THE PRACTICAL APPLICATION OF THE Slide Valve and Link Motion TO STATIONARY, PORTABLE, LOCOMOTIVE, AND MARINE ENGINES, NEW AND SIMPLE METHODS PROPORTIONING THE PARTS. / BY WILLIAM S. AUCHINCLOSS, C. E., M . AMER. S O C . C . E . XIIIth edition, revised^^TJ MAR 18 189?) 1^% - -** NEW YORK: D. VAN NOSTRAND COMPANY, 23 MURRAY, AND 27 WARREN ST3. 1895. COTYRIGHT, 1869, BY W. S. AUCHINCLOSS. Copyright, 1870, by W. S. Auchincloss. Copyright, 1895, by W. S. Auchincloss. Copyright, 1897, by W. S. Auchincloss. 1 k PREFACE. Link and Valve Motions has had a phenomenal sale during the past twenty-five years. It has proved itself both a standard authority with Mechanical Engineers and Draughtsmen, and a valued text- book with Colleges and Technical Schools. Its market has not been confined to the United States, but it has found ready sale in Great Britain. It was so favorably considered by the noted journal — " Engineering, of London " — that it closed its critical review of the book with these words : " All the matters we have mentioned are treated with a clearness and absence of unnecessary verbi- age, which renders the work a peculiarly valuable one. The Travel Scale only requires to be known to be appreciated. Mr. A. writes so ably on his subject, we wish he had written more." About ten years ago, Julius Springer, of Berlin, published Link and Valve Motions in German under the title: Schieber und Coulissensteurungen, edited by Herr A. Miiller, Chief Engineer of the Borsig Locomotive Works. In the present Edition the Author has carefully eliminated all abstruse formulae, because he considers it absurd to invoke the aid of higher mathematics for the solution of everyday problems in Link and Valve Motion. The component parts of such motions are always compact and the distances small, consequently they do not involve &uoh delicate angles, arcs, sines, cosines and tangents as in Astronomy, IV PREFACE. and should not be so treated, but all dimensions should be computed either arithmetically or graphically by the most simple and direct processes. He is deeply sensible of the generous reception accorded his Work by the Profession, and since the book deals exclusively with fundamental principles (to the neglect of patented devices), he sends it forth anew, confident that in its revised form r, will prove specially acceptable to all Engineering students and practical Machinists who appreciate quick short-hand methods. W. S. A. March. 1895. CONTENTS. PART I . PAGE The Slide Valve — Elementary Principles and General Pkoportions 11 PART II. Short-hand Method for Valve Proportions .... 55 PART III. General Proportions Modified by Crank and Piston Connections 59 PART I V . Link Motions 69 PART V. Independent Cut-Off, Clearance, Etc 127 TRAVEL SCALE. Attached to the Back Cover. PART I THE SLIDE VALVE ELEMEXTAEY PRINCIPLES GESEEAL PROPORTIONS POWER AND WORK The fundamental query in designing a steam-engine has reference to the power required to accomplish a given amount of work. The term work, when employed in a mathematical sense, signifies the continuous overcoming of an offered resistance along a definite path. The quantity of work is the product of that resist- ance into the space passed over. As the standards of weight and distance differ through- out the world, the expressions for quantity of work also differ. With the English standard of pounds avoirdupois and feet, the quantity of work is said to consist of a certain number of foot-pounds. But with the French standard of weight, the kilogramme (=2.20462 lbs. avoirdupois) and of distance, the metre (=3.28089 ft,), the expression becomes a certain number of Jcilogrammetres. Thus the quantity of work expended in raising a weight of 300 lbs. through a vertical height of 10 ft. =3,000 ft. -lbs. and that of elevating a weight of 50 kilogrammes to a height of 20 metres =1,000 kilogramme ties. The quantity of work performed by the steam in the cylinder of an engine, equals the mean effective pressure exerted upon the entire area of the piston multiplied by the space passed over in a 12 HOESE POWER given time. The interval of time usually taken is one min- ute ; hence, if the distance traveled by the piston during a single revolution of the crank be multiplied by the number of revolutions made per minute, their product will equal the required space. Suppose, for instance, the mean effective pressure on each square inch of a piston, having an area of 1,500 sq. ins., is 60 lbs. ; then the total pressure will be 1,500x60 =90,000 lbs., and if the crank makes 40 revolutions per minute, with a piston stroke of 3 ft., the speed of the piston becomes 3 ft. x 2 x 40=240 ft. per minute ; consequently the quantity of work =90,000 lbs. x240 ft. =21,600,000 ft. -lbs. I-HORSE POWER. A force capable of raising a weight of 33,000 lbs. one foot high in one minute is termed a Horse power. The expression originated at the time of the discovery of the steam-engine from the necessity which then arose for comparing its powers with those of the prevailing motor. In its early history this unit had three prefixes — Nominal, Indicated, and Actual — derived from the various methods of estimating the power. The nominal horse power was based on the general practice of the age, which dealt with low pressures and slow piston speeds. These quantities have of late years been greatly increased and the old formula in consequence, grown of less and less importance as a true expression of relative capacity. Indicated horse power designates the total unbalanced power of an engine employed in overcoming the combined resistances of friction and the load. Hence it equals the quantity of work performed by the steam in one minute, HORSE POWER. 13 divided by 33,000. Thus, in the above example, the indi- cated horse power equals ., „„„ . A , 3)21,600 2^600,000 _ y w S3 > mW 654 HP The mean effective pressure can alone be determined by means of an instrument called the Indicator. Tlie Actual or net horse power, expresses the total avail- able power of an engine, hence it equals the indicated horse power less an amount expended in overcoming the friction. The latter has two components, viz: the power required to run the engine, detached from its load, at the normal speed, and that required when it is connected with its load. It is customary in designing massive engines — in the absence of reliable data — to estimate the loss of available pressure by the unloaded friction at 2 lbs. per square inch, and sub- sequently to deduct 1\ per cent, for the friction of the load. Thus, if the mean pressure of the steam within the cylinder =60 '££!' 2 It becomes 58 after allowing for unloaded friction, 58 And lh % of this for the friction of the load = 4.4 Gives a net pressure of 53.6 n* But for small engines of the ordinary design the total loss by friction will, in many instances, amount to 15 or 20 % of the mean pressure. Thus, if the mean pressure =60 lbs. 15 % of 60 = total loss by friction . . , . = 9 " Gives an available pressure of. 51 " The French apply the term Force de cheval to a power capable of raising 4,500 kilogrammes 1 metre high 14 MEAN EFFECTIVE PRESSURE in 1 minute. Reducing these quantities to their equiva- lents in pounds and feet and multiplying together, we find that their horse-power equals a force capable of raising 32,549 lbs. 1 foot high in a minute, which is about Y \ less than the English unit of measure. The following Table furnishes the Force de cheval equivalents of horse powers ranging between 10 and 100 : Horse Power. Force de cheval. Horse Power. Force de cheval. IO IO.14 60 60.83 15 15.20 65 65.89 20 20.28 70 70.97 25 2 5-34 75 76.03 30 30.41 80 8l.II 35 35-48 85 86.17 40 4o.55 90 9I.25 45 45.62 95 96.3I 5° 50.69 100 IOI.3856 55 55-75 For powers greater than 100, and less than 1,000, multi- ply these terms by 10 ; or, if in excess of 1,000, multiply by 100. II.