Draw lines, as H and I, representing the tooth breadth. From W, as a centre, draw on each side of G G dotted lines, as P, representing the height of the tooth above and below the pitch line G G. At a right angle to G G draw the line J K; and from where this line meets B, as at Q, mark the arc a, which will represent the pitch circle for the large diameter of the pinion D. [The smallest wheel of a pair of gears is termed the pinion.] Draw the arc b for the height, and circle c for the depth of the teeth, thus defining the height of the tooth at that end. Similarly from P, as a centre mark (for the large diameter of wheel C,) arcs g, h, and i, arc g representing the pitch circle, i the height, and h the depth of the tooth. On these arcs draw the proper tooth curves in the same manner as for spur wheels; that is, obtain the curves by the construction shown in Figures 237, or by those in Figures 238 and 239.

To obtain the arcs for the other end of the tooth, draw line M M parallel to line J K; set the compasses to the radius R L, and from P, as a centre, draw the pitch circle k. For the depth of the tooth draw the dotted line p, meeting the circle h and the point W. A similar line, from i to W, will give the height of the tooth at its inner end. Then the tooth curves may be drawn on these three arcs, k, l, m, in the same as if they were for a spur wheel.

Similarly for the pitch circle of the inner and small end of the pinion teeth, set the compasses to radius S L, and from Q as a centre mark the pitch circle d. Outside of d mark e for the height above pitch lines of the tooth, and inside of d mark the arc f for the depth below pitch line of the tooth at that end. The distance between the dotted lines as p, represents the full height of the tooth; hence h meets p, which is the root of the tooth on the large wheel. To give clearance and prevent the tops of the teeth on one wheel from bearing against the bottoms of the spaces in the other wheel, the point of the pinion teeth is marked below; thus arc b does not meet h or p, but is short to the amount of clearance. Having obtained the arcs d, e, f, the curves may be marked thereon as for a spur wheel. A tooth thus marked is shown at x, and from its curves between b and c, a template may be made for the large diameter or outer end of the pinion teeth. Similarly for the wheel C the outer end curves are marked on the arcs g, h, i, and those for the other end of the tooth are marked between the arcs l, m.



Figure 243 represents a drawing of one-half of a bevil gear, and an edge view projected from the same. The point E corresponds to point E in Figure 241, or W in 242. The line F shows that the top surface of the teeth points to E. Line G shows that the pitch line of each tooth points to E, and lines H show that the bottom of the surface of a space also points to E. Line 1 shows that the sides of each tooth point to E. And it follows that the outer end of a tooth is both higher or deeper and also thicker than its inner end; thus J is thicker and deeper than end K of the tooth. Lines F G, representing the top and bottom of a tooth in Figure 243, obviously correspond to dotted lines p in Figure 242. The outer and inner ends of the teeth in the edge view are projected from the outer and inner ends in the face view, as is shown by the dotted lines carried from tooth L in the face view, to tooth L in the edge view, and it is obvious from what has been said that in drawing the lines for the tooth in the edge view they will point to the centre E.



To save work in drawing bevil gear wheels, they are sometimes drawn in section or in outline only; thus in Figure 244 is shown a pair of bevil wheels shown in section, and in Figure 245 is a drawing of a part of an Ames lathe feed motion. B C D and E are spur gears, while G H and I are bevil gears, the cone surface on which the teeth lie being left blank, save at the edges where a tooth is in each case drawn in. Wheel D is shown in section so as to show the means by which it may be moved out of gear with C and E. Small bevil gears may also be represented by simple line shading; thus in Figure 247 the two bodies A and C would readily be understood to be a bevil gear and pinion. Similarly small spur wheels may be represented by simple circles in a side view and by line shading in an edge view; thus it would answer every practical purpose if such small wheels as in Figures 246 and 247 at D, F, G, K, P, H, I and J, were drawn as shown. The pitch circles, however, are usually drawn in red ink to distinguish them.



In Figure 248 is an example in which part of the gear is shown with teeth in, and the remainder is illustrated by circles.

In Figure 250 is a drawing of part of the feed motions of a Niles Tool Works horizontal boring mill, Figure 251 being an end view of the same, f is a friction disk, and g a friction pinion, g' is a rack, F is a feed-screw, p is a bevil pinion, and q a bevil wheel; i, m, o, are gear wheels, and J a worm operating a worm-pinion and the gears shown.

Figure 249 represents three bevil gears, the upper of which is line shaded, forming an excellent example for the student to copy.



The construction of oval gearing is shown in Figures 252, 253, 254, 255, and 256. The pitch-circle is drawn by the construction for drawing an ellipse that was given with reference to Figure 81, but as that construction is by means of arcs of circles, and therefore not strictly correct, Professor McCord, in an article on elliptical gearing, says, concerning it and the construction of oval gearing generally, as follows:



"But these circular arcs may be rectified and subdivided with great facility and accuracy by a very simple process, which we take from Prof. Rankine's "Machinery and Mill Work," and is illustrated in Figure 252. Let O B be tangent at O to the arc O D, of which C is the centre. Draw the chord D O, bisect it in E, and produce it to A, making O A=O E; with centre A and radius A D describe an arc cutting the tangent in B; then O B will be very nearly equal in length to the arc O D, which, however, should not exceed about 60 degrees; if it be 60 degrees, the error is theoretically about 1/900 of the length of the arc, O B being so much too short; but this error varies with the fourth power of the angle subtended by the arc, so that for 30 degrees it is reduced to 1/16 of that amount, that is, to 1/14400. Conversely, let O B be a tangent of given length; make O F=1/4 O B; then with centre F and radius F B describe an arc cutting the circle O D G (tangent to O B at O) in the point D; then O D will be approximately equal to O B, the error being the same as in the other construction and following the same law.



The extreme simplicity of these two constructions and the facility with which they may be made with ordinary drawing instruments make them exceedingly convenient, and they should be more widely known than they are. Their application to the present problem is shown in Figure 253, which represents a quadrant of an ellipse, the approximate arcs C D, E, E F, F A having been determined by trial and error. In order to space this off, for the positions of the teeth, a tangent is drawn at D, upon which is constructed the rectification of D C, which is D G, and also that of D E in the opposite direction, that is, D H, by the process just explained. Then, drawing the tangent at F, we set off in the same manner F I = F E, and F K = F A, and then measuring H L = I K, we have finally G L, equal to the whole quadrant of the ellipse.



Let it now be required to lay out twenty-four teeth upon this ellipse; that is, six in each quadrant; and for symmetry's sake we will suppose that the centre of one tooth is to be at A, and that of another at C, Figure 253. We, therefore, divide L G into six equal parts at the points 1, 2, 3, etc., which will be the centres of the teeth upon the rectified ellipse. It is practically necessary to make the spaces a little greater than the teeth; but if the greatest attainable exactness in the operation of the wheels is aimed at, it is important to observe that backlash, in elliptical gearing, has an effect quite different from that resulting in the case of circular wheels. When the pitch-curves are circles, they are always in contact; and we may, if we choose, make the tooth only half the breadth of the space, so long as its outline is correct. When the motion of the driver is reversed, the follower will stand still until the backlash is taken up, when the motion will go on with a perfectly constant velocity ratio as before. But in the case of two elliptical wheels, if the follower stand still while the driver moves, which must happen when the motion is reversed if backlash exists, the pitch-curves are thrown out of contact, and, although the continuity of the motion will not be interrupted, the velocity ratio will be affected. If the motion is never to be reversed, the perfect law of the velocity ratio due to the elliptical pitch-curve may be preserved by reducing the thickness of the tooth, not equally on each side, as is done in circular wheels, but wholly on the side not in action. But if the machine must be capable of acting indifferently in both directions, the reduction must be made on both sides of the tooth: evidently the action will be slightly impaired, for which reason the backlash should be reduced to a minimum. Precisely what is the minimum is not so easy to say, as it evidently depends much upon the excellence of the tools and the skill of the workman. In many treatises on constructive mechanism it is variously stated that the backlash should be from one-fifteenth to one-eleventh of the pitch, which would seem to be an ample allowance in reasonably good castings not intended to be finished, and quite excessive if the teeth are to be cut; nor is it very obvious that its amount should depend upon the pitch any more than upon the precession of the equinoxes. On paper, at any rate, we may reduce it to zero, and make the teeth and spaces equal in breadth, as shown in the figure, the teeth being indicated by the double lines. Those upon the portion L H are then laid off upon K I, after which these divisions are transferred to the ellipse by the second of Prof. Rankine's constructions, and we are then ready to draw the teeth.

