Page:The Kinematics of Machinery.djvu/629

 NOTES. 607

47 (P. 290.) [The lines A B and D c (Fig. 208) cut 1, 4 and 2, 3 in such a w#y as to make the alternate angles 1 and 3 (and also of course 4 and 2) equal. Hence the name anti-parallel. See e. g. Reuleaux's Constructeur, 3rd ed., p. 71.]

48 (P. 327.) It was Willis who first pointed out the nature of the conic crank-trains, and their analogy to the cylindric crank trains. (Principles of Mechanism, 2nd ed., 1870, p. 249, ff.) He called the trains " solid angular link work," and indicated several of their more important forms and character- istics. He had not, however, the idea of the kinematic chain, and missed therefore, some of their most essential properties ; as a kinematist of the old school, too, the fourth (fixed) link altogether escaped him, as also the possi- bility of inversion, and with these some very remarkable practical applications of the chain, of which we shall have more to say further on.

49 (P. 341.) The treatment of compound chains belongs to the more diffi- cult problems of Kinematics. I refer to them again in Chapter XIII., par- ticularly in 160. The full advantage of the idea of chain reduction only makes itself felt in the study of these applications of Kinematics. I recom- mend the teacher to give his pupils exercises in the re-completion of reduced chains.

50 (P. 384.) I have certainly not exhausted the list of chamber-trains which have been constructed from (C P- 1 -)*, although so many of them have been investigated. It is interesting to note that lately the crossed slider- crank chain (see 73) has also been used in chamber-trains. Gibson's rotary steam-engine (American Artisan, Feb. 1874, p. 30) is an example of

this ; it is a combination of two trains of the form (C 3 P )i &.

61 (P. 399.) For the determination of the axoids of the links b and d in (Cj C ) we have the following (see Fig. 448) : W 1 __ r _ sin y

�i\ sin y l 1 sin* oo sin 2 a

We require to find the values of y and y l corresponding to different values of o>. We have

�hence" ] r

sin y l = sin (y -f- a) = sin y cos a + cos y sin a,

and from this, putting - - c ? 8 a. = A, we obtain & 1 w s sin* a

sin y A (sin y cos a -f- cos y sin a). - = cos a -f cot y sin a,

1

T -- cos a

whence cot y = - ,

sin a

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