Set a pair of compasses to represent the length of the connecting rod on the same scale as the circle b d represents the path of the crank; thus, if the connecting rod is three times the length of the stroke, the compasses would be set to three times the diameter of the circle b d.
A straight line from b to d and passing through the centre c of the crank will represent the line of centres of the engine, which must be prolonged to the right sufficiently to rest the compasses on it and draw the arc y, which will give at h the position of the crank when the piston is at r, and the cut off is to occur.
We have thus found that the amount of circular path the crank will move through from the dead centre to the point of cut off is from b to h, and as the eccentric is fast upon the same shaft, it will, in the same time, of course, move through the same part of a circle.
One half of its motion will be to open and one half to close the port, so that we may by means of the arcs at f get the point f, which is midway between b and h, and with the compasses set from b to f, mark from d the two arcs v and v′ whose distance apart will obviously be the same as from b to h.
Then from v to v′ draw the line p, and from this line to the centre c of the crank shaft is the amount of steam lap necessary for the valve, while from this line (p) to d is the width of the steam port.
The proof of the diagram is as follows:
When the crank is on the dead centre, the centre of the eccentric is at v, its throw line being represented by the line from v to c, and the valve is about to open the port as shown in the figure.
While the eccentric is moving from v to d, the valve will move in the direction of the arrow and will fully open the port, while the crank pin will move from b to f.
Then, while the crank moves from f to h, the eccentric will have moved the valve to the position it occupies in the figure, having closed the port and effected the cut off.
We have here found the amount of lap and the position of the eccentric necessary for a given point of cut off when the latter is given in terms of the piston stroke. If, however, the point of cut off had been given in terms of the crank pin position, we might find the required amount of lap at once, by simply drawing a line from the centre b, the point to h where the crank pin is to be when the cut off occurs.