The outlines of these, as of any other teeth upon pitch-curves which roll together in the same plane, depend upon the general law that they must be such as can be marked out upon the planes of the curves, as they roll by a tracing-point, which is rigidly connected with and carried by a third line, moving in rolling contact with both the pitch-curves. And since under that condition the motion of this third line, relatively to each of the others, is the same as though it rolled along each of them separately while they remained fixed, the process of constructing the generated curves becomes comparatively simple. For the describing line we naturally select a circle, which, in order to fulfil the condition, must be small enough to roll within the pitch ellipse; its diameter is determined by the consideration that if it be equal to A P, the radius of the arc A F, the flanks of the teeth in that region will be radial. We have, therefore, chosen a circle whose diameter, A B, is three-fourths of A P, as shown, so that the teeth, even at the ends of the wheels, will be broader at the base than on the pitch line. This circle ought strictly to roll upon the true elliptical curve; and assuming, as usual, the tracing-point upon the circumference, the generated curves would vary slightly from true epicycloids, and no two of those used in the same quadrant of the ellipse would be exactly alike. Were it possible to divide the ellipse accurately, there would be no difficulty in laying out these curves; but having substituted the circular arcs, we must now roll the generating circle upon these as bases, thus forming true epicycloidal teeth, of which those lying upon the same approximating arc will be exactly alike. Should the junction of two of these arcs fall within the breadth of a tooth, as at D, evidently both the face and the flank on one side of that tooth will be different from those on the other side; should the junction coincide with the edge of a tooth, which is very nearly the case at F, then the face on that side will be the epicycloid belonging to one of the arcs, its flank a hypocycloid belonging to the other; and it is possible that either the face or the flank on one side should be generated by the rolling of the describing circle partly on one arc, partly on the one adjacent, which, upon a large scale, and where the best results are aimed at, may make a sensible change in the form of the curve.

The convenience of the constructions given in Figure 252 is nowhere more apparent than in the drawing of the epicycloids, when, as in the case in hand the base and generating circles may be of incommensurable diameters; for which reason we have, in Figure 254, shown its application in connection with the most rapid and accurate mode yet known of describing those curves. Let C be the centre of the base circle; B, that of the rolling one; A, the point of contact. Divide the semi-circumference of B into six equal parts at 1, 2, 3, etc.; draw the common tangent at A, upon which rectify the arc A 2 by process No. 1; then by process No. 2 set out an equal arc A 2 on the base circle, and stepping it off three times to the right and left, bisect these spaces, thus making subdivisions on the base circle equal in length to those on the rolling one. Take in succession as radii the chords A 1, A 2, A 3, etc., of the describing circle, and with centres 1, 2, 3, etc., on the base circle, strike arcs either externally or internally, as shown respectively on the right and left; the curve tangent to the external arcs is the epicycloid, that tangent to the internal ones the hypocycloid, forming the face and flank of a tooth for the base circle.



In the diagram, Figure 253, we have shown a part of an ellipse whose length is ten inches, and breadth six, the figure being half size. In order to give an idea of the actual appearance of the combination when complete, we show in Figure 255 the pair in gear, on a scale of three inches to the foot. The excessive eccentricity was selected merely for the purpose of illustration. Figure 255 will serve also to call attention to another serious circumstance, which is, that although the ellipses are alike, the wheels are not; nor can they be made so if there be an even number of teeth, for the obvious reason that a tooth upon one wheel must fit into a space on the other; and since in the first wheel, Figure 255, we chose to place a tooth at the extremity of each axis, we must in the second one place there a space instead; because at one time the major axes must coincide; at another, the minor axes, as in Figure 255. If, then, we use even numbers, the distribution, and even the forms of the teeth, are not the same in the two wheels of the pair. But this complication may be avoided by using an odd number of teeth, since, placing a tooth at one extremity of the major axes, a space will come at the other.

It is not, however, always necessary to cut teeth all round these wheels, as will be seen by an examination of Figure 256, C and D being the fixed centres of the two ellipses in contact at P. Now P must be on the line C D, whence, considering the free foci, we see that P B is equal to P C, and P A to P D; and the common tangent at P makes equal angles with C P and P A, as is also with P B and P D; therefore, C D being a straight line, A B is also a straight line and equal to C D. If then the wheels be overhung, that is, fixed on the ends of the shafts outside the bearings, leaving the outer faces free, the moving foci may be connected by a rigid link A B, as shown.



This link will then communicate the same motion that would result from the use of the complete elliptical wheels, and we may therefore dispense with the most of the teeth, retaining only those near the extremities of the major axes, which are necessary in order to assist and control the motion of the link at and near the dead-points. The arc of the pitch-curves through which the teeth must extend will vary with their eccentricity; but in many cases it would not be greater than that which in the approximation may be struck about one centre; so that, in fact, it would not be necessary to go through the process of rectifying and subdividing the quarter of the ellipse at all, as in this case it can make no possible difference whether the spacing adopted for the teeth to be cut would "come out even" or not, if carried around the curve. By this expedient, then, we may save not only the trouble of drawing, but a great deal of labor in making, the teeth round the whole ellipse. We might even omit the intermediate portions of the pitch ellipses themselves; but as they move in rolling contact their retention can do no harm, and in one part of the movement will be beneficial, as they will do part of the work; for if, when turning, as shown by the arrows, we consider the wheel whose axis is D as the driver, it will be noted that its radius of contact, C P, is on the increase; and so long as this is the case the other wheel will be compelled to move by contact of the pitch lines, although the link be omitted. And even if teeth be cut all round the wheels, this link is a comparatively inexpensive and a useful addition to the combination, especially if the eccentricity be considerable. Of course the wheels shown in Figure 255 might also have been made alike, by placing a tooth at one end of the major axis and a space at the other, as above suggested. In regard to the variation in the velocity ratio, it will be seen, by reference to Figure 256, that if D be the axis of the driver, the follower will in the position there shown move faster, the ratio of the angular velocities being P x D/P x B; if the driver turn uniformly, the velocity of the follower will diminish, until at the end of half a revolution, the velocity ratio will be P x B/P x D; in the other half of the revolution these changes will occur in a reverse order. But P D = L B; if then the centres B D are given in position, we know L P, the major axis; and in order to produce any assumed maximum or minimum velocity ratio, we have only to divide L P into segments whose ratio is equal to that assumed value, which will give the foci of the ellipse, whence the minor axis may be found and the curve described. For instance, in Figure 255 the velocity ratio being nine to one at the maximum, the major axis is divided into two parts, of which one is nine times as long as the other; in Figure 256 the ratio is as one to three, so that the major axis being divided into four parts, the distance A C between the foci is equal to two of them, and the distance of either focus from the nearest extremity of the major axis is equal to one, and from the more remote extremity is equal to three of these parts.



CHAPTER XII.

PLOTTING MECHANICAL MOTIONS.



Let it be required to find how much motion an eccentric will give to its rod, the distance from the centre of its bore to the centre of the circumference, which is called the throw, being the distance from A to B in Figure 257. Now as the eccentric is moved around by the shaft, it is evident that the axis of its motion will be the axis A of the shaft. Then from A as a centre, and with radius from A to C, we draw the dotted circle D, and from E to F will be the amount of motion of the rod in the direction of the arrow.

This becomes obvious if we suppose a lead pencil to be placed against the eccentric at E, and suppose the eccentric to make half a revolution, whereupon the pencil will be pushed out to F. If now we measure the distance from E to F, we shall find it is just twice that from A to B. We may find the amount of motion, however, in another way, as by striking the dotted half circle G, showing the path of motion of B, the diameter of this path of motion being the amount of lateral motion given to the rod.



In Figure 258 is a two arm lever fast upon the same axis or shaft, and it is required to find how much a given amount of motion of the long arm will move the short one. Suppose the distance the long arm moves is to A. Then draw the line B from A to the axis of the shaft, and the line C the centre line of the long arm. From the axis of the shaft as a centre, draw the circle D, passing through the eye or centre E of the short arm. Take the radius from F to G, and from E as a centre mark it on D as at H, and H is where E will be when the long arm moves to A. We have here simply decreased the motion in the same proportion as one arm is shorter than the other. The principle involved is to take the motion of both arms at an equal distance from their axis of motion, which is the axis of the shaft S.



In Figure 259 we have a case in which the end of a lever acts directly upon a shoe. Now let it be required to find how much a given motion of the lever will cause the shoe to slide along the line x; the point H is here found precisely as before, and from it as a centre, the dotted circle equal in diameter to the small circle at E is drawn from the perimeter of the dotted circle, a dotted line is carried up and another is carried up from the face of the shoe. The distance K between these dotted lines is the amount of motion of the shoe.