— MEAN EFFECTIVE PRESSURE. The character of the connections between the boiler and steam, cylinder, their length, degree of protection, number of bends, shape of valves, etc., must all be considered in forming an estimate of the initial steam pressure in the cyl- inder ; while the mean effective pressure will depend upon the point of cut-off of the steam, and the freedom with which it exhausts. The exact portion of the stroke that should be completed before this closure or cut-off takes place is a vexed question among engineers, and its discussion is foreign to the object of this Treatise, in which— with the exception of noting cer- MEAN EFFECTIVE PRESSURE. 15 tain limits prescribed by different valve motions — it will be considered as predetermined. Having chosen a point of cut-off, and having estimated the initial pressure of the steam for a given boiler pressure, the question of mean pressure exerted by the steam through- out the piston's stroke, can be approximately solved by the subjoined Table, which has been computed in the ordi- Mean Pressure, Volume, and Temperature Table. 6 •j E STROKE = r. U 75 3 . s-s a •a > V MEAN PRESSURE FOR VARIOUS CUT-< JFFS. -or I 01 ' i or 1 or lor 1 or I or "£ Lbs. Deg. f2 0.25 0.375 0.5 0.625 0.666 0.75 0.875 Lbs. Lbs. Lbs. 20 260 765 II.9 14.9 16.9 18.4 18.7 19-3 I9.8 25 267 677 I4.9 18.6 21.2 23- 2 3-3 24.1 24.7 3° 274 608 I7.9 23-3 25-4 27.6 28. 28.9 29.7 35 28l 552 20.9 26. 29.6 32.1 32.7 33-7 34-6 40 287 506 23-9 29.7 33-9 36.8 37-3 3*S 39-6 45 293 467 26.8 33-4 38.1 413 42. 43-4 44-5 50 298 434 29.8 37-i 42.3 45-9 46.7 48.2 49-5 55 303 406 32.8 40.S 46.6 50-5 5i-3 53- 54-4 60 308 38i 35-8 44-5 50.8 55-i 56. 57-8 59-4 65 312 359 3 8.8 48.2 55- 59-7 60.7 62.6 64-3 70 316 34o 41.7 52. 59-3 64-3 65-3 67-5 69-3 75 320 323 44-7 55-7 63-5 68.9 69.9 72.3 74.2 80 324 307 47-7 59-4 67.7 73-5 74.6 77.1 79.2 85 328 293 5°-7 63.1 71.9 78.1 79-3 81.9 84.1 90 332 281 53-7 66.8 76.2 82.7 84. 86.7 89.1 95 335 269 56.7 7o-5 80.4 87-3 88.7 91.6 94- 100 33* 259 59-7 74.2 84.6 91.9 93-3 96.4 99. i°5 34i 249 62.6 77-9 88.9 96.5 97-9 IOI.I 103.9 1 ro 344 239 65.6 81.6 93- 1 IOI.I 101.6 105.9 108.9 "5 347 231 68.6 85-3 97-4 105.6 106.3 1 10.8 113. 8 120 35° 223 71.6 89. 101.6 1 10.2 1 10.9 115. 6 118.8 125 353 216 74.6 92.7 105.8 114.8 115. 6 120.5 J 23.7 130 356 209 77.6 96.4 no. ii9-4 120.3 J 25-3 128.7 J 35 358 203 80.6 IOO.I 114.2 124. 125. 130.1 J 33- 6 140 360 197 83-5 103.8 118.5 128.6 130.6 *34-9 138.6 J 45 363 191 86.5 107.5 122.7 J 33-2 135-3 r 39-7 H3-5 150 365 186 89.5 III. 2 126.9 137-8 140. 144.5 148.5 5.o Common dif erence . 3-° "77 4.3 4.6 4-7 4.8 16 31 E A EFFECTIVE PEESSUEE. nary manner with the aid of logarithms (Naperian Base). The first column is given for pressures above that of the atmosphere, or the same as registered by an ordinary steam-gauge. The second and third, for temperature and volume, are taken from Mons. Regnault's Experiments on Saturated Steam. In the estimate for volume, that of the water producing the steam was considered equal to Unity. The Table makes no allowance for clearance. If from the mean pressure we subtract the mean value of the back pressure, or that which may arise from imper- fections in the exhaust, which is usually taken for low- pressure engines at from 1 to 2 lbs. per square inch, the resulting pressure will be the mean effective pressure (in pounds) exerted on each square inch of the piston and may be represented by the letter P. For high-pressure engines (having an ordinary slide valve) a more exact determination of the mean effective pressure may be secured from the subjoined table, which embodies the results of 50 experiments made by Mr. Gooch, in 1851, with the locomotive " Great Britain," whose boiler pressure varied from 60 to 150 lbs. per square inch. Mean Effective Pressures incident to a Simple Slide- Valve Motion for various Cut-offs. Cut-Off at— Mean Pressure. (Boiler press. = i.oo.) 0-15 Cut- Off at— Mean Pressure. (Boiler press. = i.oo.) O.I o-45 O.62 O.I25=^ 0.2 0.5 =1 O.67 O.15 O.24 °-55 O.72 0-I75 O.28 o.62 5 = § O.79 0.2 O.32 o.666 = § O.82 0-25 =i O.4 0.7 O.85 0.3 O.46 o.75 =i O.89 O -j n -> ' O.5 =± 0.8 0-93 °-375 = i °-55 o-875 = I O.98 0.4 o-57 .... SPEED OF I' 1ST ON. 17 EXAMPLE. ( Boiler pressure = 70 lbs. per sq. in. 1 ( Steam cut off at § of the stroke. Required.— The mean effective pressure P % We learn from the table that this pressure for a cut-off of f the stroke is 0.82 of the boiler pressure. Then 70x0.82 = 57.4, or The mean effective pressure P = 57.4 lbs. per sq. in. III.-SPEED OF PISTON. The speed S, or number of feet travelled by the piston in one minute, like the subject of cut-off, rests with the judgment of the individual designer. Nothing more will be attempted in this connection than the presentation of quantities most frequently found in ordinary practice : Small stationary engines from 170 to 230 ft. per min. Large stationary engines 250 to 300 " (Rarely as high as 350 ft. ) River and Sound steamer engines 350 to 500 " Marine engines 250 to 600 " The Corliss stationary engine 400 to 500 " (Usually 50 revolutions.) Locomotive engines about 600 " (Occasionally 700 or 800 ft.) The Allen engine 600 to 800 " (Generally the former speed.) It is interesting to note that a line specimen of the latter 2 18 DIAMETER OF PISTON. form of engine was operated successfully by Mr. Charles T. Porter, during the late "Exposition Universelle," at the astonishing speed of 1,400 feet per minute. IV.-DIAMETEK OF PISTOJST. Having decided the questions relating to indicated horse power, mean available pressure P and piston speed S, all the elements are at hand for determining the area of the piston, and consequently its diameter. The formula for indicated horse power, solved with ref- erence to such area, will read : . _ 33,000 x Horse power A ~~ ~^P or, Area of piston is found by multiplying the required indicated horse power by 33,000, and dividing the pro- duct by speed of piston multiplied by the mean available pressure. The corresponding diameter can be obtained from an Area Table. EXAMPLE. Suppose that the indicated horse power=100. Piston speed =300 ft. per minute. Mean available pressure =21 lbs. Then the A 33,000x100 fcooo Area= ' — ^—=523.8 sq. m, 300 x 21 x Which gives a diameter of about 26 inches. 8TK0KL OF 1'IS T O N . V.) T.-STEOKE OF PISTON. The general expression for the stroke of an engine (in feet) is, Strokes- , - Pist, ' , L S P e ! d . 2xNo. of Revolutions' conversely, No. of Revolutions ^ "^ 66 * 2 x Stroke There are many circumstances tending to limit the stroke of a piston. Among other considerations the diam- eter of a paddle-wheel influences the number of revolutions that can advantageously be made by the crank of a side- wheel steamer, and consequently determines the stroke when the piston speed is chosen. Peculiarities of design frequently make it desirable that an engine should be run at a slow speed and transmit its power through gearing. Again, the diameters of pulleys for shafting exert an influence, as when the main shaft of a shop is required to run at 120 revolutions per minute, then 60 revolutions for the crank of the engine, will allow a ratio of 2 : 1 between the diameter of the band wheel and shaft pulley. With a very rapid piston speed, the stroke of the engine is due more to a length imposed on the connecting rod by the necessities of the design, than to the number of revolu- tions of the crank. In the case of the locomotive, the stroke is generally about 24 inches, and the piston speed 600 feet per minute, while the speed of the engine which depends on its power and the diameter of its drivers, ranges between 20 and 60 miles per hour. The accompanying table has been calculated, for drivers of different diameters, to represent the number of revolu- 20 TROKE OF PISTON. tions they will make per minute, irrespective of slip, when the engine travels at given speeds per houi . Revolutions made by Driving [r//cv/y of Locom oth r at git 129 150 172 2l6 258.6 7 » o " p4 120 140 160 200 240. The subjoined table is applicable to stationary and No. of Revolutions of Crank for Given Stroke and (approximate) Piston Speed. Stroke. PISTi )\' SP 5ED. Ft. Ft. Ft. 200 &70 70 220 73 225 75 230 76 HO 80 WO 83 260 S6 £70 90 280 93 290 97 300 100 320 106 &J0 113 350 116 i ft. 6 in. 67 1 " 8 " 60 63 66 68 70 72 75 7« 8l 84 87 90 96 100 105 1 "10 " 55 57 60 61 63 66 68 7i 74 76 79 82 88 93 96 2 " " 50 52 55 56 57 60 63 65 67 70 72 75 80 85 87 2 " 3 " 44 47 49 5o 5i 53 55 5^ 60 62 64 66 72 76 78! 