Page:The Kinematics of Machinery.djvu/410

 388 KINEMATICS OF MACHINERY.

a channel or groove in which it slides, and which forms a part of the chamber d. We thus have in the links a, I, c, d, the kinematic chain

which is placed upon the right-angled link d adjacent to the acute- angled link d.

It is most important that the arrangement of the chamber and piston should be rightly understood. The link I forms the piston. It has the form of a plane disc provided with spheric surfaces to work in contact with the chamber both at its centre and periphery. The form of the interior of the chamber d is that of two circular cones, which are the envelopes to the motion of the plane sides of the disc. These cones are indicated in Fig. 2 by the letters A H and C IK. The surfaces A B and CD of the piston touch them always in one generator, for the axis 2 always makes the same angle a, the complement of the vertex angle of the cones, with their axis.

It will be noticed that the geometrical axis of the pin 3 moves always in one plane, in the figure the plane of the paper. Parallel to this plane there is a diaphragm 4 fixed in the chamber. It has plane sides ; in reality, however, it is nothing but a portion of a revolute upon an axis which is perpendicular to the plane of the paper and passes through the centre of the chamber. In other words, it is a part of the same figure as the ring channel within which the block c slides. A corresponding continuation of the block c itself also exists, as the section in Fig. 2 shows. This figure is a projection upon a plane somewhat inclined to the hori- zontal, so as to show a portion of one side of the diaphragm. It shows at L the continuation of c in the form of two portions of a cylinder paired internally with the diaphragm d, and externally with an open cylinder in the disc 1). Both pairings are lower, so that these continuations of the block serve as packing pieces. Between them and the external sliding-block c there is no kine- matic difference ; the pair 4 externally takes the form E^R~ (or CtC~) and internally the form R2R+ (or C~C+) ; and the pair 3 takes the forms C~C+ and C+C~ respectively.

If we assume that it is possible to obtain a tight joint by the higher pairing between the surfaces of the disc and the walls of