In Figure 260 we have the same conditions as in Figure 259, but the short arm has a roller acting against a larger roller R. The point H is found as before. The amount of motion of R is the distance of K from J; hence we may transfer this distance from the centre of R, producing the point P, from which the new position may be marked by a dotted circle as shown.



In Figure 261 a link is introduced in place of the roller, and it is required to find the amount of motion of rod R. The point H is found as before, and then the length from centre to centre of link L is found, and with this radius and from H as a centre the arc P is drawn, and where P intersects the centre line J of R is the new position for the eye or centre Q of R.



In Figure 262 we have a case of a similar lever actuating a plunger in a vertical line, it being required to find how much a given amount of motion of the long arm will actuate the plunger. Suppose the long arm to move to A, then draw the lines B C and the circle D. Take the radius or distance F, G, and from E mark on D the arc H. Mark the centre line J of the rod. Now take the length from E to I of the link, and from H as a centre mark arc K, and at the intersection of K with J is where the eye I will be when the long arm has moved to A.



In Figure 263 are two levers upon their axles or shafts S and S'; arm A is connected by a link to arm B, and arm C is connected direct to a rod R. It is required to find the position of centre G of the rod eye when D is in position E, and when it is also in position F. Now the points E and F are, of course, on an arc struck from the axis S, and it is obvious that in whatever position the centre H may be it will be somewhere on the arc I, I, which is struck from the centre S'. Now suppose that D moves to E, and if we take the radius D, H, and from E mark it upon the arc I as at V, then H will obviously be the new position of H. To find the new position of G we first strike the arc J, J, because in every position of G it will be somewhere on the arc J, J. To find where that will be when H is at V, take the radius H, G, and from V as a centre mark it on J, J, as at K, which is the position of G when D is at E and H is at V. For the positions when D is at F we repeat the process, taking the radius D, H, and from F marking P, and with the radius H, G, and from P as a centre marking Q; then P is the new position for H, and Q is that for G.



In Figure 264 a lever arm A and cam C are in one piece on a shaft. S is a shoe sliding on the line x, and held against the cam face by the rod R; it is required to find the position of the face of the shoe against the cam when the end of the arm is at D.

Draw line E from D to the axis of the shaft and line F. From the shaft axis as a centre draw circle W; draw line J parallel to x. Take the radius G H, and from K as a centre mark point P on W; draw line Q from the shaft axis through P, and mark point T. From the shaft axis as a centre draw from T an arc, cutting J at V, and V is the point where the face of the shoe and the face of the cam will touch when the arm stands at D.



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.



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.



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 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.



The two cams are bolted to a collar that is secured to the crank-shaft, and are made in halves, as shown in the figures and also in Figures 270 and 271, which represent cams removed from the other mechanism. To enable a certain amount of adjustment of the cams upon the collar, the bolts which hold them to the collar fit closely in the holes in the collar, but the cams are provided with oblong bolt holes as shown, so that the position of either cam, either with relation to the other cam or with relation to the crank-pin, can be adjusted to the extent permitted by the length of the oblong holes.



The crank is assumed in the figures to be on its dead centre nearest to the engine cylinder, and to revolve in the direction of the arrows. The cams are so arranged that their plain unflanged surfaces bolt against the collar.

The method of drawing or marking out a full stroke cam, such as C in Figure 267, is illustrated in Figure 272, in which the dimensions are assumed to be as follows:

Diameter of crank shaft, 7-1/2 inches; travel of cam, 3 inches; width of yoke, 18 inches.



The circumference of the cam is composed of four curved lines, P, P', K 1, and K 2. The position of the centre of the crank shaft in this irregularly curved body is at X. The arcs K 1 and K 2 differ in radius, but are drawn from the same point, X, and hence are concentric with the crank shaft.

The arcs P, P', are of like radius, but are drawn from the opposite points S, S', shown at the intersection of the arcs P, P', with the arc K 1. Thus arcs P, P', are eccentric to the crank shaft.



To draw the cam place one point of the dividers at X, which is the centre of the crank shaft, and draw the circle E equal to width of yoke, 18 inches. Through this centre X, draw the two right lines A and B. On the line B, at the intersection of the curved line E, draw the two vertical lines A 1, A 1. With a radius of 10-1/2 inches, and with one point of the dividers at X, draw the arc K 1. With a radius of 7-1/2 inches, and one point of the dividers at X, draw the arc K 2. With a radius of 18 inches, and one point of the dividers at the intersection of the arc E, with the vertical line A 1 at S, draw the arc P opposite to S, and let it merge or lose itself in the curved line K 2. Draw the other curved line P' from the other point S, and we have a full stroke cam of the dimensions required, and which is represented in Figure 273, removed from the lines used in constructing it.



The engravings from and including Figure 274 illustrate the lines embracing cut-off cams of varying limits of cut-off, but all of like travel and dimensions, which are the same as those given for the full stroke cam in Figure 272.

In drawing cut-off cams, the stroke of the engine plays a part in determining their conformation, and in the examples shown this is assumed to be 4 feet. Figure 274 illustrates the manner of finding essential points in drawing or marking out cut-off cams. With X as a centre, and a radius of 2 feet, draw the circle E 1, showing the path of the crank-pin in making a revolution. This circle has a diameter of 4 feet, equal to the stroke of the engine. Draw the horizontal line B, passing through the centre of circle E 1. Within the limits of circle E 1, subdivide line B into eight equal parts, as at 1, 2, 3, 4, etc. Draw the vertical lines, 1, 2, 3, 4, etc., until they each intersect the circle E 1.



With X as a centre, draw the circle E, having a diameter of 18 inches, equal to the space in the yoke embracing the cam.

From the centre X draw the series of radial lines through the points of intersection of the vertical lines 1, 2, 3, 4, etc., from the circle E 1, and terminating at X. We will now proceed to utilize the scale afforded by Figure 274, in laying off the cut-off cam shown in Figure 276, of half stroke limit.



With X as a centre, draw the circle E, Figure 275, having a diameter of 18 inches. Bisect this circle with the straight lines A and B, which bear the same relation to their enclosing circle that the lines A, B, do to the circle E in Figure 274.



It will be observed, in Figure 274, that the vertical line A is (at the top half) also No. 4, representing 4/8, or half of the stroke. With a radius of 18 inches, and one point of the dividers placed at V, which is at the intersection of the circle E with the horizontal line B in Figure 275, draw the arc P. With the same radius and with one compass point rested at V', draw the arc P'; then two arcs, P and P', intersecting at the point S.

With the same radius and one point of the compasses at S, draw the arc H H. The arcs K 1 and K 2 are drawn from the centre X, with a radius of 10-1/2 for K 1 and 7-1/2 inches for K 2, and only serve in a half stroke cam to intersect the curved lines already drawn, as shown in Figure 275. In practice, the sharp corner at S would be objectionable, owing to rapid wear at this point; and hence a modification of the dimensions for this half stroke cam would be required to obtain a larger wearing surface at the point S, but the cam of this limit (1/2 stroke) is correctly drawn by the process described with reference to Figure 275, the outline of the cam so constructed being shown in Figure 276.



In Figure 278 is shown a cam designed to cut off the steam at five-eighths of the piston stroke, the construction lines being given in Figure 277, for which draw circle E and straight lines A and B, as in the preceding example. By reference to Figure 274 it will be observed that the diagonal line drawn through circle E at 5 is drawn from the straight line marked 5, which intersects circle E 1, and as this straight line 5 represents five-eighths of the stroke laid off on line B, it determines the limit of cut-off on the five-eighths cam in Figure 277.



Turning then to Figure 274, take on circle E the radius from radial line 4 to radial line 5, and mark it in Figure 277 from the vertical line producing V'.

Now, with a radius of 18 inches, and one point of the dividers fixed at point V, forming the intersection of the circle E with the horizontal line B, draw the arc P. With the same radius, and one point of the dividers fixed at point V', draw the opposite arc P'. With a radius of 10-1/2 inches from the centre X, draw the arc K 1, intersecting lines P P', at S S. With a radius of 7-1/2 inches, draw the curved line K 2, opposite to curved line K 1. Now, with a radius of 18 inches, and one point of the dividers fixed alternately at S S, draw the arcs H, H, from their intersection with the circle E, until they merge into the curved line K 2. These curved lines embrace a cut-off cam of five-eighths limit, shown complete in Figure 278.



From the instructions already given it should be easy to understand that the three-fourths and seven-eighths cams, shown in Figures 279, 280, 281 and 282, are drawn by taking the points of their cut-off from the same scale shown in Figure 274, at the diagonal points 6 and 7, intersecting circle E in that figure; and cut-off cams of intermediate limit of cut-off can be drawn by further subdividing the stroke line B, in Figure 274, into the required limits.



