Page:The Kinematics of Machinery.djvu/325

 ISOSCELES SLIDER-CRANK TRAINS.

303

call it, carrying out the system of nomenclature already adopted, an isosceles turning slider-crank.

If the chain be placed on a or b we obtain the second of its possible mechanisms, for which the formula runs (G * ^ (7 // P- L ) a=b . It is represented in Fig. 228. The crank a has become the frame, the coupler I the crank. The block c transmits the rotation of the latter to the slide d, or vice versd. We shall call the mechanism an isosceles turning block.*

Fit;, 'I'll.

FIG. 2-2

The links I and d both rotate, they revolve in the same direction, and have the constant angular velocity ratio 2:1; the motion is exactly what it would be if b and d were two spur wheels having internal contact and having the ratio 1 : 2 between the numbers of their teeth. In fact the toothed gearing shown in Fig. 229, in which the smaller wheel a has two teeth with cylindrical profiles (pin-teeth), is very similar to the mechanism before us, although it has one link less. The four-toothed wheel b corresponds to the turning slide d. The similarity becomes less apparent if we make the numbers of teeth 3 and 6, as in Fig. 230, and Disappears almost entirely if other forms of teeth be used. The real relation between the mechanisms is however very obvious ; they have identical centroids. The whole matter gives us an interesting illustration

nation given, should it be necessary to do so. I think that it will very seldom be
 * Here, as in former cases, the words " slider-crank " can be added to the desig-

required.