Page:The Kinematics of Machinery.djvu/560

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538 KINEMATICS OF MACHINERY.

Among cam pairs we have also to include (as we know from 120) the click-pairings in such trains as are shown in Figs. 370 and 371. These may be written in the general case

OHi) and (:),

respectively (see 119), and these classes subdivide themselves as in the case of toothed-wheels. The case of the toothed-rack occurs here also, as the limiting case of C = P.


�146. Recapitulation of the Pairs of Rigid Elements.

We have seen in the foregoing sections that the pairs which are obtained from the rigid elements can be systematically arranged in divisions and subdivisions so that each special form may fall under the more general case to which it naturally belongs. Of the divisions obtained in this way we may call the highest and most general the order, and the next lower the class, while special subdivisions of the latter we have treated as groups. The following table gives a general view of the pairs of elements which we have considered, arranged in this way. 59


�(P) (C,) ?,) (Q


�VII (#,:) . . . (fi,:) , (.:) , ((?,:) . . . (H;) , (KJ , (&)

We have here all the pairs already considered, in their numerous varieties, included in seven orders. Those special classes and groups which are obtained by the use of the limiting case C = P,


�I.


Orders.

/ rt \ (&,) . . ,


Pair;


3 Of E

Classes,

C


igid Elements.

f,<n


Groups.

, OB)






II.


\-tlj ) ...


()


, W


. (Q


. . . (ff,)


. (^)


III.


(#0 ...


(#,)


, ()


> (^0


. . . (#.)


, (JQ


IV.


(Hi) ...


Oft)


, (JT;)


//v_\

, I Ug )


. . . (5-J


, W


V.


(.-) . . :


(5J


. C^".;)


- (e,-0


. . . (ZTJ


, (^)


vi.


(H^\


(T z .)


fir \

, I XV. z . )


//V A

, IL/ Z .)


(^0


/ 1^ \ , (J\. . 1