2 " 6 " 40 42 44 45 46 48 50 5~ 7 54 56 S^ 60 64 68 70 2 " 9 " 36 3« 40 41 42 43 45 47 49 5i 53 55 58 62 64 3 " « 33 35 36 37 3« 40 42 43 45 47 48 50 53 56 58 3 " 3 " 3i 32 33 34 35 37 3« 40 4i 43 44 46 50 52 54 3 « 6 " 29 30 3 1 32 33 34 36 37 3« 40 4i 43 46 48 5o 3"9" 27 28 29 30 3i 32 33 34 36 37 39 40 43 45 47 4 " « 25 26 27 28 29 3° 3 1 32 34 35 36 3* 40 42 44 4 " 3 " 2 3 24 25 26 27 28 29 30 32 -■> -> 00 34 35 3« 40 4i 4 " 6 " 22 23 24 25 26 27 28 29 3° 3i 32 33 35 38 39 4 " 9 " 21 22 23 23 24 25 26 27 28 29 30 3 1 33 36 37 5 " " 20 21 22 22 23 24 25 26 27 28 29 30 32 34 35 A R E A F S T i: A M PORT. 21 These dimensions, the stroke of piston and diameter of cylinder, are so constantly used in comparing engines of different powers, that, as far as possible, they should consist of whole numbers quite Ire.' from all fractions of an inch. VL-AREA OF STEAM POET. This dimension ranks next to cut-off in its controlling influence upon the proportions of the valve seat and face. It may justly be considered as a Base from which all the other dimensions are derived in conformity with certain laws. Its value depends greatly upon the manner in which the port is employed, whether simply for admitting the steam to the cylinder, or for purposes both of admission and exit. In cases of admission it is evident that the pres- sure will be sustained at substantially a constant quantity by the flow of steam from the boiler. But in cases of exit or exhaust, a limited quantity of steam, impelled by a con- stantly diminisliiiH/ pressure, forces its way into the atmo- sphere with less and less velocity. If, then, the engine is supplied with two steam and two exhaust passages, the ports will be correctly -proportioned when the areas of the latter exceed those of the former by an amount indicated by careful experiment. When, however, one passage j)er- fornis l)otli duties, it should have an area suitable for the exhaust and be opened only a limited amount for the admission of the steam. Very excellent results have been found to attend the employment of an area equal to 0.04 of that of the piston, and n steam-pipe area of 0.025 of the same, when the speed of the piston does not exceed 200 ft. 22 AREA OF STEAM POET. per minute, but widely -different factors are demanded "by higher speeds, like those peculiar to locomotives. In the year 1844 M. M. Gouin and Le Chatelier insti- tuted a series of experiments for ascertaining the value of such terms. These were continued about six years later by Messrs. Clark, Gooch, and Bertera, upon engines of British manufacture. The various results having been collated and analyzed by Mr. Clark, were finally presented to the public in his valuable work on " Railway Locomotives." From this it appears that with a piston speed of 600 ft. per minute, an area of 0.1 that of the piston was found to give practically a perfect exhaust, a steam-pipe area of 0.08 a free admission of steam to the chest, and a port opening of from 0.6 to 0.9 the entire width of the port, depending on the humidity of the steam, a free admission to the cylinder. The following table has been prepared for intermediate speeds of the piston on the assumption that for average lengths of pipe the area increases as the speed, and that a higher speed is usually attended by increased pressure ; Speed of Piston. Port Area. 1 Steam-Pipe Area. 2oo feet per minute. .04 area of piston. .025 area of piston. 2 ^O .047 " " .032 300 " 35° " 400 45o " 500 " .055 " " .062 .07 .077 " " .085 " " .039 .046 .06 .067 55° " 600 .092 .074 .08 Having determined the area of the steam port, the next step will be to resolve it into its factors, length and breadth. When a small travel of the valve is essential, the length should be made as nearly equal to the diameter of the cyl- inder as possible ; then the port area divided by the length, furnishes of course the value of the breadth or S in Fi g. 1. A R E A F 8 T E A M PORT. I 1 I TJie extent to loliiclt the valve should open this port for the admission of the steam will equal from 0.6 to 0.9 of the value of 8, and the mini mum travel of the valve, that which with a given cut-off just opens the steam port the amount of this limit. The maximum travel is governed by expediency, the general tendency of an excess over the minimum travel is to render the events of the stroke more decisive, the cut-offtakes place with greater brevity, avoid- ing unnecessary wire drawing of the steam and the release opens rapidly, affording a more perfect exit. Where the travel is small, these good qualities should be secured by increasing the travel, until the valve gives an opening equal to or even greater than the width of the steam port. With a large travel no such attempt should be made, since it would inevitably sacrifice much work in friction and cause a far greater loss than gain. EXAMPLE. Diameter of a certain piston = 26 inches. Area =531. Piston speed = 350 ft. per minute. Required. — Width of steam port, minimum width of port opening and diameter of supply steam pipe. From the Tables we have : Sq. inches. Area of steam port =531 x .062=33 sq. inches. The length of the port=diameter of cylinder=26". And the width=||=1.3 inches or lf ( .. Minimum width of port opening=0.0 x 1.3=| inch. Sq. inches. Area of steam pipe =531 x .046=24.4 sq. inches. Consequently the diameter=5^ inches. In the Corliss Engine, where the steam is admitted and exhausted through different valves, it is customary to give the steam passage an area of ^ to -^ that of the piston, and the exhaust an area of from T V to -, 1 ,. 24 AREA OF ST E A 31 PORT. In this connection a few remarks may approjsaiately Ibe made with reference to the formation of the valve edge and the walls of the steam port. The experiments of scientists like Weisbach, W Aubuisson and Koch, prove that the vari- ous phenomena of contraction in the fluid vein observed in the flow of water are equally true for gases, the formulae of discharge however have slightly different coefficients of efflux. The character of the discharge will evidently vary with the extent of opening offered by the valve edge, from what is termed "discharge through a thin plate" at the commencement, to that through a "short tube" with the full opening. Fig. 1 illustrates the natural convergence Fig. 1. Ml I . l) P S w which takes place in the filaments of the steam vein with the common slide valve. If the edge were formed as in Fig. 2 the discharge would be much improved and ren- dered similar to that which occurs through an ordinary "mouth piece." The curvature of the valve edge should commence far AREA OF STEAM POUT. 2o Fig. 2. \\v ' .^r-'"" enough above the rubbing surfaces to permit a limited amount of wear without altering the proportion of the parts. Every effort should also be made to reduce the amount of clearance for the steam and loss of head by friction, to a minimum value. Hence the passage from the port to the cylinder must be constructed as short as possible, be of uniform cross section and bend with easy curves if bending is indispensable. In the moulding of a cylinder casting, the cores for the steam and exhaust passages should be faced with very great care, in order to secure surfaces along which the steam will flow with perfect freedom. PISTON, CEANK VALVE MOTIONS In essaying the study of an intricate subject like the relative motions of the piston and the ordinary slide valve of a steam engine, it is of the utmost importance to first divest the parts of all the complicating influences which arise from special constructions and present them in such simple and elementary forms, that the discovery of the fun- damental laws governing their motions may be facilitated. If these are clearly defined, the deduction of others adapted to special cases will subsequently be accomplished with comparative ease. The entire series of events which take place within the cylinder of an engine, occur when the piston has reached definite positions in its complete stroke. It follows (since there is in practice no fixed limit to the stroke) that an in- finite number of such positions may be occupied, and in order to express them by a standard which shall apply equally to all cases, a unit scale must be adopted. The stroke of all pistons therefore will be regarded throughout this Treatise as equal to Unity, and their positions at cer- tain important periods, as decimal portions of the entire stroke. If a movable point is caused to travel around a fixed PISTON, CEANK AND VALVE MOTIONS. 