170 KINEMATICS Off MACHINERY.
ously, and make the direction of this force opposite to, and its mag- nitude not less than, those of the former. If, for example, the greatest anticipated disturbing force be = P, then in order to neutra- lise it we must cause an opposite force of the magnitude P to act upon the supposed element a. This force restrains a in the place of a portion of the enveloping partner-element I ; if for the sake of security we give to it the magnitude P-+-Q, then in the worst case a is held at the opposite point of restraint by the force P P-\- Q Q, this pressure being balanced by latent forces in the element b. The general conditions of equilibrium are thus fulfilled. Any such force as the supposed one P-\- Q closes, as it were, in the direction (P-f- Q\ the pair of elements left unclosed or incom- plete in that direction; we shall therefore call it a closing force. Such pairs of elements as require closing forces are evidently in- complete in themselves; their usefulness depends upon the applica-
��FIG. 120. FIG. 121. FIG. 122.
tion of the closing force, or upon what we may call in one word force-closure.
Force-closed pairs occur frequently in machinery. ^The shafts and bearings of most water-wheels are illustrations of them, where the great weight of the wheel is almost always sufficient in itself to prevent any vertical motion of the axle without the employ- ment of a plummer-block cover (Fig. 120). The crosshead some- times used for large horizontal engines gives us another illustration (Fig. 121) ; the heavy pistons and rods here prevent any rising of the crosshead, which is guided only beneath and at the sides. The knife-edge of a balance (Fig. 122) is also kept in continuous con- tact with its bearings by the weight of the beam and scales. The railway turn-table is another example, the whole table being here held by its own weight and that of the load upon it on a roller path completely open above ; a similar thing often occurs in wharf- cranes. Railway-wheels, lastly, are common and well-known
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