312 APPLIED MECHANICS 
D 
Fig. 484. Fiaq. 485. 
21. In a horizontal steam-engine the indicator reducing gear consists of a 
radial arm AB suspended from a fixed centre A above the line of stroke; the 
end B of the radial arm is connected to the cross-head by a link BO, and the 
cord passes off from a sector fixed to the arm AB, its centre being A and the 
radius AD, If, for any position of the gear, a vertical line drawn through A 
cuts the link BC in N, show that oo gives the ratio of the piston speed to the 
cord speed. [U.L.] 
22. In the four-bar mechanism shown in the sketch (Fig. 486), the bar A is a 
fixed bar; the bars B and D rotate about the fixed centres OAB and OAD, and 
they are coupled together at their outer ends by the bar C; the bar B revolves 
in a clockwise direction, with uniform velocity round its fixed axis OAB at 50 
revolutions per minute. Find in any way you please the positions of the bar 
D for twelve equidistant positions of the bar B during one complete revolution, 
and draw up a table showing (1) angle turned through by the bar B, in degrees ; 
OAB 
Fig. 486. Fig. 487. 
(2) angle turned through by the bar D, in degrees ; (3) mean angular velocity of 
the bar D, in radians per second, during each interval ; (4) mean angular accelera- 
tion of the bar D, in radians per second per second. Draw curves showing 
angular velocity and angular acceleration at any time. The lengths of the bars 
.are 15, 30, 25. and 35 inches respectively. [B. E.] 
23. The diagram (Fig. 487) shows a radial valve gear. The crank CP turns 
uniformly at 12 radians per second, and is pinned at P to the rod PR, the point 
Q in this rod being guided in the circular path SS, centre T. For the position 
of the mechanism shown in the diagram, determine and measure the velocities 
-and accelerations of the points R and V, [B.E.] 