27 one, in the same plane, at a constant distance therefrom, it will describe a curved line called a circle. For the pur- pose of locating any position in the path of the movable point, the circle has from remote ages — though not wisely — been divided into 300 equal parts called degrees (360°), each degree into 60 minutes and each minute into 60 seconds. While the piston of an engine perforins a single stroke, the crank-pin makes a semi-revolution (180°) about the centre of the main shaft, each position of the former conse- quently corresponds with some angular position of the crank-arm, and if these angles are arranged in a Table we can instantly determine therefrom the number of degrees over which the pin must pass in order to bring the piston to any desired position. Fia. 28 PISTON, CBANK AND VALVE MOTIONS. Since the "slotted cross-head" shown in Fig. 3 is the only form of connection between the crank-pin and piston, in which the piston moves from one extremity of the stroke to the other at the same speed as the crank-pin — measured on the stroke line — it will answer our purpose for deter= mining the fundamental principles of the piston and valve motions. The arrangement of the parts are clearly shown in the Figure. The crank-pin is surrounded by blocks BB, these slide freely up and down the solid frame FH to which the piston-rod is welded, so that while the crank-pin ad- vances from D to G the block mounts towards F, returns as it approaches E and descends towards H on the return stroke ED. For convenience, the cylinder will always be regarded as lying on the riglit-liand side of the main shaft and the point of the crank-pin circle nearest to the cylinder as the zero or starting point of the forward stroke. TABLE A. Piston Position. Crank Angle. Piston Position. Crank Angle. Piston Position. Crank Angle. Deg. Deg. Deg. O.I 3^ 0.5625 = -^ 97* 8l3=!l I28g O.I25=l 4i| 0-575 98^ O.82 I29J 0-I5 45^ O.6 IOI \ O.83 13 ii o- J 75 49^ O.625 = g 1 04 \ O.84 J 32s 0.2 53g O.65 107.1 O.85 i34i 0.225 5^ O.666 ='j 1 09 \ O.86 *$H ; 0.25 =1 60 O.68 ml O.87 "371 0.275 63{ O.687 =11 112 0.875=| 138^ °-3 66* O.69 112; O.88 1 39 } > 0-325 69.I 0.7 "3§ O.89 i 4 i| o-333 = i 70.J O.7I "4a O.9 I 43h o-35 72 1 O.72 Tl6^ O.9I J 45s °-375 = f 75^ 0-73 "7^ O.92 H7s 0.4 78A 0.74 n8| °-93 149" 0.425 81? 0.75 =| 120 0.94 I5i| o.437 = i\ 824 O.76 I2lf 0-95 154^ o-45 84! 0.77 I22§ 0.96 I56J o.475 87! O.78 !24i 0-97 160! 0.5 =i 90 O.79 I2 5^ 0.98 163I 0.525 92I O.8 126 7 0.99 1 684 o.55 951 0.8l 128} 1. 00 180* N , CRA N K A N J) \ A L V E M T I N S . 29 The foregoing Table furnishes angular positions of tin crank-arm corresponding with the various points in the stroke which may at times be occupied by the piston. To illustrate its application, suppose for — EXAMPLE. The stroke of a certain piston— 36 inches. Qui /••//• — How many degrees will the crank have passed over when the piston reaches points respectively 9" and distant from the commencement of its stroke I 6 )9.00 1st. -^=6)1.50=0.25 of the stroke. 3b 025 2d. 2 || = -|| 8 = 0. 649 of the stroke. Then by the Table : 0.25 of the stroke— an angular passage of 60°. o.65 " = " " 1071° The required angles. Again : Suppose the stroke of a piston =36", and that the crank lias passed over 112°. How far will the piston have advanced ? The Table gives for 112° a piston position of 0.687 of the stroke. Therefore 0.687 x 36" =24|" the distance advanced by the piston while the crank has advanced 112 degrees. There is securely fastened to the crank shaft a device called an " eccentric," which serves to impart a recipro- cating motion to the slide valve. Upon close inspection it appears that this is only a mechanical subterfuge for a small cranlc. The travel of any valve being small compared with that 30 PISTON, CRANK AND VALVE MOTIONS. of its piston, the crank required for its motion lias fre- quently an arm or "throw" c b shorter than one-half the diameter a e of the main shaft, Fi^. 4. Hence to avoid cut- Fig. 4 ting the shaft and the expense of forming the crank c b, the pin m, n, and enclosing strap of the rod are greatly en- larged until they attain the common diameter M N, the former may then be slipped on, and keyed fast to the shaft a e. Of course the motion will not be altered by this change, but the same reason that led to the adoption of the slotted cross head for tracing the piston's progress, now compels us to substitute a small slotted cross head and rod for the eccentric rod. In the sequel therefore both the crank pin and the eccentric pin (or centre of eccentric) will be considered as transmitting their motions through slotted cross-heads to the piston and the valve. (See Fig. 5.) The axes of the cylinder and of the valve stem do not always pass through the centre of the main shaft. When that of the latter lies above and parallel to the former, as shown in the figure, some expedient must be adopted for carrying the motion of the eccentric pin up from the point q in the central plane of the engine to e in that of the valve. SS3S5T A ??^m^Wm>S^SS^~: ~ ^ ~ s B py - -:--.A-- H ~£ oid PISTON, CRANK AND VALVE MOTIONS 31 This is frequently accomplished by aid of a bar q d e called a " rocker," free to oscillate on its firmly supported axis d. The direction of the motion then becomes the reverse of thai produced by the eccentric pin and if the pins q and e are made to operate in vertical slots no irregularity will be introduced by this arrangement. Having explained the general features of these control- lers of motion, the crank and the eccentric, and having resolved them into their elementary forms, we pass to con- sider the parts moved and seek the law of their proportions. The plain slide valve of a steam-engine is a device by which the entrance and exit of the steam is regulated for the opposite ends of the cylinder. It is essentially a case A, resting on a plane surface c c as seen in cross section in Figs. 5 and 11. Through this surface are cut three passages S', S", and E, separated by the partition walls B, B, called "bridges." The two former lead to the opposite extremi- ties of the cylinder, and the passage E called the " ex- Jiaust" leads through an oval pipe to the atmosphere. The valve A is sufficiently large to cover both the passages S', S", when standing in its neutral position. A second case D, D, called the "steam chest" encloses the valve .V and is secured rigidly to the plane surface c c. Being- larger than the valve it leaves over it much unoccupied space to which the only entrance is through the aperture F. This space is the "reception room" — so to speak — of the cylinder ; to it, the steam is admitted from the boiler through F and kept in waiting during such times, as the valve in its motion completely covers the two ports. Figure o represents the crank-pin at the zero point of its path, the piston at the extremity H of its stroke, the valve in the neutral position and all the parts ready for motion. A complete revolution of the crank will carry the piston 32 PISTON, CRANK AND VALVE MOTIONS. forward to K and return it to the starting point H. What- ever events take place in the journey from H to K should be repeated in the same order on the return route from li to H, hence in studying the motion we will seek to render it perfect for the trip from H to K and leave the parts when the latter point is reached in the same relative positions as those occupied for H, so that the one will become simply a counterpart of the other. The first point evident, is that the port S' must be opened and again closed for the proper admission of the steam during the stroke of the piston from H to K ; in other words, while the piston is making one entire stroke the valve must accomplish a half and a return half of its stroke. Such an operation can only be brought about by securing the eccentric pin in the position/ or b on a line