Cut-off cams of any limit are necessarily imperfect in their operations as to uniformity of cut-off from opposite ends of the slides, not from any defect in the rule for laying them off, but from the well-known fact of the crank pin travelling a greater distance, while driven by the piston from the centre of the cylinder, through its curved path from the cylinder, over its centre, and back to the centre of the cylinder, than in accomplishing the remaining distance of its path in making a complete revolution; and, although the subdivisions of eighths of the stroke line B, in Figure 274, does not truly represent a like division of the piston stroke, owing to deviation, caused by inclination of the connecting rod in traversing from the centres to half stroke, still it will be found that laying off a cut-off cam by this rule is more nearly correct than if the divisions on stroke line B were made to correspond exactly with a subdivision of piston stroke into eighths.



The cut-off in cams laid off by the rules herein described is greater in travelling from one side of the slides than in travelling from the opposite end, one cut-off being more than the actual cut-off of piston stroke, and the other less; and in practical use, owing to play or lost motion in the connections from cam to valve, the actual cut-off is less than the theoretical; hence cut-off cams are usually laid off to compensate for lost motion; that is, laid off with more limit; for instance, a five-eighths cam would be laid off to cut-off at eleven-sixteenths instead of five-eighths.



Figure 283 represents the motion a crank, C, imparts to a connecting rod, represented by the thick line R, whose end, B, is supposed to be guided to move in a straight line. The circle H represents the path of the crank-pin, and dots 1, 2, 3, etc., are 24 different crank-pin positions equidistant on the circle of crank-pin revolution. Suppose the crank-pin to have moved to position 1, and with the compasses set to the length of the rod R, we set one point on the centre of position 1, and mark on the line of motion m the line a, which will be the position rod end B will have moved to. Suppose next that the crank-pin has moved into position 2, and with the compass point on the centre of 2 we mark line 2, showing that while the crank-pin moved from 1 to 2, the rod end moved from a to b; by continuing this process we are enabled to discern the motion for the whole of the stroke. The backward stroke will be the same, for corresponding crank-pin positions, for both strokes; thus, when the rod end is at 7 the crank-pin may be at 7 or at 17. This fact enables us to find the positions for the positions later than 6, on the other side of the circle, as at 17, 16, 15, etc., which keeps the engraving clear.



In Figure 284 a pinion, P, drives a gear-wheel, D, on which there is a pin driving the sliding die A in the link L, which is pivoted at C, and connected at its upper end to a rod, R, which is connected to a bolt, B, fast to a slide, S. It is required to find the motion of S, it moving in a straight line, dotted circle H' representing the path of the pin in the sliding die A, arc H representing the line of motion of the upper end of link L, and lines N, O, its centre line at the extreme ends of its vibrating motion. In Figure 285 the letters of reference refer to the same parts as those in Figure 284. We divide the circle H' of pin motion into 24 equidistant parts marked by dots, and through these we draw lines radiating from centre, C, and cutting arc H, obtaining on the arc H the various positions for end Z of rod R, these positions being marked respectively 1, 2, 3, 4, etc., up to 24. With a pair of compasses set to the length of rod R from 1 on H, as a centre, we mark on the line of motion of the slide, line a, which shows where the other end of rod R will be (or in other words, it shows the position of bolt B in Figure 284), when the centre of A, Figure 284, is in position 1, Figure 285.



From 2 on arc H, we mark with the compasses line b on line M, showing that while the pin moved from 1 to 2, the rod R would move slide S, Figure 284, from a to b, in Figure 285. From 3 we mark c, and so on, all these marks being above the horizontal line M, representing the line of motion, and being for the forward stroke. For the backward stroke we draw the dotted line from position 17 up to arc H, and with the compasses at 17 mark a line beneath the line M of motion, pursuing the same course for all the other pin motions, as 18, 19, etc., until the pin arrives again at position 24, and the link at O, and has made a full revolution, and we shall have the motion of the forward stroke above and that of the backward one below the line of motion of the slide, and may compare the two.



Figures 286 and 287 represent the Whitworth quick return motion that is employed in many machines. F represents a frame supporting a fixed journal, B, on which revolves a gear-wheel, G, operated by a pinion, P. At A is an arm having journal bearing in B at C. This arm is driven by a pin, D, fast in the gear, G; hence as the gear revolves, pin D moves A around on C as a centre of motion. A is provided with a slot carrying a pin, X, on which is pivoted the rod, R. The motion of end N of the rod R being in a straight line, M, it is required to find the positions of N during twenty-four periods in one revolution of G. In Figure 288 let H' represent the path of motion of the driving pin D, about the centre of B, and H the path of motion of X about the centre C; these two centres corresponding to the centres of B and C respectively, in Figure 287. Let the line M correspond to the line of motion M in Figure 286. Now since it is the pin D, Figure 287, that drives, and since its speed of revolution is uniform, we divide its circle of motion H' into twenty-four equal divisions, and by drawing lines radiating from centre C, and passing through the lines of division on H' we get on circle H twenty-four positions for the pin X in Figure 286. Then setting the compasses to the length of the rod (R, Figure 286), we mark from position 1 on circle H as a centre line, a; from position 2 on H we mark line b, and so on for the whole twenty-four positions on circle H, obtaining from a to n for the forward, and from n to y for the motion during the backward stroke. Suppose now that the mechanism remaining precisely the same as before, the line M of motion be in a line with the centres C, B, instead of at a right angle to it, as it is in Figure 286, and the motion under this new condition will be as in Figure 289; the process for finding the amount of motion along M from the motion around H being precisely as before.



In Figure 290 is shown a cutter-head for a wood moulding machine, and it is required to find what shape the cutting edge of the cutter must be to form a moulding such as is shown in the end view of the moulding in the figure. Now the line A A being at a right angle to the line of motion of the moulding as it is passed beneath the revolving cutter, or, what is the same thing, at a right angle to the face of the table on which the moulding is moved, it is obvious that the highest point C of the moulding will be cut to shape by the point C of the cutter; and that since the line of motion of the end of the cutter is the arc D, the lowest part of the cutter action upon the moulding will be at point E. It will also be obvious that as the cutter edge passes, at each point, its length across the line A A, it forms the moulding to shape, while all the cutting action that occurs on either side of that line is serving simply to remove material. All that we have to consider, therefore, is the action on line A A.

It may be observed also that the highest point C of the cutter edge must not be less than 1/4 inch from the corner of the cutter head, which gives room for the nut N (that holds the cutter to the head) to pass over the top of the moulding in a 2-1/2 inch head. In proportion as the heads are made larger, however, less clearance is necessary for the nut, as is shown in Figure 291, the cutter edge extending to C, and therefore nearly up to the corner of the head. Its path of motion at C is shown by dotted arc B, which it will be observed amply clears the nut N. In practice, however, point C is not in any size of cutter-head placed nearer than 1/4 inch from corner X of the cutter-head.

To find the length of the cutter edge necessary to produce a given depth of moulding, we may draw a circle i, Figure 292, equal in diameter to the size of the cutter head to be used, and line A A. The highest point of cutting edge being at e, and the lowest at g, then circles d and f represent the line of motion of these two points; and if we mark the cutter in, the necessary length of cutting edge on the cutter is obviously from a to b.



Now the necessary depth of cutter edge being found for any given moulding, or part of a moulding, the curves for the edge may be found as follows: Suppose the moulding is to be half round, as in the end view in Figure 290. The width of the cutter must of course equal the width of the moulding, and the length or depth of cutting edge required may be found from the construction shown in Figure 292; hence all that remains is to find the curve for the cutting edge. In Figure 293, let A A represent the centre of the cutter width, its sides being F F', and its end B B. From centre C draw circle D, the upper half of which will serve to represent the moulding. Mark on A the length or depth the cutting edge requires to be, ascertaining the same from the construction shown in Figure 292, and mark it as from C to K'. Then draw line E E, passing through point K. Draw line G, standing at the same angle to A A as the face h b, Figure 292, of the cutter does to the line A A, and draw line H H, parallel to G. From any point on G, as at I, with radius J, draw a quarter of a circle, as K. Mark off this quarter circle into equal points of division, as by 1, 2, 3, etc., and from these points of division draw lines, as a, b, c, etc.; and from these lines draw horizontal lines d, e, f, etc. Now divide the lower half of circle D into twice as many equal divisions as quarter circle K is divided into, and from these points of division draw perpendiculars g, h, i, etc. And where these perpendiculars cross the horizontal lines, as d, will be points through which the curve may be drawn, three of such points being marked by dots at p, q, r. If the student will, after having drawn the curve by this construction, draw it by the construction that was explained in connection with Figure 79, he will find the two methods give so nearly identical curves, that the latter and more simple method may be used without sensible error.



