304 APPLIED SCIENCE 



of the bearings ab and be. The bent arrows show the direction 

 of rotation of pins fixed in the element a, relatively to b 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 link 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 a, b, 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 M D is 



applied between b and a, it produces two forces equal to D ' 



B 



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 direction of the dotted arrow 2. The force 



M 



~, is transmitted through the tooth to act on c ; it produces 

 B 



an equal force at the distance C, forcing c down on its pin in o, 

 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 - " , and this is the resisting couple M R , 

 B 



which the driving couple M D can overcome. The forces and 

 couples are the same as would be produced if we could con- 

 struct a material frame of the link 5 and the bars ABC of the 

 dimensions shown, and having the driving 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 corre- 

 sponding to spur-wheels. This arrangement is shown 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 



