Page:The Kinematics of Machinery.djvu/72

 If we suppose a h (that is a A o) again to be

fixed, k 1 will have a yet more complex motion than

d e; the method of building up the chain further allows the

possibility of obtaining motions according to more and more com- plex laws, and so to serve as the means of procuring a great, indeed an infinite number of different forms of motion. It holds equally good with the compound as with the simple chain that it can be set in motion after fixing any one of its links; in as many ways, that is to say, as it has links.

Closed mechanisms also can again combine, and so unite into higher forms; we may however allow these compound me- chanisms to class with those built up from compound chains.

We have now before us a general view of the method of con- struction of Mechanisms:

The mechanism is a closed kinematic chain; the kine- matic chain is compound or simple, and consists of kine- matic pairs of elements; these carry the envelopes required for the motion which the bodies in contact must have, and by these all motions other than those desired in the mechanism are prevented.

A kinematic mechanism is moved if a mechanical force or effort be applied to one of its movable links in such a way as to alter its position. The effort thus applied performs mechanical work which is accompanied by determinate motions; the whole, that is to say, is a Machine.

The arrangement by which the natural force is thus brought into action must correspond to the purpose for which the machine is intended. If for example the natural force act continuously, the machine receives a continuous motion, as in water-wheels, tur- bines, and so on. If the part acted upon by the force comes after a time into such a position that the latter exercises no further influence upon it, then, if the motion is to be continued, artificial means must be provided for restoring it to a position where such influence can again be exerted; as for instance in the clock. In many machines the action is limited to very small alterations of position of the moving parts, as in the balance, after which alter- ation they must be restored to their original position. This much by way of illustration only, later on we shall have to consider these questions systematically.