444 KIN EM A TICS OF MA CHINE R Y.
ing " rings of metal over bodies which it is desired to strengthen or unite. The rings are put on their place hot, and of course exert an enormous pressure when they contract in cooling. The same result has of late years been obtained by pressure merely, without previous heating, and in many very important cases this is super- seding the older process ; in fixing railway carriage wheels on their axles for instance, and in securing the cranks and crank-pins of locomotives, etc. Looked at as a whole the two processes lie very near each other, the latter might almost be called cold riveting. We shall therefore not look at them as distinct, but shall include them both under the name of forced or strained joints.
Kinematically, strained joints represent fastenings of a kind which may be regarded as cylinder or prism pairs, (0) or (P), in which the elements are so closely pressed together that as regards the action of any ordinary forces they form one body only, and which therefore serve for the formation of kinematic links. This close union of the elements is effected essentially by the friction produced by the straining pressure. We shall have occasion once more to return to this point.
no. Pins, Axles, Shafts, Spinclles.
A pin considered kinematically forms one element of the pair - ; it is the element C + , or more strictly E + if we use the more general symbol (R) instead of (C). The pin and its bearing, the combinations of elements Rt=R~, may be considered the most common pair of elements ; it occurs in almost every kinematic chain, in large and small dimensions, under light and under heavy pressures, moving slowly and moving rapidly. We shall return to the element R~ in 112.
Axles are pins joined conaxially ; that is, kinematic links of the form (7+ ... | ... (7+. The word axle is used specially in those cases where the forces to be resisted tend chiefly to bend the link.
Shafts are also links of the form C + ... \ ...C+. They are there- fore kinematically identical with the axles, but the name shaft is used specially in those cases where torsion is the force chiefly acting.
