For this problem we have to combine all the foregoing problems. Through the center C of axle draw the horizontal line AD, and the line KL perpendicular to it. Find the positions of crank at full and half stroke, as per Problem 1. Locate the rocker, draw the center line of motion CT, and amount of offset in lower rocker-arm, according to Problem 2. Next, locate the relative positions of eccentrics when the crank stands at full and half stroke, as explained in Problem 3. Then with a radius equal to the correct length of eccentric-rods, as explained in Problem 4, draw
Locate the points ½B3 and ½F3, indicating the position of the center of lower rocker-pin when steam is cut off at half stroke; find the points x1x2 indicating the positions of the point of suspension when the link is lifted into the position to cut off at half stroke, as explained in Problem 5, and shown in [Fig. 25].
Now, in order to find the position of lifting-shaft and length of arms, we must find four more additional points,—first, the position of the point of suspension of the link when the piston is at full stroke forward end of cylinder, and the crank-pin at F, the valve having 1/16 of an inch lead, and the engine moving forward, as indicated by the arrow-point 1; also the position of the point of suspension of the link when the piston is at full stroke at the opposite end of the cylinder, valve 1/16 inch lead, and engine going in the same direction. To find these two points, we must know the corresponding position of the center of lower rocker-pin. In [Fig. 8a] we see, that when the piston is at full stroke forward, and valve with 1/16 inch lead, the center of valve is 13/16 of an inch in the rear of the center line of exhaust, and consequently the lower rocker-pin will be 13/16 of an inch in front of the line QU. In the same manner we can show that the center of lower rocker-pin will be 13/16 of an inch in the rear of the line QU when the piston is at the opposite end of the cylinder.
Let us now locate the positions of the lower rocker-pin in [Fig. 26], by drawing a line parallel to and in front of QU, with 13/16 of an inch between them: this line will intersect the arc RS in the point F3, and this point will be the center of lower rocker-pin when the piston is at full stroke forward. Draw another line 13/16 of an inch in the rear of QU and parallel to it: this line will intersect arc RS in the point B3, and this point will be the center of rocker-pin when the piston is at full stroke in the rear end of the cylinder. Now place the paper template with the line ee below the center line of motion CT, the point f1 on the arc x1x2, the point f2 on the arc y1y2, and the link-arc c3c4 just touching the point F3, and, while in this position, mark the point X of the template on the paper, which can be done with the aid of a needle, and indicate the point on the paper by x3. This point will be the position of the center of saddle-pin when the piston is at full stroke in the forward end of the cylinder, the valve having 1/16 inch lead. Again, slide the template along until the point f1 is on the arc a1a2, the point f2 on the arc b1b2, and the link-arc c3c4 in contact with the point B3; mark the point X of the template on the paper, and indicate this point by x4. This point will be the position of the center of saddle-pin when the piston is at full stroke in the rear end of the cylinder, the valve having 1/16 inch lead. Secondly, to find the position of the point of suspension of the link when the piston is at full stroke in the forward end of the cylinder, valve having 1/16 of an inch lead, and the engine moving backward, as indicated by the arrow-point 2; also the position of the point of suspension of the link when the piston is at full stroke at the opposite end of the cylinder, valve 1/16 of an inch lead, engine going in the same direction. For this purpose, slide the template along until the line ee is above the line CT, and f1 in the arc a1a2, the point f2 in the arc b1b2, and the link-arc c3c4 in contact with the point B3; mark the point X on the paper, and indicate this point by x5. This point will be the position of the center of saddle-pin when the piston is at full stroke in the rear end of the cylinder, valve having 1/16 of an inch lead. Again, slide the template along until the point f1, will be in the arc x1x2, point f2 in the arc y1y2, and the link-arc c3c4 in contact with the point F3; mark the point X on the paper, and indicate this point by x6. This point will be the position of the center of saddle-pin (or the point of suspension) when the piston is at full stroke in the forward end of the cylinder, valve 1/16 of an inch lead, engine moving backward. Now, once more, with the point x3 as a center, and with the length of the link-hanger as a radius, describe an arc; and with the point x4 as a center, and the same radius, describe another arc. These two arcs will intersect each other in the point g. Again, with the length of the link-hanger as a radius, and the points x1x2 as centers, describe two arcs intersecting each other in the point g1, with the points x5x6 as centers; and, with the same radius, describe another two arcs intersecting each other in the point g2. Lastly, through the points g, g1g2, draw an arc. The center h, from which the arc has been described, will be the center of the lifting-shaft, and the radius hg or hg2 will be the length of the lifting-shaft arms; that is, the length of the two arms to which the link-hangers are attached: the length of the other lifting-shaft arm, to which the reach-rod is attached, is made to suit the other details of the engine.
When the admittance of steam ceases at the same time that the piston has reached the half stroke, the practical man would say “that the valve is cutting off equal at half stroke.” When the greatest equal volume of steam is admitted alternately in each end of the cylinder, the valve is said to be cutting off equal when the link is in full gear.
It is always conceded among engineers, that when the link-motion is adjusted to cut off equal at half stroke, and also to cut off equal when the link is in full gear, equal volumes of steam will be admitted alternately when the link hangs at any intermediate point.
If, now, we examine Problem 5, we find, that, to obtain an equal cut-off at half stroke, it is necessary to find the proper position of saddle-pin.
Again, if we examine Problem 6, we find, that, in order to obtain an equal cut-off when the link is in full gear, also an equal cut-off for any point between full gear and half stroke, we have to determine the proper position of the center of lifting-shaft and the correct length of its arms.
Lastly, if we examine the first four problems, we find them simply to be preparatory problems.