THE WORK-PIECE. 495
are combined into a pair of elements, in this case a sliding pair P+P-. In the screwing and tapping machines the pairs S^S~ and ti~S + respectively are formed in the same way. We see that in every case the body to be worked upon becomes itself a kinematic element or the part or whole of a kinematic link. In the screwing machine this is specially noticeable, for as soon as the screw is started it itself causes the forward motion of the dies. The body to be worked is therefore not something external to the machine but actually forms a part of it. We shall therefore give this body, to which we shall often have to refer, a special name, calling it the work-piece of the machine.
That the work-piece has formed an element in a lower pair is only accidental to the particular machines chosen for illustration. In other cases we find higher pairs exist. In the rolling-mill, for example, the work-piece forms with the rolls the higher pair jR+, P+, the work-piece itself forming here a complete link "of the chain. In the carding engine the symmetrically placed wires of the cards, compel the fibres of the tangled mass of wool to assume the enveloping forms corresponding to their motion, that is, to lie parallel to each other. In the corn-mill there is a very complex higher pairing, in which force-closure plays an important part, between the grain and the mill-stones.
Our analysis therefore leads us to the following proposition: In form-changing machines the work-piece is a part or the whole of a kinematic link, and is paired or chained with the tool by so arranging the latter that it itself changes the original form of the work-piece into that of the envelope corresponding to the motion in the pair or linkage employed.
This proposition is free from the indistinctness which charac- terised the older conception of the machine. We see from it, in the first place, that the kinematic chain is not broken at the tool or the working point, but continues through it. It is not the end of the chain, but only a point in it having special importance in reference to the object of the machine. We find here also the answers to several of the questions which came up in 129. The thread in the spinning-machine, as a link in the kinematic chain, is necessarily a transmitter of force. The spindle, on the upper end of which it first winds and then immediately unwinds itself