at right angles to the crank-arm, that off being suit- able for a direction of the crank indicated by the arrow. Let us trace the two motions throughout one revolution of the crank. Moving it from the zero to the 90° point will draw the piston from the position H to the half stroke or the line c", c", will advance the eccentric pin from / to 1c, the rocker from e q to e' q\ the centre of the valve from V to V" and completely open the port S'. As the crank pro- gresses from 90° to 180° the eccentric pin will travel from h towards Z>, gradually closing the port S' and completely covering it when the 180° point is reached, thus leaving the valve in the same position at the terminus of the stroke that it occupied at the commencement. On the return stroke from K to H the port S" will in like manner be opened and again closed. In thus hastily following the two entrances of the steam to the cylinder, we have lost sight of its mode of escape after performing the work of forcing along the piston. Let us suppose that one revolution has been com- pleted and the piston is prepared for a second journey fror» ( ! R A N K A N I) V A L V i . M T I N S 33 the position H. The space J is now iilletl with steam and some passage of escape must be opened. This is provided in the port and pipe E, which are thrown into immediate communication with the passage S" when the valve com- mences its motion, the opening becoming wider and wider as the travel progresses, onty closing when the piston reaches the point K and is ready to receive fresh steam through the passage S" for the return stroke. Such is a brief outline of the parts and functions of the simplest form of slide valve, in which the steam is admitted at the commencement of the piston's stroke and not ex- cluded until that stroke is completed. This arrangement, however, is not attended with econo- mic results, for it entirely ignores that remarkable property of steam, its elasticity. To render this latent power availa- ble, the steam should be admitted during only a portion of the piston stroke, the valve should then be closed and the confined volume of steam allowed to complete the remain- ing portion, by developing its power of expansion. But how can our elementary form of valve and position of eccentric be modified for attaining this desirable result % Suppose a cut-off were required at a piston position of 0.93 of the stroke. By carrying the crank to the 150° posi- tion (as in Fig. 6) we observe that the port S remains opened a distance I and the most ready means for effecting its closure is to lengthen the valve face by this amount. Since the cut-off must take place at relatively the same piston position in both strokes, an equal addition must be made to the other edge of the valve. Such additions to the outer edges of the valve, for the purposes of cut-off, are called overlap or simply " lap." The extent of this lap in the present case is evidently equal to the horizontal dis- tance of the eccentric's centre/" from the 90° line, because 3 34 PISTON, CRANK AND VALVE MOTIONS., without lap it would naturally close at this line. The same distance expressed in degrees would be equivalent to a "lap angle" of 30°. But on referring to Fig. 6 it is clear that no such addi- tion can be made without necessitating a change also in the eccentric location, for it would render the admission 30 3 too late. Hence if we add a lap to the valve equivalent to an eccentric motion of 30° from its neutral position, we must at the same time unkey the eccentric, and having advanced it also 30° refasten it on the main shaft. The number of de- grees by which the eccentric is thus carried forward from a position at right angles to the crank-arm is termed the "angular advance" of the eccentric. When the eccentric stands at right angles to the crank the exhaust closes and release commences at the extremi- ties of the stroke, consequently if the eccentric be moved ahead 30° not only will the cut-off take place 30° earlier, or at a crank angle of 120° instead of 150°, but the release as well as the exhaust will take place 30° earlier or at the 150° crank angle. Although we have not secured by this pro- cess the cut-off aimed at, yet the investigation distinctly points out the means at our command for the accomplish- ment of any cut-off and will enable us to construct a Scale for determining the magnitudes of such alterations. For a cut-off of 140° there would be required an angular advance of 20° and a lap equivalent to the distance these degrees remove the eccentric centre from the line at right angles to the crank ; for a cut-off of 160°, an advance of 10° with a corresponding lap, and so on ; the exhaust closure taking place respectively at the 160° and 170° crank angles. This closure of the exhaust confines the steam in the cyl- inder until the port is again opened for the return stroke ; consequently the piston in its progress will meet with in- PIS T N , C E A N K A X I ) V A L V E M olio X 8 . 35 creasing resistance from the steam which it thus compresses into a less and less volume. Such opposition when prop- erly proportioned aids in overcoming the momentum stored up in the reciprocating parts and tends t;> bring them economically to a state of rest at the end of each stroke. Since the closure of one port is simultaneous with the open- ing of the other, a release will take place of the steam which was previously impelling the piston. Within cer- tain limits this also is conducive to a perfect action of the parts, for an early release enables a greater portion of the steam to escape before the return stroke commences, where- as a release at the end of the stroke would be attended by a resistance of the piston's progress, from the simple fact that steam cannot escape instantaneously through a small passage, but requires a certain definite portion of time de- pendent on the area of the opening and the pressure. The larger the opening then the less the occasion for antici- pating the moment of exhaust. "We learn therefore that the moments of exhaust closure and release are, when the valve has neither "inside lap" nor its converse " inside clearance" directly dependent upon the angular advance of the eccentric, and that an an- gular advance of 20° produces a closure at a crank angle of 160°, one of 30° at 150° and so on, the resistance becom- ing continually greater as the angular advances increase. A limit at length is reached where this resistance really becomes detrimental, and an amount of power is absorbed quite inconsistent with economy of action. On this account the single eccentric is rarely used to effect cut-offs of less than | the stroke. Earlier cut-offs require two valves and two eccentrics, the one set for regulating the cut-off of the steam, the other its admission and escape. This subject will be more fully discussed in Part V. 36 PISTON, CRANK AND VALVE MOTIONS. The principles just developed can be embodied in a sin- gle Diagram called the Travel Scale, whose construction is illustrated by Fig. 7. Fig. 7. 7tRAVEl\MM m. B To the Reader— & Cop- per-plate engraving of the TRAVEL SCALE will be found attached to the back eoTCr. rilA N K A N I) VA L V E M (> T I N 8 . 