Page:The Kinematics of Machinery.djvu/206

 184

�KINEMATICS OF MACHINERY.

��unnecessary by substituting for it the action of the latent forces in the frame d. In the second place, it entirely constrains the axoid roll- ing, the securing of which by force-closure we discussed in 40. The pulleys being cylindric, the axoids here are on the one hand the sur- faces of the belts continually running off and on, and on the other the peripheral surfaces of the pulleys. These surfaces are brought so firmly into contact by the latent forces acting through d, that they cannot slide upon each other. The chain obtained has four links : the two pulleys a and c with their shafts, the band b, and the frame d, with the shaft bearings. The motions in the chain occur exactly as if its elements were completely rigid. Every angular motion of

the one pulley is- accompanied by a corresponding motion of the other ; the chain can also be inverted, that is, any one of its links may be fixed, assuming, of course, that no lateral disturbing force be allowed to act upon the belt itself.

The kinematic chain shown in Fig. 143 may be considered the contra- positive of this mechanism. The two pistons a and c, fitting tightly into a connecting vessel d, are made to form sliding pairs * with it, and are kinematically linked by means of the fluid columns b and e enclosed in d. If the piston a be moved to the left, the descending column of water b causes the piston c to move to the right ; just as much water is moved up one column as moves down the other. If care be taken to fill the vessel d perfectly, all air being re- moved from the water, the action of the mechanism is complete, and the chain is as perfectly closed as if it consisted of rigid elements only. Herr Anderssohn has shown this convincingly in his interesting experiments with tubes as long as 3000 metres, used as water-rods, as in Fig. 139.-f- Every small sliding of one piston is accompanied by the corresponding motion of the other. This mechanism, the tardily acknowledged contra-positive of the familiar


 * See note p. 168.

t Zeitschrift des V. deittscher Ingenicure. Vol. xiii. (1869) p. 402.

�FIG. 143.

