Page:The Kinematics of Machinery.djvu/353

 UNIVERSAL JOINT. 331

rod 4, Fig. 258) perpendicular to the plane of the paper, we substitute the small section 4 of a cylinder, sliding upon a comP spending section d of another cylinder ; c is now the block, d the frame, a the crank and I the coup]er as before. Below the conic chain a similar cylindric chain is shown; the juxtaposition of the two makes it very easy to realise that the latter is simply the conic chain with the point M removed to an infinite distance. The conic slider-crank chain, like its cylindric counterpart, gives us six me- chanisms, four principal forms and two secondary ones. We shall give them the same names as before with the prefix conic to each. There appears to be very little, if any, use made of them in practice.

C. Conic (normal) double slider chain (<?^-), Fig. 260. Here the links b, c and d are right-angled, and a only acute-angled. This chain corresponds to the one bearing the same name in the cylindric series, and by applying the method of pin-expansion, it can be brought into a very similar form, as in Fig. 261. The me- chanism of Fig. 262 is essentially identical with that of the one before it. The slide d is nothing more than a portion of a cross section of the cylinder which in Fig. 261 appears as a round bar, marked with the same letter. The link b subtends an angle of 90, and is thus identical with the sector b in Fig. 261. This chain, like the cylindric double slider, gives us three mechanisms, which will be called

15.* The conic (turning) double slider, ) (rirtL.\&=i> or conic swinging cross-block j ^ 3 '

16. The conic (turning) cross-block ...

17. The conic swinging double-slider ...

Considerable use is made of these mechanisms in practice. One well-known application of No. 16 is to be found in the mechanism known as the universal or Hooke's joint.f Writing out the formula (^G L -) & in full we have

b c d a

- C+......C C-...

and this formula, corresponding to the chain in Fig. 260, we have already found (.58) to be that of the universal joint Fig. 263.

t In Germany also as Carclano's coupling.
 * The chains (0$~) and G^C^} together, as we have seen, give 14 mechanisms,