37 Let E F D represent the path traversed by the eentre of an eccentric whose throw equals 3^ inches, consequently the travel of its valve=7 inches. Then C F at right angles to D E will be the normal position of the eccentric from which the angular advances must be laid off. Extend this line to some convenient point A and join the extremity D of the travel with A. Divide the line C A into 7 equal parts, and through these points draw lines parallel to D E to represent all the travels less than 7 inches. Finally pro- ject each degree of the arc D F upon the line D C and join the points thus found with the point A. The distances from the Base Line C A, at which tin's group of lines intersect the travel lines, will indicate what lap should be given to accomplish various cut-offs, and their distances from the extreme travel line D A will give the width of the steam-port opening due to these travels and cut-offs. Thus for 7" travel and a cut-off of 120° the eccen- tric must have an angular advance of 30° and the valve a lap equal to V C, giving thereby a port opening V J) ; while a travel of 4 inches with the same cut-off only require^ a lap of r C 3 and has a port opening of V d\ The exhaust closure of course takes place in both cases at a crank angle of 150, or piston position of 0.93 the stroke. It will be observed that this Scale may be applied with perfect accuracy to travels greater than 7 inches by making these lines represent their multiples ; for instance, a 4-inch travel may stand for one of 8 or 12 inches ; a 6-inch travel for one of 12 or 18 inches, and so on. In such cases the values of the true la]) and lead will be double or thrice those given by the Scale. Since the same principle holds for travels less than 2 inches, it is clear that the Scale must apply to all possible dimensions. A slip of paper and a pencil are the only paraphernalia of the Travel Scale. To illustrate its use take for — 38 PISTON, CRANK AND VALVE MOTIONS. EXAMPLE. Extreme width of port opening must =1 J inches and the valve must cut off steam at 0.82 the stroke. Required. — Angular advance of the eccentric, travel of valve, lap and point of exhaust closure. Table A gives for a piston position of 0.82 the stroke a crank angle of 130°, for this cut-off an angular advance of 25° will be required (see line C D of the Travel Scale). Apply the edge of a slip of paper to the Inch Scale and mark off the desired width of the port opening a, b, as in Fig. 8. 90° ANGULAR ADVANCE. 2S° o° a 4 3 / s TRAVEL M PORT OPENING.^ \—~ L /\p = — —it --i ; 6 ) CUT 0FF = 130° \ [EXHAUST CLOSURE =155.} c i Carry the same to the Travel Scale, place the mark a over the 90° line C A and slide the edge — parallel to the line C D — until the mark b stands directly over the 25° an- gular advance or lap-angle line. The 4| inches line of travel, upon which the slip of paper here stops, will be the correct travel for the valve. Before removing the paper mark the position c of the Base line. Finally return the slip to the Inch Scale and measure the lap b c, which gives ^| of an inch. The exhaust closure on one side and release on the other will of course take place at the 155° angle of the crank (see line C D) or at a piston position of about 0.95 of the stroke. f Angular Advance =25°. j Travel of valve =4| inches. Lap = if inch. Exhaust closes at 0.95 of the stroke. The solution of such problems as the subjoined, will Answers. D I F. S C T I O JS OF CBANK MOTIO N : ■ tend to familiarize the Reader with the method of using this Travel Scale : 1st. To cut off at | the stroke, with port opening of 1\ inches. Required. — Angular advance of the eccentric, travel of valve, lap and point of exhaust closure. 2d. To cut off at § the stroke, with port opening uf If ins. oa cc it 7 a a a a tt o a Aih " " 7 u u ii U U 13 << 16 DIRECTION OF CEAXK MOTION. The direction of any crank motion depends on two con- ditions — 1st. The presence or absence of a rocker for trans- mitting the motion ; 2d. The location of the angular ad- vance with reference to the central line of the valve motion. Both of these may be conveniently expressed in a single Diagram like the accompanying Fig. 9, in which the posi- Fig. 9. tive sign (-f) represents a motion in the direction of the hands of a watch, the negative (— ) a reverse motion. To 40 L EA D . produce a positive motion in any engine, whose eccentric acts through a rocker, lay off the angular advance from the line bfm the 1st quadrant (the crank standing at the zero), but for one without a rocker, the angular advance must he laid off from the same line in the 3d quadrant. The 4th and 2d quadrants in like manner belong to the negative motion. The reason for making such a disposition of the angular advance will at once appear upon tracing out either of these motions. When the power of an engine is transmitted through a wide belt to the machinery, the direction of its crank mo- tion will be determined by the relative locations of the main and crank shafts. The strain should invariably be made to fall upon the lower portion of the belt, the upper being thereby relaxed, sags upon its pulleys, increases the frictional surface, and materially improves the adhesion of the belt. LEAD. This term is applied to an alteration made in the plan of the valve motion for the purpose of concealing and neu- tralizing an effect, due to imperfect workmanship as well as continual wear in the boxes of the crank and cross head pins. The difficulty may be best explained with the as- sistance of Fig. 10. Suppose, for instance, both boxes of the connecting rod A B, fit loosely upon the crank and cross-head pins, that the crank moving in the direction indicated by the arrow, has reached a location C A within 8 degrees of the zero, and that the piston (on account of the lost motion in the boxes) /lalls short of its true position B, a distance B B. If now \he LEAD. 41 momentum of the motor carries the crank-pin pasl its zero, the piston, which at the moment of passage is no longer urged or restrained by the connecting rod, will by virtue Fig 10. K ISU . CONNECTING ROD. of its own momentum continue moving in the direction of H until all the lost motion being expended, its progress is suddenly checked and it is itself again brought under the control of the connecting rod, which then draws it forward upon the return stroke. These concussions are reprodu 1 at the end of each stroke with a degree of force and sound directly dependent on the extent of the lost motion and the momentum of the piston with its connecting rod. Where the parts are of great weight, as in a marine engine, the sound becomes very loud and the engine is said to "thump" or "pound" on the "centres:' Two ways pre sent themselves for counteracting this effect ; the one, by making the boxes so durable and the workmanship so per- fect that lost motion becomes almost impossible ; the o by introducing a resistance to the momentum of the piston capable of completely overcoming it before the end of the stroke, in other words by allowing the steam to enter the cylinder a short time previous to the termination of the stroke. With small engines the first method is practicable, but in large ones both are more commonly employed be- 42 LEAD. cause with these, a very small amount of lost motion suf- fices to produce a disagreeable sound. The width of port opening given by any valve at the moment its crank passes either centre, is called the " lead" of the valve ; and the angular distance of the crank from its zero at the instant this opening commences, the "lead angle." The opening together with the angle (or time) limit the power of the steam in its effect upon the lost motion ; for even a small opening continued through a long time may prove as efficient for the admission as a large opening during a very short time. Since sound, the effect of lost motion, depends upon the weight and velocity of the reciprocating parts, the lead re- quisite must vary for different engines and also for the same engines at different velocities. The exact amount can- not be predicated in any particular case, but after the en- gine has been constructed it may be experimentally deter- mined by gradually increasing the angular advance of the eccentric until some position is found which results in a smooth and noiseless movement of the reciprocating parts. We have before alluded to the effect of compression by a premature closure of the exhaust, but it must be distinctly understood that this agency unassisted cannot neutralize the evils of lost motion without injuring the admission of the return stroke. In this respect it differs from lead. It should then usually be supplemented by lead in order to accomplish a smooth action of the parts and free opening of the steam port for the return stroke. Observe also, that so long as the lead angle amounts to only a few degrees no impression can be produced on the contiuuity of the crank motion, for the lever arm will be too small for the power to exert any influence over the crank. I. E A I) . 