HIGHER PAIRING AT CHANGE-POINTS. 197
As a further example we may take a remarkable mechanism, obtained from the chain of Fig. 153 by altering the lengths of its links. If we make two pairs (a and d, c and 1} of adjacent links equal, the opposite links being unequal, as in Fig. 158, we obtain, by fixing one of the links, a mechanism which has two change- points. The first occurs if a be brought by a left-handed rota- tion into the position 1, 4 ; 3 will then have come to 3', and if no closure be arranged, the chain becomes simply a turning-pair, with 4 as its centre. The second change-point occurs if a makes a further complete rotation about 1, so as again to come into the position 1, 4, but with 3 at 3" instead of 3'. The result is the same ; the links b and c, coinciding, can turn about 4.
�at ai
��FIG. 158.
Thus for one whole revolution of the crank a t suitable closure being supposed to exist, c makes half a revolution, or conversely one whole revolution of c causes a to make two revolutions. This mechanism was first described by Galloway, who used force- closure derived from a fly-wheel for the passage of the dead points. He assumed the ratio of the lengths of the cranks a and c to be 1 : 2, a limitation which we see to be unnecessary.*
- This particular form of the four-link chain with four parallel turning-pairs forms
the mechanism called by Prof. Sylvester the "kite," The centroids are the curves known as Limacons, a special (nodal) case of Cartesians. It is worth noticing that if the centroids be placed with their axes coinciding, the node 2 falling upon the point 4 and A upon C, then any line drawn through 2 will cut off equal arcs from both centroids, i.e. will cut them in a pair of points
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