APPLICATION OF GRAPHIC METHODS 303 



and 4 are drawn tangent to the friction circles for o/> and oc, 

 and the frame is completed by joining A A,. Each wheel is an 

 element having three joints, and therefore fives three half links 

 to the frame. These three half links for wheel b 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 cd>. Wheel c 

 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 e, Fig. 23, turning a winch handle b, 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 b 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 , completes the frame. 

 The friction between the man's hand and the handle is impor- 

 tant. A friction circle is accordingly shown at the joint be. 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 