43 The limits of the lead angle are commonly zero and 8° for stationary engines ; while for any given angle the width of opening will depend upon the travel of the valve and the point of its cut-off. It remains to be shown that the Travel Scale is quite as applicable to valves having a certain lead as to those with- out any. Referring again to Fig. 6, imagine an increase in its angular advance of 5°, the valve will then close at 115° instead of 120° and reopen its port 5° before the crank reaches the extremity of the stroke; but if the lap be re- duced 5° when the angular advance is increased 5 , the cut off will still remain 120°, while the port com- mences to open 10° before the end of the stroke. Con- sequently if we wish to arrange a valve for a certain number of degrees lead, without altering the point of cut- off, it will simply be necessary to find the angular advance for a valve without lead, add \ the lead angle for a new angular advance^ and subtract the other \ for an angle by ich ich to measure the lap. If in the Example of Fig. 8 a lead of 8 degrees had been required, with the same cut-off, the angular advance ^ would have become 25° + 4° =29° j \ and the lap angle 25°-4°=21 \ and by applying the port opening marks a and b to the 90° and 21° lines, — instead of the 90° and 25° lines, — we would have obtained a travel of 3 J inches and a lap of \\ inch ; while the distance between the angular advance line of 29° and the lap angle line of 21° would have equaled \ inch, the width of the lead opening at the extremity of the piston stroke. The change in the angular advance of course changes the exhaust closure from 155° to 151° or about 0.93 of the piston's stroke. 44 LEAD. Supposing then a lead angle of 8° for the same problem the answers become : — Angular Advance =29°. Lap angle , . . = —21. Travel =SJ inches. Lap =-!£ inch. Lead •••• =1 inch. Exhaust closes at 0.93 of the stroke. Similar suppositions made and applied to the other trial problems will give all the practice requisite for successfully using the Travel Scale. It seems almost unnecessary to observe that the Scale effects with equal readiness and precision solutions directly the converse of that just accomplished. Thus, if the above lap, lead and travel were given, to determine the exhaust closure and cut-off, we would mark the lap and lead on a strip of paper as in Fig. 12, apply the same to the 3 1 inch travel line of the scale, which would show at once an angular advance of 29° and consequently exhaust closure of 0.93 the stroke ; also a lap angle of 21° with lead, or 25° without, the same as a cut-off of 130°=0.S2 the entire stroke. A moment's reflection will also show that— during the progress of the crank— the varying width of the port open- ing from the simple lead out to the maximum width and back again to the period of cut-off, might readily be traced on the Scale, and all the information common to the popu- lar method of ellipse or other construction, be immediately obtained. But the facts thus gained, would prove of very trifling moment, so long as the valve had received a correct maximum port opening. WIDTH OF BBIDG 4? \VI DTE OF BEIDGE. This dimension is usually made of equal thickness with the cylinder, in order to secure a perfect casting, but at times it becomes necessary to increase its width. The only danger from a narrow bridge is an overtravel of the valve, by which the exhaust passage would be placed in direct communication with the u live steam" in the chest, and followed by continual waste of the power. Obviously this cannot occur while the difference between the port opening and the steam port does not exceed the width of the bridge. (Fig. 11.) But to prevent even the possibility of a leak- age : — dd about \ of an inch to the width of the opening and from their sum subtract the width of the steam port. Thus the width of the steam port in the example of Fig. B, should have been at least : — 1J + J'-— l" = i inch. When however the width of the opening is less than that of the steam port, the danger of such an escape entirely vanishes. WIDTH OF EXHAUST POET. The main difficulty to be avoided in proportioning the width of this port is the possibility of a reduction in its area, when the valve attains extreme travel, to an opening materially less than that of the steam port from which it derives its supply. Suppose that the valve in Figure 11 has reached the end of its half travel, or the exhaust edge V moved a distance 48 INSIDE LAP. R from its neutral position V 2 ; then by the above condi- tion, E will evidently equal (S + R— B). Which furnishes the following general EULE For determining width of Exhaust port. Add the width of the steam port to J the travel and from their sum subtract the width of the bridge. When called upon to perform the addition or subtrac- tion of many fractional portions of an inch, it will generally be found more convenient to express these decimally tnan by those very awkward subdivisions sixty-fourths, thirty- seconds, etc. Fractions of an inch expressed decimally. g L of inch = .0156 1 a- 3 4 ' 3 2 of inch = .3 43 8 1 + T6 °f i ncn 3 2 = .0313 3 8 it 375 5 1 3 a 8 + 32 1 T6 = .0625 l + ¥ a 4063 3 U 4 3 3 2 = .0938 S +T6 tt 4375 3 1 1 it 4 > 32 8 = .125 3 1 3 a 4688 3 1 1 a 4 + T6 1 4- ! S + 32 -•1563 £ tt 5 3 j_ 3 (i 4+32 8+T6 ' =-1875 l + A tt — 53i3 7 it 8 l 1 3 8 +32 = .2188 i + A it 5625 7 _i_ 1 a 8^32 ± 4 = .25 i+A tt — 5938 7 1 1 u 8+76 i+A ' =-2813 5 8~ tt — 625 7 1 3 tt 8 + 32 j+l's =-3 I 25| 5 + 32" it — 6563 1 inch .6875 .7188 •75 •7813 .8125 .8438 •075 .9063 •9375 .9688 = T OOO INSIDE LAP. The effect on a valve motion of inside laT) is to— Prolong the Expansion, and Hasten the Compression. (A contrary effect for inside clearance.) INSIDE LAP 40 The former is occasionally added in the case of high- speed engines having very late cut-offs. In such instances the compression is arranged to commence at about J of the stroke, or at an angle of 138 degrees, and the release at an angle not exceeding 160°. For example, if the angular advance equals 32° (with a travel of 4§ inches) the compres- sion would commence at a crank angle of 148° or 10° later than the above limit ; hence if we give the valve an inside lap of 10° or | of an inch found as in Fig. 12, the expan- Fig. 12. ANGULAR ADVANCE si on will continue from the point of cut-off to 148° +10 = 158 degrees, and the compression commence at 148°-— 10°= 138 degrees, instead of both events taking place at the 148° angle of the crank. We think the foregoing investigations fully sustain our remarking in conclusion that any questions, relating to the travel of the valve, the varying widths of the exhaust and steam-port openings for every possible position of the crank, the moments of closure and release, and other points of interest, can not only be determined with perfect pre- cision by means of the Travel Scale, but their solution will prove well nigh instantaneous when compared with the indirect and tedious methods that have heretofore ob- tained in popular usage. 50 GENETCAL EXAMPLE. GEJSTEEAL EXAMPLE. What dimensions should he given to the cylinder and valve of an engine like Fig. 5 to secnre an indicated horse power of 150 with Pressure of steam in boiler at 65 lbs. ; The crank to make 50 revolutions per minute, and the steam to be cut off at § the stroke 1 The mean effective pressure (page 16) =65x0.82=53.3 lbs. Piston speed (page 17)= say 250 ft. per minute. Area of piston, page 18, . 33,000x150 132x150 _ . , A = 250x53.3 ~ = -53T3- =371 S * mches ' Therefore diameter of piston = 21 f ins., say 22 inches. 250 Stroke of piston (page 19) = v— = 2. 5 ft. =2 ft. 6 inches. Port area (page 22) =371 sq. inches x .047=17.4 sq. inches. If the length of the steam port =20 inches then its width 17 4 will = -z^r- = I inch. 20 8 Width of port opening W (by page 23) may vary be- tween 0.6 and 0.9 the width of the entire port, but for the sake of greater precision in the cut-off and freer opening of the port at the commencement of the stroke, let us make its width equal about 1.5 width of steam port, or— W=1.5xJ"=l^ inches. Area of steam pipe (page 22) =371 sq. inches x. 032= 11.9 square inches. Area of exhaust pipe = area of steam port =17, 4 sq. ins. The respective diameters of these pipes will therefore be 4 and 4f inches. By the Travel Scale, the angular advance GENERAL E X A M P L E . 