THE KINEMATICS OF MACHINERY. S3 



These pair of elements are called higher pairs. They have 

 only a few applications in practice, their interest being chiefly 

 theoretical. From our present point of view their theoretic 

 interest is considerable, because of their exact analogy with 

 the lower pairs. 



There is another difference between the two kinds of pairs 

 which deserves notice, for reasons which will be better under- 

 stood afterwards. The pair of elements determines the rela- 

 tive motion of the two bodies connected by it. If one body 

 be stationary on the floor or the earth, the moving body has the 

 same motion relatively to the floor or earth that it has to the 

 other element. If I move about both bodies in my hand, both 

 have motion relatively to the earth, but the relative motion 

 of the one to the other remains unchanged. It is of course only 

 a case differing in degree from the former one, for in the 

 former one both bodies had the motion of the earth itself, 

 while one had the additional motion which I gave it. We may, 

 however, not to be pedantic, speak of anything as "fixed," or 

 ** stationary " which has the same motion as the earth. 



Now (in this sense) we may fix either element of a pair, and 

 with the lower pairs the relative motion taking place remains 

 the same whichever element be fixed. With the higher pairs, 

 on the other hand, the relative motion is altered, and the point- 

 paths become entirely different. The point-paths of the 

 duangle relatively to the triangle are, for instance, quite dif- 

 ferent from those of the triangle relatively to the duangle. This 

 change of the fixed element is called the inversion of a pair. 

 The ultimate result of our analysis of mechanisms is then 

 pairs of elements ; we cannot go below this. The pairs we 

 have noticed are of two kinds, each having their own 

 definite characteristics. If now two or more elements of as 

 many different pairs be joined together we get a combination 

 which is called a (kinematic) link. It is obvious that the 

 form of such a link is, kinematically, absolutely indifferent. 

 The choice of its form and material belongs to machine- 

 design. It may be brick and mortar, cast-iron, timber, as 

 we shall see afterwards, but the fact that this is indifferent 

 kinematically cannot be too distinctly kept in mind. 



We can make combinations of links by pairing the elements 

 which each contain to partner elements in other links, and 

 such combinations are called kinematic chains. Thus if we 

 denote similar elements by similar letters, aa, bb cc, &c. and 



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