and yet positive coupling for the shafts. The theory of this coupling 
will now be considered. 
Referring to the lower part of Fig. 657, ¢ and d are two shafts whose 
axes are assumed to be horizontal and to intersect at 0, the acute angle 
between them being 6. The ends of the shafts are forked, and the forks 
carry between them a cross aa,bb,, the arms of which are at right angles 
to one another, and the axes of these arms intersect at 0. The arms of 
