RULES FOR LAYING DOWN THE CENTER LINES OF THE MOTION.
Fig. 29.
Lay down the center line aa ([Fig. 29]) of the cylinder, and that of the valve-stem bb, at the relative distances required for the engine to which the application is to be made; the valve-stem center line being, however, in the plane of the vibration of the connecting rod. Draw the path of the crank-pin, and the center lines of the connecting rod cc1c1 for both upper and lower positions when the piston is at half stroke. Take a point d on the center line of the connecting rod, where its vibration between d1 and d2 is equal to about double the length of the full stroke of the valve (it is better to allow rather more than less). It may, however, be chosen very much to suit the other arrangements of the engine, such as the position of the guides, brackets, etc., getting, however, if possible, a vibration of the connecting rod fully equal to double the stroke of the valve, to avoid too great an angle of the slide-link when put over for full forward or backward gear.
Having chosen the point d, draw a vertical line zz through it and at right angles to aa, and mark off the two points e, e, on each side, these being the extreme positions of the point d on the connecting rod for front and back stroke; from these points draw lines to a point f on the vertical, so far down that the angle between them shall not be more than 90°,—less is better, if there is room to allow of it (these will represent the center lines of the first link pinned to the connecting rod). The point f, which will rise and fall with the vibration of the connecting rod, is to be controlled as nearly as may be on the vertical line by a link pinned forward near the cylinder at f1, or, if more convenient, it can be pinned backward.
Next, on the valve-stem center line bb, mark off on each side of the vertical zz the amount required for lap and lead together, at g-g1 and g-g2; g-g1 being lap and lead for the front end of the cylinder, and g-g2 being lap and lead for the back end of the cylinder. Then, assuming the piston to be at the front of the cylinder, and the centers of the connecting rod to be at hh1 (h being the crank-pin), the point d, which we have chosen to take motion from, will be at e1, and the link pinned to the connecting rod, for transmitting motion to the valve, will be at e1 f. From a point on this link, which has at first to be assumed, say at j (which will be about the half vibration of the connecting rod; that is, d1 to d), draw the center line of the lever actuating the valve, that is joining j and g; the point where this line crosses the vertical zz, will be the center or fulcrum of the lever, and will also be the center of oscillation of the curved links in which the blocks carrying the center of the lever slide; this center is marked m. The function of the link e1 f, and the attachment of the valve-lever to it at j, is to eliminate the error in vibration of the lever, center m, which would otherwise arise from the arc passed through by the lower end of that lever. Although the position of the point j may be found by calculation, it is much more quickly found by a tentative process; and, to test it the assumed point j be the correct one, we mark off on each side of m, vertically, the correct vibration required, n1 n2, which will be the same as the vibration of the connecting rod on the vertical line zz. Then apply the distance e1—j to d1—j1 and d2 j2. Then, if the length jm be applied to j1 n1 (measuring from j1), and to j2 n2 (measuring from j2), and the point m fall below n1 n2 in each case, it will be necessary to take a point on e1 f higher than j; or if, on the other hand, m falls above n1 n2, then a point must be taken on e1 f lower than j. This point will generally be found on a second trial.
The point m, as said, now represents the center of oscillation for the links and the center or fulcrum of the lever. And these must coincide, when the piston is at each end of the stroke, the lead being then fixed; and the links can be pulled over from forward to backward, or any point of expansion, without altering the lead. This may be taken as a test of the gear being set out correctly.
The point g will be the point of attachment for the valve-stem link, which may be made any convenient length; but, from that length as a radius, the curve of the links must be drawn from a center m1 on the parallel line m-m1; the angle at which this curve is set from the vertical (which is mid-gear), will give forward or backward gear,—the angle leaning forward s1, or to the front of the engine, being forward gear, and the reverse s2 being backward gear. The amount of the angle, marked on the curve of extreme vibration at s-s1 or s-s2, will be equal to one-quarter more than the full opening of the port at that angle (that is, if 1″ opening of port is required, then the amount of angle s to s1 must be 1¼″), and the point of cut-off will be about 75 per cent. Laid out in this form, the leads and cut-offs for both ends of the cylinder, and for backward and forward going, will be practically perfect and equal, and the opening of ports also as near as possible equal. If a longer cut-off than 75 per cent is required, it is only necessary to increase the angle of the curve oo beyond s1 for forward gear, or beyond s2 for backward gear. It will be noticed, that, in this gear, the lap and lead are entirely dependent on the action of the lever j, m, g, as a lever, and may be varied according to the length of mg. And the opening of the port (beyond the amount given as lead) is dependent on the amount of angle imparted to the curved link oo, and will be, as above said, about four-fifths of the amount of that angle from the vertical measured on the line of extreme vibration.
Deviations from the above positions and proportions may be made without materially altering the correctness of the results.