When the curves of the moulding are not arcs of circles they may be marked as follows:

Take the drawing of the moulding and divide each member or step of it by equidistant lines, as a, b, c, d, e, f, g, in Figure 294; above the moulding draw lines representing the cutter, and having found the depth of cutting edge for each member by the construction shown in Figure 292, finding a separate line, a b, for each member of the moulding, transfer the depths so found to the face of the cutter; divide the depth of each member of the cutter into as many equal divisions as the corresponding member of the moulding is divided into, as by lines h, i, j, k, l, m, n. Then draw vertical lines, as o, p, q, r, etc.; and where these lines meet the respective lines h, i, j, etc., are points in the curve, such points being marked on the cutter by dots.



CHAPTER XIII.

EXAMPLES IN LINE-SHADING AND DRAWINGS FOR LINE-SHADED ENGRAVINGS.

Although in workshop drawings, line-shading is rarely employed, yet where a design rather than the particular details of construction is to be shown, line-shading is a valuable accessory. Figure 295, for example, is intended to show an arrangement of idle pulleys to guide belts from one pulley to another; the principle being that so long as the belt passes to a pulley moving in line with the line of rotation of the pulley, the belt will run correctly, although it may leave the pulley at considerable angle. When a belt envelops two pulleys that are at a right angle to each other, two guide pulleys are needed in order that the belt may, in passing to each pulley, move in the same plane as the pulley rotates in, and the belt is in this case given what is termed a quarter twist.

It will be observed that by the line-shading even the twist of the belt is much more clearly shown than it would be if left unshaded.

An excellent example of shading is given in Figure 296, which is extracted from the American Machinist, and represents a cutting tool for a planing machine. The figure is from a wood engraving, but the effect may be produced by lines, the black parts being considered as simply broad black lines.



The drawings from which engravings are made are drawn to conform to the process by which the engraving is to be produced. Drawings that are shaded by plain lines may be engraved by three methods. First, the drawing may be photo-engraved, in which process the drawing is photographed on the metal, and every line appears in the engraving precisely as it appears in the drawing.



For this kind of engraving the drawing may be made of any convenient size that is larger than the size of engraving to be produced, the reduction of size being produced in the photographing process. Drawings for photo-engraving require to have the lines jet black, and it is to be remembered that if red centrelines are marked on the drawing, they will be produced as ordinary black lines in the engraving.

The shading on a drawing to be photo-engraved must be produced by lines, and not by tints, for tints, whether of black or of colors, will not photo-engrave properly.

It is generally preferred to make the drawing for a photo-engraving larger than the engraving that is to be made from it, a good proportion being to make the drawing twice the length the engraving is to be. This serves to reduce the magnitude of any roughness in the lines of the drawing, and, therefore, to make the engraving better than the drawing.

The thickness of the lines in the drawing should be made to suit the amount of reduction to be made, because the lines are reduced in thickness in the same proportion as the engraving is reduced from the drawing. Thus the lines on an engraving reduced to one-half the dimensions of the drawing would be one-half as thick as the lines on the drawing.

Drawings for photo-engraving should be made on smooth-faced paper; as, for example, on Bristol board; and to make the lines clean and clear, the drawing instruments should be in the best of condition, and the paper or Bristol board quite dry. The India rubber should be used as little as possible on drawings to be photo-engraved, because, if used before the lines are inked in, it roughens the surface of the paper, and the inking lines will be less smooth and even at their edges; and for this reason it is better not to rub out any lines until all the lines have been inked in. If used to excess after the lines have been inked in it serves to reduce the blackness of the lines, and may so pale them that they will not properly photo-engrave.

To make a drawing for an engraver in wood it would be drawn directly on the face of the box-wood block, on which it is to be engraved. The surface of the block is first whitened by a white water color, as Chinese white. If the drawing that is to be used as a copy is on sufficiently thin paper, its outline may be traced over by pencil lines, and the copy may then be laid face down on the wood block and its edges held to the block by wax, the pencilled lines being face to the block. The outline may then be again traced over with a pencil or pointed instrument, causing the imprint of the lead pencil lines to be left on the whitened surface of the block. If the copy is on paper too thick to be thus employed, a tracing may be made and used as above; it being borne in mind that the tracing must be laid with the pencilled lines on the block, because what is the right hand of the drawing on the block is the left hand in the print it gives. The shading on wood blocks is given by tints of India ink aided by pencilled lines, or of course pencilled lines only may for less artistic work be used. Another method is to photograph the drawing direct upon the surface of the wood block; it is unnecessary, however, to enter into this part of the subject.

The third method of producing an engraving from a drawing is by means of what is known as the wax process. Drawings for this process should be made on thin paper, for the following reasons: The process consists, briefly stated, in coating a copper plate with a layer of wax about 1/32 inch deep, and in drawing upon the wax the lines to compose the engraving, which lines are produced by means of tools that remove the wax down to the surface of the copper.

The plate and wax are then placed in a battery and a deposit of copper fills in the lines and surface of the wax, thus forming the engraving. Now if the drawing is made on thin paper, the engraver coats the surface of the drawing with a dry red pigment, and with a pointed instrument traces over the lines of the drawing, which causes them to leave a red imprint on the surface of the wax, and after the drawing is removed the engraver cuts these imprinted lines in the wax. If the drawing is on thick paper, this method of transferring the drawing to the wax cannot be used, and the engraver may take a tracing from the drawing and transfer from the tracing to the wax. It is obvious, also, that for wax engravings the drawing should be made of the same size that the engraving is required to be, or otherwise the tracing process described cannot be used. Figure 297 represents an engraving made by the wax process from a print from a wood engraving, and it is obvious that since all the lines drawn on the wax sink down to the surface of the copper plate, the shading is virtually composed of lines, the black surfaces being where the lines have been sufficiently close together and broad to remove all the wax enclosed within those surfaces.



The wax process is, however, more suitable for engravings in plain outline only, and is especially excellent when the parts are small and the lines fall close together; as, for example, in Figures 298 and 299, which are engravings of a boiler drilling machine, and were produced for the American Machinist by tracing over a wood engraving from London, "Engineering" in the manner already described. The fineness and cleanness of the lines in the wax process is here well illustrated, the disposition of the parts being easily seen from the engraving, and easily followed in connection with the following description:

The machine consists of two horizontal bed-plates A 1 and A 2, made with $V$ slides on top, and placed at right angles to each other. Upon each of the bed-plates is fitted a vertical arm B 1 and B 2, each of which carries two saddles, C 1 and C 2, these being each adjustable vertically on its respective arm by means of rack and pinion and hand wheels D 1 and D 2. The saddles are balanced so that the least possible exertion is sufficient to adjust them. The vertical arms, B 1 and B 2, are cast each with a round foot by which the arms are attached to the square boxes E 1 and E 2, which are fitted to the $V$ slides on the horizontal beds A 1 and A 2, and are adjustable thereon by means of screw and ratchet motion F 1 and F 2. Each of the square boxes has cast on it a small arm G 1 and G 2, carrying studs upon which run pinions gearing into the circular racks at the foot of the vertical arms. The square boxes have each a circular groove turned in the top to receive the bolts by which the vertical arms are connected to them, and thus the vertical arms, and with them the drill spindles N 1 and N 2, are adjustable radially with the boiler—the adjustment being effected by means of the pinions and circular racks. The pinions are arranged so that they can be worked with the same screw key that is used for the bolts in the circular grooves.

The shell to be drilled is placed upon the circular table H, which is carried by suitable framework adjustable by means of screw on a $V$ slide I, placed at an angle of 45 deg. with the horizontal bed-plates. By this arrangement, when the table is moved along I, it will approach to or recede from all the drills equally. J 1 and J 2 are girders forming additional bearings for the framework of the table. The bed-plates and slides for the table are bolted and braced together, making the whole machine very firm and rigid. Power is applied to the machine through the cones K 1 and K 2, working the horizontal and vertical shafts L 1 and L 2, etc. On the vertical shafts are fitted coarse pitch worms sliding on feather keys, and carried with the saddles C 1 and C 2, etc. The worms gearing with the worm wheels M 1 and M 2 are fitted on the sleeves of the steel spindles N 1 and N 2. The spindles are fitted with self-acting motions O 1 and O 2, which are easily thrown in and out of gear.

