Page:The Kinematics of Machinery.djvu/454

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KINEMATICS OF MACHINERY.

ones, namely at 1 and 2, but their points of contact, and indeed the whole of their teeth are beyond our observation; they disappear from the mechanism, and only the two finite wheels c and d remain. The epicyclic train is thus reduced by two wheels, of which one revolves about 1, while the other turns round the first, carried by the frame e. The form at which we have arrived is dif- ferent from that of Fig. 281, for there the central wheel a was fixed, while here the only central wheel left, d, turns about its axis. In order, however, that the chain may remain closed, it must contain some representative of the wheels which have disappeared. The use of the latter has taken the point of contact, or instantaneous centre, to an infinite distance ; it will be seen therefore that they

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FIG. 283.

may be replaced by any arrangement which will prevent the wheel c from making any rotation about its own axis, by means of which, that is, its motion may be restricted to one of translation only, every line upon it moving parallel to itself. This might be done by the addition of a kinematic chain (which we may call accurately a parallel train or motion), so attached to c as to constrain it in the required manner.

It is evident, however, that so far as the total motion (in each period) of d is concerned, c may be allowed to oscillate about its centre 2 to a certain extent, so long as it never completely rotates. This is exactly what occurs in Watt's " Sun and Planet " wheels, Fig. 284, where the upper end of the connecting rod b is connected