Page:The Kinematics of Machinery.djvu/397

 ROOT, WITTY. 375

rectangular cross section. All the joints have thus to be made with plane surfaces, a construction which presents some practical diffi- culties, but (as the surfaces belong to lower pairs) at least allows a steam-tight joint to be made. In its special formula we have to in- dicate that both b and c are driving links, it will therefore run ((7"P-^)b+~c. The sources from which we obtain our information about the machine call it the "very quintessence of simplicity, " a judgment in which we can concur only to a limited extent if it be based on considerations as to practical usefulness.

Chamber-crank Trains from the Turning Cross- block.

(Plate XXIV.)

By plating the chain of the last-mentioned mechanism on a we obtain the turning cross-block, ( C^P-^)*, the motions in which we have already considered in 72. This mechanism has also been employed in chamber trains intended for use as rotary steam- engines.

Plate XXIV. Fig. 1 shows the steam-engine of Witty, con- structed in 1811.* This machine is a simple inversion of the mechanism of Fig. 2, Plate XXIII. omitting the pump! The crank a is the fixed link or frame, the cylinder d and block 1) rotate, and the cross-block c makes the cardioidic motions which we now know, for its centroids and that of a are Cardanic circles of which the larger belongs to c. The circles are shown in the figure. The cross-block c is paired to d both by the sliding- pairs at 4 and as a piston. It must therefore be placed in the exponent as the driving-link.

Witty appears to have been interested in the motions of his machine, and to have examined the point-paths of the cro^s- block, for he constructed a second machine (in Hull) in which the chain was reduced by the block &, and higher pairing conse- quently used between c and a, (Fig. 2, PL XXIV) The frame a is provided with a rim which has for its profile a curve equi-


 * Severin's Alhandlungfiw, lS2n, p. 62.