Page:The Kinematics of Machinery.djvu/205

 COMPLETE CLOSURE OF FLECTIONAL ELEMENTS. 183

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Complete Kinematic Closure of the Flectional

Elements.

We have seen that the Sectional elements may receive, by means of pair-closure and force-closure, important, practical and in the highest degree valuable kinematic applications. We found force-closure to be always necessary, but to a different extent in different cases. In the case of the cord in Fig. 124 we required the absolute prevention of every force not acting as a direct pull upon the cord itself; for the force-closure in the hydraulic press nothing more is necessary than that downward force should be caused to act upon the pistons. If we go one step further we can make even this unnecessary ; we can, that is, admit the Sectional elements unreservedly into what we have called ( 1) machinal systems.

The removal of the force-closure is effected by the use of suitably

��FIG. 142.

combined force-closed chains. The common arrangement of belt pul- leys (Fig. 142) gives us a familiar example of this. Here we have two cylindric pulleys, a and c, fitted with conaxial shafts, and connected by a bar or frame d which carries the bearings for the latter ; the belt belonging to a is made in one piece with that of c, the two forming the common endless band b. By this means we obtain a kinematic chain in which the flectional element no longer requires external force-closure. We might regard it as a combination of two chains, each of the form of Fig. 125, their closure acting con- tinuously in opposite directions.

The chain-closure here is twofold. In the first place, as has been mentioned, it makes the force- closure of the flectional element b

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