22 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
drawn making the stated angle with joint bc, and by its intersection with 1 
gives joint C,. The frame is completed by drawing the link 3 from C to C,. 
The element ¢ has four joints, the pressures on these joints are the stresses in 
the links 1, 4, and 2,6. The equal and opposite resultants of these two pairs 
are met by the link 3, supplied in the original machine by the rigidity of c. 
The machine will cease to work when the joint C, falls inside the triangle CAB. » 
The diagram suggests another arrangement of the wedge machine in which the 
wedge might be employed to open a pair of jaws corresponding to links 3 and 
4, hinged at C.. The analogy between the wedge machine and the direct-acting 
engine is curious. The connecting rod acts like a wedge, opening or closing 
the jaws, represented by the crank and bed-plate. 
§ 20. Spur Wheels.—A simple complete machine can be made of two spur 
wheels 0 and ¢, with bearings in the same element a, and having a driving link 
e between a and J, and a resisting link f between ¢ and a. The simplest type 
of this machine is shown in fig. 22, and its dynamic frame is given in fig. 22a ; 
the frame is drawn as follows:—Links 1 and 6 are tangent to the friction circles 
for elements ¢and/ Link 5 passes through the pitch-point of the spur wheels,and | 
makes the stated angle with the surface of the teeth ; in other words, it makes 
an angle equal to ¢ with the normal, which is called by RAnxrvz the line of con- 
nection. ¢ here as elsewhere signifies the angle whose tangent is p, the coefficient 
of friction. The intersection of 5 with 1 and 6 gives the joints B and C; from 
B and C links 2 and 4 are drawn tangent to the friction circles for ab and ae, 
and the frame is completed by joing AA, Each wheel is an element having 
three joints, and therefore gives three half links to the frame. These three half 
links for wheel 6 meet at B, and represent the pull of the spring e, the push 
from the joint where the teeth meet, and the reaction from the bearing ab. 
Wheel ¢ gives the three corresponding half links at C ; the frame is completed 
by link 3, so placed as to receive the equal and opposite resultants of the second 
halves of the links 1 and 4, 2 and 6. This link 3 lies in the direction of the 
stress on the element a. A practical example of this machine is afforded by a 
man @, fig. 23, turning a winch handle 8, and lifting a weight / by the rope on 
an axle c, driven by a spur wheel gearing with a pinion on the shaft of 
the winch handle. The man stands on the element a, which also supports the 
bearings of the spur wheels. The dynamic frame, fig. 23a, for this example is 
drawn precisely as for the previous typical example. As before, we know the 
directions of the effort in link 1 and of the resistance in link 6 (the latter is 
shown shifted outward to allow for the stiffness of the rope). The effort of the 
man need not be perpendicular to the crank, but must be exerted between 
elements a and 0; the resisting link is the attraction between the weight and 
the earth, that is to say, as before, it is a link between C and A. | Links 5, 2, 
and 4 are drawn as before, and link 3, supplied by the rigidity of element a, 