The machine is also used for turning the edge of the flanges which some makers prefer to have on the end plates of marine boilers. The plates are very readily fixed to the circular table H, and the edge of the flange trued up much quicker than by the ordinary means of chipping. When the machine is used for this purpose, the cross beam P, which is removable, is fastened to the two upright brackets R 1 and R 2. The cross beam is cast with $V$ slides at one side for a little more than half its length from one end, and on the opposite side for the same length, but from the opposite end. The $V$ slides are each fitted with a tool box S 1 and S 2, having a screw adjustment for setting the tool to the depth of cut, and adjustable on the $V$ slides of the cross beam to the diameter of the plate to be turned. This arrangement of the machine is also used for cutting out the furnace mouths in the boiler ends. The plate is fastened to the circular table, the centre of the hole to be cut out being placed over the centre of table; one or both of the tool boxes may be used. There is sufficient space between the upright brackets R 1 and R 2, to allow that section of a boiler end which contains the furnace mouths to revolve while the holes are being cut out; the plate belonging to the end of a boiler of the largest diameter that the machine will take in for drilling. The holes cut out will be from 2 feet 3 inches in diameter and upwards. Power for using the turntable is applied through the cone T. The bevel wheels, worms, worm wheels, and pinions for driving the tables are of cast steel, which is necessary for the rough work of turning the flanges.



As to the practical results of using the machine, the drills are driven at a speed of 340 feet per minute at the cutting edges. A jet of soapsuds plays on each drill from an orifice 1/32 in. in diameter, and at a pressure of 60 lbs. per square inch. A joint composed of two 1-inch plates, and having holes 1 and one-eighth in. in diameter, can be drilled in about 2-1/2 minutes, and allowing about half a minute for adjusting the drill, each drill will do about 20 holes per hour. The machine is designed to stand any amount of work that the drills will bear. The time required for putting on the end of a boiler and turning the flange thereon (say 14 feet diameter) is about 2-1/2 hours; much, however, depends on the state of the flanges, as sometimes they are very rough, while at others very little is necessary to true them up. The time required for putting on the plate containing the furnace mouths and cutting out three holes 2 feet 6 in. in diameter, the plate being 1 and one-eighth in. thick, is three hours. Of course, if several boilers of one size are being made at the same time, the holes in two or more of these plates can be cut out at once. The machine is of such design that it can be placed with one of the horizontal bed-plates (say A 1), parallel and close up to a wall of the boiler shop; and when the turning apparatus is being used, the vertical arm B 2 can be swiveled half way round on its square box E 2, and used for drilling and tapping the stay holes in marine boiler ends after they are put together; of course sufficient room must be left between bed-plate A 2, and the wall of boiler shop parallel with it, to allow for reception of the boiler to be operated upon.

It would obviously be quite difficult to draw such drawings as in Figures 298 and 299 on thin paper, so as to enable the drawing to be traced on the wax direct by the process before described, unless indeed the draftsman had considerable experience in fine work; hence, it is not uncommon to make the drawing large, and on ordinary drawing paper. The engraver then has the drawing photographed on the surface of the wax, and works to the photograph. The letters of reference in wax engravings are put in by impressing type in the wax, and in this connection it may be remarked that the letters I and O should not be used on drawings to be engraved by the wax process, unless they are situated outside the outlines of the drawing, because the I looks so much like part of a dotted line that it is often indistinguishable therefrom, while the O looks like a circle or an ellipse.



CHAPTER XIV.

SHADING AND COLORING DRAWINGS.

The shading or coloring of drawings by tints is more employed in large drawings than in small ones, and in Europe than in the United States; while on the other hand tinting by means of line-shading is more employed in the United States than in Europe, and more on small drawings than on large ones.

Many draftsmen adopt the plan of coloring the journals of shafts, etc., with a light tint, giving them the deepest tint at the circumference to give them a cylindrical appearance. This makes the drawing much clearer and takes but little time to do, and is especially advantageous where the parts are small or on a small scale, so that the lines are comparatively close together.

For simple shading purposes black tints of various degrees of darkness may be employed, but it is usual to tint brass work with yellow. Cast iron with India ink, wrought iron with Prussian blue, steel with as light purple tint produced by mixing India ink, Prussian blue and a tinge of crimson lake. Copper is tinted red. On plane surfaces an even tint of color is laid, but if the surfaces are cylindrical they are usually colored deeper at and near the circumference, and are tinted over the colors with light tints of India ink to show their cylindrical form.

If a drawing is to be colored or shaded with India ink the paper should be glued all around its edges to the drawing board, and then dampened evenly all over with a sponge, which will cause the paper to shrink and lay close to the surface of the drawing board. If, in applying a color or a tint, the color dries before the whole surface is colored, the color will not be of an equal shade; hence it is necessary before applying the color to dampen the surface, if it is a large one, so that the color at one part shall not get dry before there has been time to go over the whole surface; a more even depth of color is attained by the application of several coats of a light tint, than with one coat, giving the full depth of color. But if the paper is not allowed to dry sufficiently between the coats, or if it has been made too wet previous to the application of the colors, it will run in places, leaving other hollows into which the color will flow, making darker-colored spots. To avoid this the paper may be dried somewhat by the application of clean blotting paper.

To maintain an even shade of color, it is necessary to slightly stir up the color each time the brush is dipped into the color saucer or palette, especially when the coloring is composed of mixed colors, because the coloring matter is apt to separate from the water and sink to the bottom.

So, also, in mixing colors it is best to apply the end of the color to the surface of the palette and not to apply the brush direct to the cake of color, because the color is more completely mixed by contact with the palette than it can be by the brush, which may retain a speck of color that will, unless washed out, make a streak upon the drawing.

To graduate the depth of tint for a cylindrical surface, it is best to mix several, as, say three depths or degrees of tint, and to first use the darkest, applying it in the direction in which the piece is to be shaded darkest. The width this dark application should be is obviously determined by the diameter of the piece. The next operation is to lighten or draw the part, line or streak thus dark colored, causing it to get paler and paler as it approaches the axial line of the piece or cylinder. This lightening is accomplished as follows: The dark streak is applied along such a length of the piece that it will not dry before there has been time to draw it out or lighten it on the side towards the axis. A separate brush may then be wetted and drawn along the edge of the dark streak in short strokes, causing the color to run outwards and become lighter as it approaches the axis. It will be found that during this process the brush will occasionally require washing in water, because from continuous contact with the dark streak the tint it contains will darken. When the first coat has been laid and spread or drawn out from end to end of the piece, the process may be repeated two or three times, the most even results being obtained by making the first dark streak not too dark, and going over the drawing several times, but allowing the paper to get very nearly dry between each coat. In small cylindrical bodies, as, say 1/4 inch in diameter, the darkest line of shadow may be located at the lines representing the diameter of the piece, but in pieces of larger diameter the darkest line may be located at a short distance from the line that denotes the diameter or perimeter on the shadow or right-hand side of the piece, as is shown in many of the engravings that follow. It is obvious that if a drawing is to have dimensions marked on it, the coloring or tinting should not be deep enough to make it difficult to see the dimension figures.

The size of the brush to be used depends, of course, upon the size of the piece to be shaded or colored, and it is best to keep one brush for the dark tint and to never let the brush dry with the tint in it, as this makes it harsh. In a good brush the hairs are fine, lie close together when moistened, are smooth and yet sufficiently stiff or elastic to bend back slightly when the pressure is removed. If, when under pressure and nearly dry, the hairs will separate or the brush has no elasticity in it, good results cannot be obtained. All brushes should be well dried after use.

The light in shading is supposed to come in at the left-hand corner of the drawing, as was explained with reference to the shade line.

Excellent examples to copy and shade with the brush are given as follows:

Figure 300 represents a Medart pulley, constructed by the Hartford Steam Engineering Company; the arms and hub are cast in one piece, and the rim is a wrought iron band riveted to the arms, whose ends are turned or ground true with the hub bore. The figure is obviously a wood engraving, but it presents the varying degrees of shade or shadow with sufficient accuracy to form a good example to copy and brush shade with India ink. Figure 301 represents a similar pulley with a double set of arms, forming an excellent example in perspective drawing, as well as for brush-shading.



In brush-shading as with line-shading, the difficulties increase with an increase in the size of the piece, and the learner will find that after he has succeeded tolerably well in shading these small pulleys, it will be quite difficult, but excellent practice to shade the large pulley in Figure 302.

One of the principal considerations is to not let the color dry at the edges in one part while continuing the shading in another part of the same surface, hence it is best to begin at the edge or outline of the drawing and carry the work forward as quickly as possible, occasionally slightly wetting with water edges that require to be left while the shading is proceeding in another direction.



