Fig. 25b.
In [Fig. 8] ([p. 274]) we have placed the slide-valve centrally over the ports, that is, it laps over each steam-port an equal amount, namely, ¾ of an inch, which is equal to the lap. In this position of the valve, the center line of the upper rocker-arm will stand perpendicular to the line drawn parallel to the valve-face, and the center line of the lower rocker-arm will stand perpendicular to the center line of motion CT: hence the center line of upper rocker-arm MQ in [Fig. 8] will coincide with the line MQ in [Fig. 25], and the center of lower arm QU in [Fig. 8] will coincide with the line QU in [Fig. 25].
Now let us follow the relative movement of the valve and piston. We find, that, when the piston commences its backward motion, the valve moves in the same direction, as shown by the arrow-points in [Fig. 8a]; and, during the time that the piston is completing the half stroke, the valve has finished its full travel backward, and commenced moving forward, as indicated by the arrow-points, [Fig. 8b]; and, at the time that the piston stands exactly at half stroke, the forward edge of the valve is just closing the forward steam-port, and consequently cutting off steam at half stroke when the piston is moving backward. From this we see, that, when the piston has completed the half stroke when moving backward, the center of the valve will be a little in the rear of the center of exhaust-port; the distance between the center of valve and the center of exhaust-port being ¾ of an inch, the amount of the lap: the upper rocker-pin will stand ¾ of an inch behind the line MQ, and the lower rocker-arm pin will be ¾ of an inch in front of the line QU, as shown in [Fig. 8b]. We therefore draw in [Fig. 25] a straight line parallel to QU, and ¾ of an inch in front of it: this line will intersect the arc RS in the point ½F3; and this point is the position of the center of lower rocker-arm pin when the crank stands at ½F, and steam cut off at half stroke. Let the piston complete its backward stroke, and then commence moving forward towards half stroke, as shown by the arrow-point, [Fig. 8c]. During this time the valve has completed its full travel forward, and commenced traveling backward, as indicated by the arrow-point, [Fig. 8c]; and, when the piston stands exactly at half stroke, the rear edge of the valve is just closing the rear steam-port, and consequently cutting off steam at half stroke when the piston is moving forward. In this position the center line of the valve will be ¾ of an inch in front of the center of exhaust, the center of the upper rocker-arm pin will be ¾ of an inch in front of the line MQ, and lower rocker-pin ¾ of an inch in the rear of the line QU, as shown in [Fig. 8c]. We therefore draw in [Fig. 25] a line parallel to QU, and ¾ of an inch behind it; this line will intersect the arc RS in the point ½B3; and this point will be the position of the center of lower rocker-arm pin when the crank stands at ½B, and steam cut off at half stroke. Now, remember, that when the crank stands at ½F, [Fig. 25], the forward eccentric will be ½x, and the backward eccentric at ½y; and, if the link is raised or lowered while the eccentrics remain at ½x and ½y, the forward eccentric-rod pin will move in the arc ½x1 ½x2, and the backward eccentric-rod pin will move in the arc ½y1 ½y2.
Let us now find the position of link when steam is cut off at half stroke at either end of the cylinder.
The points ½F3 and ½B3 in [Fig. 25] being located, place the paper template on the drawing so that the point f will lie in the arc x1x2, and the point f2 in the arc y1y2, and the link-arc c3c4 just touching the point ½F3. While the template is in this position, draw on the paper along the edge c3c4 a portion of the link-arc, and mark the position that the line ee occupied, so that, when the template is removed, the line e1e1 can be drawn on the paper to represent the line ee of the template. Next place the template so that the point f will lie in the arc ½a1 ½a2 the point f2 in the arc ½b1 ½b2 and the link-arc c3c4 just touching the point ½B3 and, while in this position, draw part of the link-arc c3c4 on the paper, mark the position that the line ee occupied, and, after the template is removed, draw the line e2e2 on the paper to represent the line ee of the template. Now find by trial a point x1 on the line c1c1, and another point x2 on the line e2e2, so that the distances of these points from their link-arcs are equal, and that a straight line drawn through them will be parallel to the center line of motion.
The distance from x1 to the link-arc—or, which is the same thing, the distance from the point x2 to the link-arc—will be the correct distance between the center of saddle-pin and the link-arc c1c2, [Fig. 6a]. Or, in other words, the position of the point x1 or x2, [Fig. 25], will indicate the proper position of the point of suspension on the link. For future reference, let us mark this point of suspension on the template, and indicate it by X, [Fig. 6b].
Fig. 26.
Problem 6, [Fig. 26].—To find the position of the center of lifting-shaft and the length of its arms.—In the last problem we found the point of suspension of the link, so that it will cause the valve to cut off equal portions of steam when the piston stands at half stroke. It now remains for us to find the position of the lifting-shaft and the length of the lifting-shaft arms, so that the greatest equal amounts of steam will be admitted alternately at each end of the cylinder. Here a little difficulty arises which needs explanation, so that our construction may not seem inconsistent to the reader. It would be an easy matter to place our lifting-shaft to accomplish the object just stated; but, if we do this, the lead will not be equal at each end of cylinder when the piston is at full stroke. Again, if we locate our lifting-shaft in such a manner that equal lead will be obtained, then the maximum cut-off will not be equal; but the difference will be comparatively so small that it will not injure the working of the engine. This small difference of the maximum cut-off is therefore considered among practical men of little or no importance, but it is always considered good practice to have an equal lead at full stroke. Let us therefore adjust the lifting-shaft to obtain an equal lead, and allow us to consider the maximum cut-off to be equal when the lead is equal at full stroke.