Page:The Kinematics of Machinery.djvu/324

 302 KINEMATICS OF MACHINERY. However extraordinary this may seem at first, it is perfectly true, and requires moreover to be well remembered by anyone who wishes readily to understand existing mechanisms ; it is sufficient to cite Fig. 219 as an illustration of this. The chains which are re- presented in the four figures 223 to 226 are kinematically absolutely identical throughout. The external differences which appear in each case are merely due to that reversal of lower pairs which we emphasised so strongly, it can now be seen with how good reason, in an earlier chapter ( 16). . 70. The Isosceles Slider-crank Chain. We have seen that the difference between the two mechanisms ((7g P-*-) 1 * and (C'JP- 1 -)* is simply due to our having taken b >> a ; the difference between (C^P^ and (C'^P^ is due entirely to the same cause. We must therefore obtain an intermediate form for each pair of cases if we make a = 5 ; the chain thus obtained is the one already described in 47 and shown in Fig. 227. The links a and b are here made equal ; the links c and d are also equal, for they are the two infinite links which always form part of the chain (67 JP- 1 -). The equal links are adjacent in each case, so that the general conditions of the chain are the same as in the isosceles crank train of Fig. 211 ; the chain before us is simply a special case of the former, and we shall therefore give it a similar name, calling it an isosceles slider-crank chain. We have already considered its centroids in 47. They are two pairs of Cardanic circles, the smaller being the centroids for the links a and &, the larger those for c and d. The peripheral ratio which appears here is a general property of the isosceles quadric crank chain, we found it before where the centroids had unlike and complex forms, and we find it here also in the limiting case, which is one, as we see, of peculiar simplicity. The four mechanisms of the slider-crank here become two only, of which the first is shown in Fig. 227. Omitting the symbols for the higher pairing, its formula will be (C" 2 ^ C r// P- L ) d=c . The same mechanism is obtained whether the chain be placed on c or d, which is indicated by their equality in the exponent. We shall