Page:The Kinematics of Machinery.djvu/286

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264 KINEMATICS OF MACHINERY,

and so on. This allows us, for example, to write the chain repre- sented in Fig. 179 as :

V+... || ...(0)... H ...(60 ... || ...(0)... |1 ... (7=

Here only the elements of the first (and last) link require to be written separately with their form signs the one letter in the parenthesis standing for a pair of elements. The same method can be carried further ; it allows us to write certain simple kinematic chains in a still shorter form, for where we have the parenthesis the relations of the linked elements are sufficiently defined without the use of the dotted line, which may therefore be omitted. This is certainly the case in the present instance, where the same relation parallelism exists between all the elements forming links. In- deed we may in these circumstances extend the parenthesis so as to include several, or the whole of the links. Thus for certain cases we may compress the above formula, without making its meaning uncertain, into the symbol ((7' 4 '), in words " C parallel four," or " C four parallel," and meaning "a chain formed upon four turning pairs, consisting, that is, of four links, each connecting two parallel cylindric elements." Such a contraction presupposes in all cases a familiarity with the way in which the chain can be formed out of its elements ; its form, however, is so concise as to leave nothing to be desired in this direction. The chain forming the universal joint, Fig. 181, to take another example, allows itself to be written (Cj- C 1 -}, in words, " C normal three C oblique"; the spur- gearing of Fig. 183 may be written (CtC', in words, " C plus z C parallel two," and so on.

These concentrated symbolic forms seem at first suitable only for the kinematic chain, not for the mechanism formed by fixing one of its links ; further on, however, we shall find means for making use of them in these cases also, within certain limits.

60. Formulas for Compound Chains.

In the simple kinematic chains the choice of the link with which to begin the formula was to a certain extent arbitrary. This strikes us still more in compound chains, and makes it appear at first sight