PAIR-CLOSURE OF KINEMATIC CHAINS. 191

the fixed link a in such a way that 1465 and 3256 are parallelo- grams. Here three similar chains are combined, of which it' the points 4,3 and 6 form a triangle only one can at any instant be crossing its dead points. Applications of this mechanism occur not unfrequently.

4 7- Closure of Kinematic Chains by Pairs of Elements.

We have already found ( 42) that in certain cases pairs of ele- ments are closed" by kinematic chains. We must now examine the converse of this the closure of kinematic chains by pairs of ele- ments. This does not supersede the closure proper to the chain, but simply acts along with whatever closure already exists in posi- tions where it is insufficient.

Even in the mechanism which is once more represented in Fig. 151, we may note one thing about the sequence of the separate phases of the motion which must not be entirely disregarded. Let us suppose the dead point 2' to be reached by the left-handed

��FIG. 151.

rotation of the crank from the position 2, driven by the application of some force to the block c. If now this force be reversed, without the intervention oi either force- or chain-closure to carry a over the dead point, it remains indeterminate whether the crank shall move forwards in the lower half circle or backwards in the upper. Motion in the chain is therefore not absolutely constrained ; and the chain is not in the strict sense of the word closed, if by that expression we understand that for every motion of any link only a single motion of any other link be possible. At the same time the supposed backward motion of the crank a is not in itself different from the motion before made ; we have only to consider

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