Let it be required to find the amount of motion imparted in a straight line to a rod attached to an eccentric strap, and the following construction may be used. In Figure 265 let A represent the centre of the shaft, and, therefore, the axis about which the eccentric revolves. Let B represent the centre of the eccentric, and let it be required to find in what position on the line of motion x, the centre C of the rod eye will be when the centre B of the eccentric has moved to E. Now since A is the axis, the centre B of the eccentric must rotate about it as denoted by the circle D, and all that is necessary to find the position of C for any position of eccentric is to mark the position of B on circle D, as at E, and from that position, as from E, as a centre, and with the length of the rod as a radius, mark the new position of C on the line x of its motion. With the centre of the eccentric at B, the line Q, representing the faces of the straps, will stand at a right angle to the line of motion, and the length of the rod is from B to C; when the eccentric centre moves to E, the centre line of the rod will be moved to position P, the line Q will have assumed position R, and point C will have moved from its position in the drawing to G on line x. If the eccentric centre be supposed to move on to F, the point C will move to H, the radii B C, E G, and F H all being equal in length. Now when the eccentric centre is at E it will have moved one-quarter of a revolution, and yet the point C will only have moved to G, which is not central between C and H, as is denoted by the dotted half circle I.

Fig. 265.

On the other hand, while the eccentric centre is moving from E to F, which is but one-quarter of a revolution, the rod end will move from G to H. This occurs because the rod not only moves endwise, but the end connected to the eccentric strap moves towards and away from the line x. This is shown in the figure, the rod centre line being marked in full line from B to x. And when B has moved to E, the rod centre line is marked by dotted line E, so that it has moved away from the line of motion B x. In Figure 266 the eccentric centre is shown to stand at an angle of 45 degrees from line q, which is at a right angle to the line of motion x x, and the position of the rod end is shown at C, J and H representing the extremes of motion, and G the centre of the motion.

Fig. 266.

If now we suppose the eccentric centre to stand at T, which is also an angle of 45 degrees to q, then the rod end will stand at K, which is further away from G than C is; hence we find that on account of the movement of the rod out of the straight end motion, the motion of the rod end becomes irregular in proportion to that of the eccentric, whose action in moving the eye C of the rod in a straight line is increased (by the rod) while it is moving through the half rotation denoted by V in figure, and diminished during the other half rotation.

In many cases, as, for example, on the river steamboats in the Western and Southern States, cams are employed instead of eccentrics, and the principles involved in drawing or marking out such cams are given in the following remarks, which contain the substance of a paper read by Lewis Johnson before the American Society of Mechanical Engineers. In Figure 267 is a side view of a pair of cams; one, C, being a full stroke cam for operating the valve that admits steam to the engine cylinder; and the other, D, being a cam to cut off the steam supply at the required point in the engine stroke. The positions of these cams with relation to the position of the crank-pin need not be commented upon here, more than to remark that obviously the cam C must operate to open the steam inlet valve in advance of cam D, which operates to close it and cause the steam to act expansively in the cylinder, and that the angle of the throw line of the cut-off valve D to the other cam or to the crank-pin varies according as it is required to cut off the steam either earlier or later in the stroke.

The cam yoke is composed of two halves, Y and Y', bolted together by bolts B, which have a collar at one end and two nuts at the other end, the inner nuts N N enabling the letting together of the two halves

Fig. 267.

of the yoke to take up the wear. It is obvious that as the shaft revolves and carries the cam with it, it will, by reason of its shape, move the yoke back and forth; thus, in the position of the parts shown in Figure 267, the direction of rotation being denoted by the arrow, cam C will, as it rotates, move the yoke to the left, and this motion will occur from the time corner a of the cam meets the face of Y' until corner b has passed the centre line d. Now since that part of the circumference lying between points a and b of the cam is an arc of a circle, of which the axis of the shaft is the centre, the yoke will remain at rest until such time as b has passed line d and corner a meets the jaw Y of the yoke; hence the period of rest is determined by the amount of circumference that is made concentric to the shaft; or, in other words, is determined by the distance between a and b.

The object of using a cam instead of an eccentric is to enable the opening of the valves abruptly at the beginning of the piston stroke, maintaining a uniform steam-port opening during nearly the entire length of stroke, and as abruptly closing the valves at the termination of the stroke.

Figure 268 is a top view of the mechanism in Figure 267; and Figure 269 shows an end view of the yoke. At B, in Figure 268, is shown a guide through which the yoke-stem passes so as to be guided to move in a straight line, there being a guide of this kind on each side of the yoke.

Fig. 268.