Page:The Kinematics of Machinery.djvu/456

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KINEMATICS OF MACHINERY.

I have placed on the figures our reference letters to enable the dif- ferent parts to be more easily distinguished. In the three-cornered piston of Fig. 285 we have a spur-wheel with three teeth, the central wheel d of the planet- train Fig. 284, and in c we have the corresponding four-toothed outer wheel, which is here an- nular. In order that the motion of the wheel c, which is also the chamber, might be one of translation only, Galloway carried it (quite correctly so far as the required motion is concerned) on three equal and parallel cranks e e e. We can easily recognize in these the mechanism 2 (G" z || C" 2 ') a which we have already analysed in 66. The proper internal profile of the chamber gave the inventor

FIG. 285.

FIG. 286.

FIG. 287.

much trouble. It is, in reality, simply the profile of the teeth of a four-toothed wheel such as can work in gear (and indeed in steam-tight contact !) with the three-toothed pin wheel d. The inventor, although he starts from the idea of the annular wheel in his explanation, does not treat the bodies c and d as toothed wheels ; but says expressly : " What I propose is to substitute for toothed wheels, in the majority of cases, the arrangement shown in the figures, which I shall now explain. . . ." The figures show distinctly enough that the space between the teeth of c and d varies periodically from a maximum to a minimum, and is therefore suit- able for use with a pressure-organ which can be alternately admitted to and discharged from it. For the relative rotations of d and e we

M

have = 1 ! = J, i.e. for three revolutions of the centre of the

chamber, or (what comes to the same thing) of the small guiding cranks e, the piston d revolves once in the opposite direction. Gal- loway proposed to connect one of the cranks with the screw-shaft of the vessel, in order that this might rotate three times as fast as the

piston. In Fig. 286 -^ = 1 - f, in Fig. 287 1 - J. The inventor