Page:The Kinematics of Machinery.djvu/280

 258 KINEMATICS OF MACHINERY.

58.

Formulae for simple Kinematic Chains and Mechanisms.

In describing a complete kinematic chain by symbols written, as they must be, in lines, we cannot represent the returning back upon itself, or closure, of the chain, and must be content with merely indicating this. This disadvantage, if it be one, our notation shares with that of Chemistry, but the matter if fairly examined is seen

FIG. 179.

to be quite unimportant. Jn writing down a chain we begin with a link, and thus a single element of some pair must stand first in the formula, at the end of which, consequently, must be its partner element, and the sign of pairing annexed to the symbol of this latter sufficiently indicates the closure of the chain.

This will perhaps be made clearer by an illustration. Let it be required to write down the familiar chain shown in Fig. 179. The cylindric elements are indicated in the figure by the letters lc.de, etc., and for distinctness' sake we may in the first case add these to the symbols. Beginning then with the link b c we have to write :

g+... || ... Ct C-... || ... (7= <?+... II ... Ct C~ ... || ... C= I c de f g ha

The links, so far as the above form-symbols are concerned, appear identical. If the chain be fixed in the way shown in Fig. 180, the formula becomes (omitting the letterings of the special links) :

C+ ... || ... CtG- ... |1 ... C-C + ... || ... CtC- ... || ...(?-

At first sight it might appear to be strange, and to show a defect in our notation, that it does not show any difference in form between the links. This I deny at once, for we know from 16 that the