_ the axis of the intermediate 
MISCELLANEOUS MECHANISMS 407 
_ Hence the ratio of the fluctuation of speed to the mean speed is 
“= hee #=sin @ tan @, assuming , to be constant. 
l= cos 6 
sin 
If », be assumed constant, and be represented graphically by the 
radius of the circle AXA,Y, and if , be calculated for various values of 
a and the results be measured off from O on the projections, such as OA 
of the axis of the arm oa, the polar curve shown dotted is obtained, which 
exhibits graphically the variations in the angular velocity of ob for all posi- 
tionsof the arm oa. It will be seen that the angular velocities of oa and 
ob are equal four times in each revolution. In Fig. 657, 0 is 45°. 
 @,=, when cos@ = 1 — sin? 0 cos® a, that is, when cosa = + 
Fig. 658. Fria. 659. 
The actual form of Hooke’s joint varies greatly in practice. One 
design is shown in Fig. 658, and a more compact form, known as 
Bocorselski’s universal joint, is shown in Fig. 659. 
By using a double Hooke’s joint, as shown in Fig. 660, the shafts A and 
C will have the same angular velocity at every instant, provided that their 
axes are in the same plane 
and make equal angles with rival rw me <8 
— - 4 
shaft B. This follows at ~\"Y=--W. ss Be + (J 
once from the formula al- : 
ready proved. Thus if the 
shafts. A, B, and C turn a 
through angles a, 8, and y respectively from the position shown in the 
same time, then tan a=tan B cos @=tan y, thereforea=y, It is however 
very important to observe that for the above to be true the axes of the joints 
in the forks on the intermediate shaft B must be in the same plane as shown 
in Fig. 660, Judging from the number of examples to be met with in 
practice on motor cars and machine tools, in which the forks on the 
- intermediate shaft are arranged wrongly, it would seem that the theory of 
Hooke’s joint is not properly understood by many who have to construct 
_ it. Assuming that o,, the angular velocity of the shaft A, is constant, it 
is easy to show that if the axes of the joints in the forks on the inter- 
mediate shaft B are arranged at right angles to one another, as is 
commonly but erroneously done, the fluctuation of speed of the shaft C is 
Oy 
cos*0 
single Hooke’s joint the fluctuation of speed would only be from = 3 to 
4 
from to w, cos? 0, whereas if C were coupled direct to A with a 
w, cos 0. 
