Page:The Kinematics of Machinery.djvu/282

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KINEMATICS OF MACHINERY.

on built foundations. In the actual machine this framework, the fixed link of the chain, is of so varied a figure, so mixed up with portions of buildings, and complex in so many ways, as to afford no indication of its really simple nature ; indeed, to very many people the mechanism presents itself as one of three links only, beam, connecting-rod and crank. This has been carried so far that even in text-books, when a purely schematic or abstract represent- ation of the mechanism has beeu used, the fourth link a h is entirely omitted from the figure. The inconsistency is no doubt explained by the tacit assumption made that the paper forms as it were the frame for the three moving parts whose existence is formally recognised.

Fro. 181.

The description of the mechanism given by our formula is speci- ally suited to remove this prejudice, or rather this confusion of ideas. It might be asked, however, whether the formula should not show also the relations between the lengths of the different links. This would certainly be possible ; it would however be difficult, for of course the four lengths may have between them an enormous variety of numerical relations, and it would at the same time be of little use, for even if the lengths were added to the formula it would require a special study of the mechanism in each case to make any practical use of them. We shall, however, find it possible further on to employ a method of indicating these length-relations which is simple and very easily used.

We may take for a second illustration a universal joint, or Hooke's joint,* of which Fig. 181 gives a schematic representation.

after its inventor it should be called Cardano's joint ; for he was the first to point out its possibility.
 * Prof. Reuleaux points out in his Constructeur that if this joint is to be named