When it is required to show by the shading that the surfaces are highly polished, the lighter parts of the shading are made to contain what may be termed splashes of lighter and darker shadow, as in Figure 303, which represents an oil cup, having a brass casing enclosing a glass cylinder, which appears through the openings in the brass shell.

Figure 304 represents an iron planing machine whose line-shading is so evenly effected that it affords an excellent example of shading. Its parts are similar to those shown in the iron planer in Figure 297, save that it carries two sliding heads, so as to enable the use, simultaneously, of two cutting tools.



A superior example in shading is shown in Figures 305 and 306, which represent a plan and a sectional view of the steam-cylinder of a Blake's patent direct-acting steam-pump. The construction of the parts is as follows: A is the steam-piston, H 1 and H are the cylinder steam-passages; M is the cylinder exhaust port.



The main valve, whose movement alternately opens the ports for the admission of steam to, and the escape of steam from, the main cylinder, is divided into two parts, one of which, C, slides upon a seat on the main cylinder, and at the same time affords a seat for the other part, D, which slides upon the upper face of C. As shown in the engravings, D is at the left-hand end of its stroke, and C at the opposite or right-hand end of its stroke. Steam from the steam-chest, J, is therefore entering the right-hand end of the main cylinder through the ports E and H, and the exhaust is escaping through the ports H 1, E 1, K and M, which causes the main piston A to move from right to left. When this piston has nearly reached the left-hand end of its cylinder, the tappet arm, T, attached to the piston-rod, comes in contact with, and moves the valve rod collar O 1 and valve rod P, and thus causes C, together with the supplemental valves R and S S 1, which form, with C, one casting, to be moved from right to left. This movement causes steam to be admitted to the left-hand end of the supplemental cylinder, whereby its piston B will be forced towards the right, carrying D to the opposite or right-hand end of its stroke; for the movement of S closes N (the steam-port leading to the right-hand end), and the movement of S 1 opens N 1 (the steam-port leading to the opposite or left-hand end), at the same time the movement of V opens the right-hand end of this cylinder to the exhaust, through the exhaust ports X and Z. The parts C and D now have positions opposite to those shown in the engravings, and steam is therefore entering the main cylinder through the ports E 1 and H 1, and escaping through the ports H, E, K and M, which causes the main piston A to move in the opposite direction, or from left to right, and operations similar to those already described will follow, when the piston approaches the right-hand end of its cylinder. By this simple arrangement the pump is rendered positive in its action; that is, it will instantly start and continue working the moment steam is admitted to the steam-chest, while at the same time the piston is enabled to move as slowly as the nature of the duty may require. It will be noted that in Figure 305, the ports of C are shown through D, whose location is marked by dark shading. This obviously is not correct, because D being above C should be shaded lighter than C, and again the ports E 1 and K could not show dark through the port D. They might, of course, be shown by dotted outlines, but they would not appear to such advantage, and on this account it is permissible where artistic effect is sought, the object being to subserve the shading to making the mechanism and its operation clearly and readily understood.



Figure 307 affords another excellent example for shading. It consists of an independent condenser, whose steam-cylinder and valve mechanism is the same as that described with reference to Figures 305 and 306.



CHAPTER XV.

EXAMPLES IN ENGINE WORK.

In the figures from 308 to 328 inclusive are given three examples in engine work, all these drawings being from The American Machinist. Figures 308 to 314 represent drawings of an automatic high speed engine designed and made by Professor John E. and William A. Sweet, of Syracuse, New York. Figure 308 is a side and 309 an end view of the engine. Upon a bed-plate is bolted two straight frames, between which, at their upper ends, the cylinder is secured by bolts. The guides for the cross-head are bolted to the frame, which enables them to be readily removed to be replaned when necessary. The hand wheel and rod to the right are to operate the stop-cock for turning on and off the steam to the steam-chest.

The objects of the design are as follows: Figure 310 is a vertical section of the cylinder through the valve face, also showing the valve in section, and it will be seen that the lower steam passage enters the cylinder its full depth below the inside bottom, and that the whole inside bottom surface of the cylinder slopes or inclines towards the entrance of this passage. The object of this is to overcome the difficulty experienced from the accumulation of water in the cylinder, which, in the vertical engine, is usually a source of considerable annoyance and frequently the cause of accident.

Any water that may be present in the bottom finds its way by gravity to the port steam entrance, and is forced out by and with the exhaust steam at or before the commencement of the return stroke.

To assist in the escape of water from the top of the cylinder, the piston is made quite crowning at that end, the effect of which is to collect the water in a narrow band, instead of spreading it over a large surface. This materially assists in its escape, and at the same time presents a large surface for the distribution of any water that may not find its way out in advance of the piston.

The piston is a single casting unusually long and light, and is packed with four spring rings of 3/8 inch square brass wire.

The valve is a simple rectangular plate, working between the valve face and a cover plate, the cover plate being held in its proper position, relative to the back of the valve, by steam pressure against its outer surface, and by resting against loose distance pieces between its inner surface and the valve seat. This construction admits of the valve leaving the seat, if necessary, to relieve the cylinder from water, as in the instance of priming, and also, by the reduction of these pieces, admits of ready adjustment to contact, should it become necessary.



The cover plate is provided with recesses on its inner surface which exactly correspond with the ports in the valve face, and the corresponding ports and recesses are kept in communication with each other by means of relief passages in the valve. From this it will be seen that the valve is subjected to equal and balanced pressure on each of its sides, and hence, is in equilibrium.

The valve is operated through the valve motion, shown in Figure 311, the eccentric rod of which hooks on a slightly tapered block that turns on the pin of the rock arm, like an ordinary journal box.

The expansion, or cut-off, is automatically regulated by the operation of the governor in swinging the slotted eccentric in a manner substantially equivalent to moving it across the shaft, but is however favorably modified by the arrangement of the rock arm, which, in combination with the other motions, neutralizes the unfavorable operation of the usual shifting eccentric, and which, in connection with the large double port opening, provides for a good use of steam from 0 to 3/4 stroke.

The governor shown in Figure 312 is of the disc and single ball type, the centrifugal force of the ball being counteracted by a powerful spring. Friction is reduced to a minimum in the governor connection, by introducing steel rollers and hardened steel plates in such a manner as to provide rolling instead of sliding motion.

In order that a governor shall correctly perform its functions, it is unquestionably necessary that it have power largely in excess of the work required of it, and also that the friction shall represent a very low percentage of that power. In respect to this, especial means have been employed to reduce the friction; the valve being balanced, requires but little power to move it, while the governor ball being made heavy for the purpose of counterbalancing the weight of the eccentric and strap, its centrifugal force when the engine is at full speed is enormous, the spring to counteract it having to sustain from two to three thousand pounds. Under these circumstances, as might be expected, the regulation is remarkably good. This is a very important consideration in an engine working under the conditions of a roll-train engine.



Figure 313 represents a section of the pillow block box, crank-pin and wheel, together with the main journal. It will be seen that the end of the box next the crank wheel has a circular groove around its outside, and that a corresponding groove in the crank wheel projects over this groove. From this latter groove an oil hole of liberal size extends, as shown, to the surface of the crank-pin. Any oil placed at the upper part of the groove on the box finds its way by gravity into the groove in the crank wheel, and is carried by centrifugal force to the outside surface of the crank-pin; so that whatever other means of lubrication may be employed, this one will always be positive in its action. This cut also shows the manner in which the box overlaps the main journal and forms the oil reservoir.



Another feature in the construction of this box is the means by which it is made to adjust itself in line with the shaft. It will be observed that it rests on the bottom of the jaws of the frame on two inclined surfaces, which form equal angles with the axis of the shaft when in its normal position, and that by moving longitudinally in either direction, as may be necessary, the box will accommodate itself to a change in the alignment of the shaft. In order that it may be free to move for this purpose it is not fitted with the usual fore and aft flanges. By this means any slight derangement, as in either the outboard or inboard bearing wearing down the fastest, is taken care of, the movement of the box on the inclined surfaces being for this purpose equivalent to the operation of a ball and socket bearing.

Figure 314 gives a side and an edge view of the connecting rod, the rod being in section in the edge view, and the brasses in section lined in both views.

