TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. 23: 
completes the frame. The friction between the man’s hand and the handle is 
important. A friction circle is accordingly shown at the joint dc. A handle 
which the man can grasp firmly and which turns easily round a well-oiled axis, 
makes the machine more efficient than when the man’s hands must slip round 
the handle. 
One of two spur wheels may be driven by a couple, and the other resisted 
by a couple; this is a case frequently arising in practice, when one wheel is 
driven by a shaft, and the other drives a shaft, both shafts having such 
additional bearings as prevent the ultimate driving effort or ultimate resistance 
from having any effect on the bearings of the simple machine. Fig. 24a shows 
the dynamic frame for this case. There are three bars, as we have two couples; 
the bars are lettered as elements. Two friction circles are drawn with their 
centres at the centres of the bearings a and bc. The bent arrows show the 
direction of rotation of pins fixed in the element a, relatively to 6 and c. Link 5 
is drawn as before through the pitch-point, and making the stated angle with the 
surface of the teeth; the directions of the equal and parallel pressures on the pins. » 
form part of links 2 and 4, which no longer cut line 6; the other halves of links 2 
and 4 are the reactions from the bearings shown as dotted lines. The diagram 
is completed by drawing bars to represent @, 6, and c. The position of these bars. 
is really immaterial, but. B and C may be conveniently shown perpendicular to. 
the direction of link 5, and these letters will now be used to signify the perpen- 
dicular distances between these links. When the couple V- ‘s applied between } 
and a, it produces two forces equal to ai , the one acting to compress link 5, and 
the other to force the bar B against the pin in the direction shown by the full 
arrow 2. The first force is resisted by the tooth and wheel, as if these formed 
part of a link under compression, the other force by the element a in the direc- 
tion of the dotted arrow 2. The force is transmitted through the tooth to 
act on ¢; it produces an equal force at the distance C, forcing ¢ down on its pin 
in @, as shown by the full link 4. This force is resisted by an equal and 
opposite force, as shown by dotted link 4. Thus the couple produced in c is 
pe and this is the resisting couple Mp, which the driving couple M, can 
overcome. The forces and couples are the same as would be produced if we 
could construct a material frame of the link 5 and the bars ABC of the dimen. 
sions shown, and having the cuvine couple between B and A, with the resisting 
couple between A and C. 
§21. Rolling Contact.—The simple machine, made with two wheels which 
transmit power by a rolling contact between them, has a dynamic frame of the 
same character as that corresponding to spur wheels. This arrangement is shown 
