Page:The Kinematics of Machinery.djvu/288

 266

KINEMATICS OF MACHINERY.

We obtain the following result (using the contracted symbols for all the inner pairs) :

1

c+ ...

<7+...

1

... c-

...0~ 1

I

... c

6

The compound formula resulting from the addition and to which, for explanation's sake, we have added the numbers of the

turning-pairs may be considered as one which really allows the nature of the chain to be seen, for it distinctly re- produces its symmetrical arrangement. It is possible, however, to bring the for- mula into a still clearer shape, which may be useful in some cases. Noticing, namely, that the four turning - pairs within the brackets form by themselves a simple closed cylinder-chain (C'^) t and at the same time that this whole

chain has taken the place before occupied by a pair of elements, we see that the whole formula may be written,

186.

1

3,4,7,6

so as to take up much less space than before. The formula could be used in this shape for the mechanism, also, if the fixed link were 1.2, 2.3, 1.5 or 5.7 but if the fixed link be one of the inner group, 3, 4, 7, 6, the more extended formula must be employed.

We may choose a train of spur wheels as another illustration. Fig. 187 represents a compound mechanism of this kind with two pairs of wheels a, & and c d. The wheel c is fixed to I, the three spindles con-axial with the wheels have their bearings in the ternary link 1. 2. 3, which is here the fixed link. The formula may be arranged in several different ways.