24 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
in fig. 25, where the parts have the same names as were given in the case of 
spur wheels. The directions of links 1 and 6, fig. 25a, are known ; the direction 
of link 5 is also known, if the machine is running with its maximum efficiency ; 
that is to say, if there is no more tension on element a than is necessary. In 
that case, the line of pressure at the point of contact will make the stated angle 
with the surface of contact. Link 2 is drawn from the intersection of 5 and 1 
to the friction circle at the centre of b. Link 4 is drawn from the intersection 
of 5 and 6 to the friction circle at the centre of c. The intersection of 4 and 1 
is then joined by link 3 to the intersection of 6 and 2. The three lines meeting 
at B show the positions of the three forces under which 6 is in equilibrium, 
and the arrows show the directions of those forces. The three lines meeting at 
C show the forces under which the second wheel ¢ is in equilibrium, and the 
arrows at C show the directions of those forces. The rules given in § 8 will 
enable the draughtsman to determine on which side of each friction circle the 
link is to be tangent. Fig. 25 shows the manner in which the diagram becomes 
modified when the directions of links 6 and 1 make smaller angles than link 5 
makes with the normal to the joint Uc. Fig. 25b also shows the effect of 
rolling friction at this joint, which, however, may generally be neglected. At 
the point of contact the material is continually being crushed, and the material 
is not perfectly elastic. We have, therefore, a resisting couple analogous to 
that met with in the case of ropes, and the effect is to shift in a disadvan- 
tageous direction one part of lnk 5 by a distance equal to the arm of 
this couple.” If excessive tension is employed in a, the direction of link 5 
will be found by compounding that tension with the force transmitted at the 
periphery. The diagram where one roller is driven by a couple and the other 
roller resisted by a couple, is easily deduced from that for spur wheels. 
§ 22. Belt and Pulley.—The complete belt and pulley machine is shown in 
fig. 26. It is composed.of the pulleys b and ¢; the element a in which their 
bearings run, the flexible belt d, the driving element ¢, and the resisting element 7 
The dynamic frame without friction is given in fig. 26a. Link 5 is the direction 
of the resultant of the tensions on the two bands, which may be considered as 
together forming one split link. When we assume that no more tension is used 
than is necessary, the ratio between the tensions on the tight and slack side of the 
bands is determined by the arcs round which the belts are in contact with the 
_ pulley, and by the coefficient of friction between the belt and the pulley. 
Consequently, the position of link 5 may be taken as known. ‘The intersection 
of the driving link 1 with 5 gives joint B; the third force acting on 0 is the 
resultant of the two others, and must pass through the centre of the pulley 8, | 
this determines the direction of link 2. Similarly, C is given by the intersec- 
tion of 5 and 6; link 4 is drawn from their intersection to the centre of the 
pulley c; the diagram is completed by drawing link 1. The forces which keep 
