Page:The Kinematics of Machinery.djvu/323

 IDENTITY OF SLIDER-CRANK TRAINS.

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either end, we see that the second and third mechanisms have absolutely the same formula. Both are placed upon a link of the form C...\\... C having for its adjacent links one like itself and one of the form C..._L...P, these two last being again connected by a link C...1_...P. The difference between the mechanisms, which, as we have seen, is very great, lies solely in the ratio between the lengths of the links a and I. The names we have chosen for the mechanisms, swinging and turning block

FIG. 223.

FIG. 224.

FIG. 225.

FIG. 226.

slider-cranks respectively, give expression both to the relationship and the difference between, them.

An exactly analogous connection exists between the first and the fourth mechanisms. The fixed link is in each case (7...J_...P, having on the one side a link C...\\ ..C and on the other a link (7...J_...P, these in their turn being connected by one of the form C...\\...C. Here also the difference between the mechanisms depends upon the relative lengths of a and b, ^and we have again employed names which indicate that relationship in calling them turning and swinging slider-cranks.

We notice lastly, what is very striking, that in all four mechanisms the two adjacent links of the form (7...J_.,..7, the block and the slide, are represented by exactly the same symbols, that between them, therefore, there is absolutely no kin-e-inatic dirjfer t ence.