The cross-head pin, it will be observed, is tapered, and is drawn home in the cross-head by a bolt; the sides of the pin are flattened somewhat where the journal is, so that the pin may not wear oval, as it is apt to do, because of the pull and thrust strain of the rod brasses falling mainly upon the top and bottom of the journal, where the most wear therefore takes place. The brasses at the crossed end are set up by a wedge adjustable by means of the screw bolts shown. The cross-head wrist pin being removable from the cross-head enables the upper end of the rod to have a solid end, since it can be passed into place in the crossed and the wrist pin inserted through the two. The lower ends of the connecting-rod and the crank-pin possess a peculiar feature, inasmuch as by enlarging the diameter of the crank-pin, the ends of the brasses overlap, to a certain extent, the ends of the journal, thus holding the oil and affording increased lubrication. The segments that partly envelop the cross-head pin and crank-pin, and are section lined in two directions, producing crossing section lines, or small squares, show that the brasses are lined with babbitt metal, which is represented by this kind of cross-hatching. These drawings are sufficiently open and clear to form very good examples to copy and to trace on tracing paper.



Figures 315, 316 and 317 represent, in place upon its setting, a 200 horse-power horizontal steam-boiler for a stationary engine, and are the design of William H. Hoffman. The cross-sectional view of the boiler shell in Figure 315 shows the arrangement of the tubes, which, having clear or unobstructed passages between the vertical rows of tubes, permits the steam to rise freely and assists the circulation of the water. The dry pipe (which is also shown in Figure 316) is a perforated pipe through which the steam passes to the engine cylinder, its object being to carry off the steam as dry as possible; that is to say, without its carrying away with the steam any entrained water that may be held in suspension. Figure 316 is a side elevation with the setting shown in section, and Figure 317 is an end view of the boiler and setting at the furnace end. The boiler is supported on each side by channel iron columns, these being riveted to the boiler shell angle pieces which rest upon the columns. The heat and products of combustion pass from the furnace along the bottom of the boiler, and at the end pass into and through the tubes and thence over the top of the boiler to the chimney flue. There is shown in the bridge wall an opening, and its service is to admit air to the gases after they have passed the bridge wall, and thus complete the combustion of such gases as may have remained unconsumed in the furnace. The cleansing door at one end and that lined with asbestos at the other, are to admit the passage of the tube cleaners. The asbestos at the top of the boiler shell is to protect it from any undue rise in temperature, steam being a poorer conductor of heat than water, and it being obvious that if one side of the boiler is hotter than the other it expands more from the heat and becomes longer, causing the boiler to bend, which strains and weakens it. The sides of the setting are composed of a double row of brick walls with an air space of three inches between them, the object being to prevent as far as possible the radiation of heat from the walls. The brick-staves are simply stays to hold the brick work together and prevent its cracking, as it is apt, in the absence of staying, to do.



Figures from 318 to 330 are working drawings of a 100-horse engine, designed also by William H. Hoffman.

Figure 318 represents a plan and a side view of the bed-plate with the main bearing and the guide bars in place. The cylinder is bolted at the stuffing box end to the bed-plate, and is supported at the outer end by an expansion link pivoted to the bed-plate. The main bearing is provided with a screw for adjusting the height of the bottom piece of the bearing, and thus taking up the wear. The guide bars are held to the bed in the middle as well as at each end.

Figures 319 and 320 represent cross sections of the bed-plate.



Figure 321 represents a side elevation of the cylinder, and Figure 322 an end view of the same, the expansion support being for the purpose of permitting the cylinder to expand and contract under variations of temperature without acting to bend the bed-plate, while at the same time the cylinder is supported at both ends. The cylinder and cylinder covers are jacketted with live steam in the steam-spaces shown.



A view of the steam-chest side of the cylinder is given in Figure 323, and a horizontal cross section of the cylinder, the steam-chest and the valves, is shown in Figure 324. The main valves are connected by a right and left hand screw, to enable their adjustment, as are also the cut-off valves.

Figures 325 and 326 show the cam wrist plate and the cut-off mechanism. The cam wrist plate, which is of course vibrated by the eccentric rod, has an inclined groove, whose walls are protected from wear by steel shoes. In this groove is a steel roller upon a pin attached to the bell crank operating the main valve stem. The operation of the groove is to accelerate the motion imparted from the eccentric to the valve at one part of the latter's travel, and retard it at another, the accelerated portion being during the opening of the port for steam admission, and during its closure for cutting off, which enables the employment of a smaller steam-port than would otherwise be the case.

The shaft for the cam plate is carried in a bearing at one end, and fits in a socket at the other, the socket and bearing being upon a base plate that is bolted to the bed-plate of the engine; a side view of the construction being shown in Figure 327.

Figure 328 represents the cross-head, whose wrist pin is let into the cross-head cheeks, so that it may be removed to be turned up true. The clip is to prevent the piston rod nut from loosening back of itself.

Figure 329 represents a side view; and Figure 329 a a section through the centre of the eccentric and strap.



The eccentric is let into the strap and is provided with an eye to receive a circular nut by means of which the length of the eccentric rod may be adjusted, a hexagon nut being upon the other or outer end of the eye.

Figure 330 shows the construction of the connecting rod, the brasses of which are adjustable to take up the wear and to maintain them to correct length, notwithstanding the wear, by means of a key on each side of each pair of brasses, the keys being set up by nuts and secured by check nuts.



INDEX.

Ames' lathe feed motion, drawing a part of, 208.

Angle of three lines, one to the other, to find, 55, 56. of two lines, one to the other, to find, 54, 55, 56.

Angles, acute and obtuse, 57.

Arc of a circle, an, 50.

Arcs, construction with four, 67, 68.

Arcs for the teeth of wheels, to draw, 205.

Arrangement of different views, 94-111.

Automatic high speed engine, drawings of, 289.

Axis of a cylinder, 51. of an ellipse, 63.

Ball or sphere, representation of by line-shading, 87, 88.

Bed-plate, cross section of, 299. plan and side view of, with main bearing and guide bars, 299.

Bell-mouthed body, representation of by line-shading, 88, 89.

Bevelled gear, one-half of, and an edge view projected from the same, 207. one of which is line-shaded, 210. wheels, 203.

Bevelled gears, small, 208.

Bevelled wheels, a pair of, in section, 208.

Bisected line, 50.

Black lines of a drawing, how to produce, 32.

Blacksmith, drawings for the, 172.

Blake's patent direct acting steam pump, 284, 285.

Boiler drilling machine, a, 269, 270.

Boiler, end view of, 297. shell, sectional view of, 296.

Bolt heads and nuts, United States standard, 114, 118. to draw a square-headed, 125. with a hexagon head, to draw. 113, 114. with a square under the head, 149.

Bolts and nuts, dimensions of United States standard, 117. United States standard, forged or unfinished, 116.

Bolts, nuts and polygons, examples in, 112-151.

Bow pen, applying the ink to, 46. large, with a removable leg, 22.

Brass, representation of, by cross-hatching, 82.

Bread for rubbing out, 26.

Bristol board, use of rubber on, 26.

Brush-shading, 281.

Brushes, size and use of, 280.

Cam, a, and a lever arm in one piece on a shaft, a shoe sliding on the line, and held against the cam face by the rod, to find the position of the face of the shoe against the cam, 228. a full stroke, method of drawing or marking out, 237-241. designed to cut off steam at five-eighths of the piston stroke, 244-246. heart, to draw, 75, 76. object of using, instead of eccentric, 234.

Cam wrist plate, and cut-off mechanism, 301.

Cams, cut-off, employed instead of eccentrics on steamboats, examples in drawing, 232. finding the essential points of drawings of, 241-244. necessary imperfections in the operations of, 247-249. part played by the stroke of the engine in determining the conformation of, 241. three-fourths and seven-eighths, 246, 247.

Cap nut, to pencil in a, 143.

Cast iron, representation of, 277. representation of by cross-hatching, 82.

Centre from which an arc of a circle has been struck, to find, 52.

Centre of a circle, 51.

Centre punch in which the flat sides run out upon a circle, the edges forming curves, 150.

Chamfer circles of bolt heads, 120-123. of Franklin Institute bolt head, 119.

Chord of an arc, 50.

Chuck plate with six slots, to draw, 131.

Circle, degrees of a, 52-55. pencil and circle pen, use of, 43, 44. pens, 37, 38. that shall pass through any three given points, to draw, 51. to divide into six divisions, 56, 57.

Circles, to divide with the triangle, 129. for bolt heads, to draw, 128. German instrument for drawing, 44, 45. use of the instrument in forming, 42-45.

Circular arcs, Rankine's process for rectifying and subdividing, 210.

Circumference, 50.

Collar, a representation of, 96.

Coloring and shading, points to be observed in, 278.

Color, to maintain an even shade of, 278.

Colors, mixing, 278.

Condenser, independent, 288.

Cone, cylinder intersecting a, 186.

Connecting rod, 169, 295, 303. drawing representing the motion which a crank imparts to a, 249, 250. end, 147.