294 KINEMATICS OF MACHINERY.

angular velocity equal to half that of a, as we have already seen in 47. By fixing c (or &) we obtain the mechanism shown in Fig. 213, for which the formula (including the expression for the

( C" ^ C"}

pair-closure) is , 2 -~ ~- Its motion is no less characteristic (p}a.c

than that of the first mechanism. It is in some respects similar to that of the lever-crank (C") d . The link d has become the crank, and a the coupler; I however swings about its axis 3

02'

FIG. -21:5

symmetrically to c through such an angle that the greatest distance of 2 from 4, when the former is in either of the positions 2' or 2 ", is equal to 2a. The points 2' and 2" therefore are nearly four crank lengths apart, while in the mechanism (") d the end 3 of the lever oscillates through a distance which approximates only to two crank lengths. We shall further on have occasion to return to this interesting case.

The Cylindric Slider-crank Chain (C"> rjL )-

Continuing our examination of the chain (C") let us now some- what alter its form. We can substitute for the lever c a small sector of an annular cylinder, and inclose this in a circular slot, (Fig. 214) rigidly connected with the eye at 1. If the centre of the slot and of the sector c be placed at a distance from 1 equal to the distance 1.4 in the former case, the sector has exactly

the same relative motions as it would have had had it been