Page:The Kinematics of Machinery.djvu/419

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terminates in a cone having a spherical head. In this there is made the joint, normal to the axis 2, for the piston disc c, which passes right across the hemisphere. The mechanism is a turning cross-block in which the axes of the revolutes 1 and 2 enclose an angle of 45. The turning-pair 2 is easily recognisable, the pair 1 not quite so readily ; for this there indeed exists only one re volute, the side of the hemispherical chamber which is a plane cone having its axis in the line A A. The link a is therefore G- ... L ... C~ or more strictly K... L ... C~. The link 6 consists of two revolutes 2 and 3 normal to each other, the latter forming part of the spheric head of the link. The link d is omitted, so that the chain is reduced, and has for its general formula (C-^C 1 -)* d. It is on account of this omission of d that we have only the one revolute of the pair 1 ; and for the same reason there is a higher pairing between c and a, which is effected by rounding the edge of the piston c so that it can work upon the plane cone of the link a. It can easily be seen that only a very defective steam- joint can be made in this way. It would have been easy to have obtained a better joint, using lower pairs only, by retaining the link d and forming it as a packing-piece in some such way as is shown in Figs. 6 and 7. My sources of information about the machine are not, however, so distinct as might be wished, so that it is possible that something of the kind may actually exist in it.

In the last six machines we have had b once for piston, c once, and d four times, as chamber we have had d once and a five times.

Different forms have been given to the chamber ; most frequently, however, it has taken the form of a double cone, and by many this particular form has been looked upon as essential. It has certainly given both inventors and improvers much food for thought. They have found it exceedingly difficult to realise distinctly the half rolling, half sliding motion of the disc. Davies must have believed it to be a pure rolling motion like that of spur wheels, for in 1838 he patented a disc-pump in which both the disc and the conic surfaces were toothed like bevel wheels.* He included the machine, that is, in the class of chamber-wheel trains which we shall have to consider in the next chapter. The diaphragm


 * Newton, London Journal of Arts, &c. Conjoined Series, vol. xix., 1842, p. 153.