51 for the given cut-off of 110° equals (without lead) 35° and with a lead angle of say 6°, Angular advance will=3o° + 3 c =38 degrees, And lap angle will =35°— 3° =32 degrees. Now apply the width of port opening 1J inches to the 90° and 32° lines of the Travel Scale, as page 38, and we find that the Travel must=5f inches. After marking the Base line and angular advance we have — Lap =1 1 7 6 inches ; lead = -J inch. The bridge, page 47, should not be less than |"-j 1\"— -|" =| inch. If, however, the cylinder has a thickness of 1 inch the bridge must be made of the same width. Width of exhaust port, page 48, E=f +2f — l"=2f inches. Also we have the width of each valve face F and N= width of steam port -flap Equals, | n + l T V'=2y 5 g inches, And the total length of the valve or L= exhaust port -f 2 bridges + 2 faces=2| + 2+4|=9| inches. The angular advance being 38° the exhaust will close and release commence at the 142° angle of the crank (see Travel Scale) or at 0.895 of the stroke = 30" x 0.895 =26J inches and the cut-off take place at |x30"=20 inches; which embraces all the required dimensioiiSo PAET II. SHOET-HAND METHOD FOR VALVE PROPORTIONS. SHORT-HAND METHOD. The following table has been prepared by means of the Travel Scale: and embodies all its essential features. ■ Valve travel, Lap, The Exhaust For a cut-off should be : should be : will close at : ( width 6.6 times < of port C width 2.3 times ^ of port ( opening. 0.5 = Yz stroke. 0.85 stroke. ( opening. 0.55 6 1 a 2 " " 0.87 0625=^ " 5-3 ' i i( ,6 - - 0.89 " 0.64 " 5 c a , 5 " " 0.9 " 0.666= % " 4-7 ' t n 1.35 " 0.91 " 07 4.4 ' < 1.2 " 0.92 " 0.75 = X " 4 1 it j it a 0.93 " 0.8 36 ' t O.82 " 0.94 " 0.83 3-4 ' 1 a 07 " 0.95 " 0.875= H " 3-i ' i (< 0.54 " 0.96 " 0.9 1. 3 1 it 0.45 " 0.97 It will be remembered that in dealing with crank and piston motions we regarded the stroke as equal to Unity and their positions (at certain important periods) as decimal portions of the entire stroke. In this chapter Ave have set aside all consideration of lead, and made the extreme opening of the steam port by the valve, a Unit for measuring, how much travel and lap are necessary for a given cut-off? 56 VALVE PROPORTIONS, Take for example any extreme port opening — say 1| inches for a cut-off at § stroke ? We see by a glance at the table that the travel must be 4 times as great as the port opening, while the lap must be once the port opening, thus giving instantly the Answers : j Travel = 6 m ches. Lap = 1 J inches. 1 Exhaust closes at 0.93 stroke. Examples for Practice. Port opening = 1 inch, Cut-off = J stroke— Find the Travel, and lap.? = 1* " — 9 " Shifting Eccentric for Portable Engines. Fig. b. PART III. GENERAL PROPORTIONS MODIFIED BY CRANK AND PISTON CONNECTION CEAXK AM) PISTON CONNECTION". Thus far we have confined our attention to a form of connection called the " slotted cross-head," and have been able therewith to deduce laws governing the proportions of the various parts of the valve, as well as to devise a most simple and rapid method for determining their magnitudes. But since this connection seldom obtains in practice, it becomes necessary for us to analyze the form shown in Fig. 13, to modify their general proportions to accord with the new conditions and to eliminate as far as possible all the irregularities they tend to create. It will be observed, by inspecting this Figure, that the cross head pin is drawn a distance BB" beyond its half stroke position B", when the crank attains an angle of 90°, that this irregularity is due to the want of parallelism of the connecting rod, with its original position— during the progress of the crank pin in its semi-revolution— and that a rod of virtually infinite length produces a motion of the piston identical with that of the cross-head. It follows that the irregularity BB" will vary with the different ratios that may exist between the length of the crank arm and the connecting rod. In subsequent comparisons of these two terms, the length of the crank arm, will always be regarded 60 CRANK AND PISTON CONNECTION as the Unit measure and that of the connecting rod as a certain number of times the length of the crank arm. Let the crank arm C A "be equal to unity and the con- necting rod A B=4, then their ratio is that of 1 to 4, (1:4.) When the arm occupies the 90° position the cross-head pin will be drawn a distance B B" beyond the half stroke point Fig. 13. B". With B as a centre and A B as radius, describe the arc A A". If the occasion required, it might be readily proved that A", the point of its intersection with the line D E, is the same distance from C that B is from B". Placing the crank in other positions — as at 30°, 60°, 120° and so on — and describing similar arcs there will result like irregu- larities but of a less degree, all of which however vanish at the extremities of the stroke D and E. It becomes evident therefore that the effect of this form of connection is ; to carry the piston ahead of its proper positions throughout the forward strolce and on the return stroke to make it lag behind the positions due to the tocations of tlie crank pin. Consequently the one crank angle, for a given piston position (as in Table A), will no longer serve both the forward and return strokes, but a new table must be CKAXK AND PISTON CONNECTION. 01 constructed which shall furnish at sight the proper angles of the crank for various piston positions in both the For- ward and the Return strokes, and these for every important ratio of crank to connecting rod between 1 : 4 and 1 : 8 with which intermediate values may readily be determined by interpolation. Such is presented in the following Steoke Table. The fractional portions of a degree have been given as small as can conveniently be laid off with a protractor. By transposing the terms Forward and Return the angles in the Table will apply to the case of a "Back Action " Engine. For the irregularities of the motion are necessarily reversed in such instances, because the cross head and cylinder lie on opj)osite sides of the main shaft instead of on the same side. FIKST EXAMPLE. The connecting rod of a certain engine=8' 3" =99 fr . *o The crank arm =18 inches. Cut-off takes place at 0.65 of the stroke. Required — The forward and return stroke crank angles. Divide length of connecting rod by that of the crank arm : thus Their ratio therefore will be that of 1 : 5i. 62 CRANK AND PISTON CONNECTION. STROKE TABLE CRANK ANGLES. Piston Position. (Stroke = unity.) : (for ordinary connecting rod.) RATIO 1 : 4. RATIO 1 : 4|. RATIO 1 : 5. Forwarc l Return. Diff. Forwarc Return. Diff. Forward Return. Diff deg. deg. deg. fl&g-. deg. deg. dcg. <&£-• **■• o.i25=g 37g 46| 9s 37s 46} 8s 37g 45 1 7, 0.2 4S 59^ JI i 48J 58! 10J 48! 58g 9| 0.25 =i 54| 66| 12J 54 5 66 "8 55l 65s 5 10 0.3 6oj 73i 13 61 7 2 § "1 6i.i 72 10J °-333 = l 64! 77^ I3f 6 4 | 76* l2 S 65l 7 6;i io s" °-375 = f 68^ 8 2 | i3i 6 9 A 82 I2A 7oj 8i| 0.4 71J »5i I3b 7 2 f 84l I2± 73 844 "i o.45 77;! 9 J 2 I4s 78 g 9°,^ 12.1 781 90 nj 0.5 =\ o-55 824 97s I02§ i4s 1 8 3 | 89I 9 6i I2| 84| 95l I T "' li 8 Ilf 88^ IOlg I2 2 90 IOlj 0.6 94^ 108] i3i 95s I0 7g 12.1 95" 107 "4 0.625=1 97] nij i3i 98 110A I2i 98^ io 9 | II' 0.65 100^ "3l nl ioi B "3* * 2 s IOlf II2§ log 0.666=^ 1025 115! l 3'i ' io 3s "51 I 2 8 i°3f "4§ log 0.68 104 "7i I3l 104J n6| 12 io 5^ 116] io| 0.7 io6g ri 9i J 3 107* 119 «| 108 1 18 1 10J 0.71 107; I20| »i io85 I20| "1 109? "9! ioj °-73 110A 123] I2| 111J i22 i A1 8 112 122I IC S o-75 =! 0.76 113I 114S [2 5 2 I26| I2J 114 "5l I2 5s 126I "s 11 114JS 116J I2 4§ I2 5l IO ~9l I2 8 0.77 116^ I28J 12 1 164 I2 7| io| iiJi 127] 9| 0.78 n 7 | I29J n| -n8g 128I 10A 119 128.} 9^ 0.79 ii9i I30I "1 "9s 130! io| 120^ i2 9 | 9:1 0.8 120I 132 "I I2IJ 1313 IO] I2l| 1315 94 0.81 122^ 133] "I I22| !3 2 f IO I2 3. x 3 2 ^ 9 0.82 «3§ J 34g II I24-} 1344 9! 125 !33f 8] 0.83 I 2 5" 136 log 126 X 35,C 9i I26g i35s 8? 0.84 127 137J io± «7i 137 9l I28J 136I 8', 0.85 0.86 I28J I30A *3H IO] 1291 131? ^38i 9s _^3°_ r 3i| i3»i 139! 84 8| 140I 9l 140 8| 0.87 I 3 2 l 142 9i 133 1413 8| !33 2 141? 71 o.875 = I *33\ i 4 2| 9! !33f 142J 82 I 34i !4 2 S 7 V 0.88 J 34l r 43i 9i !34t x 43? 8 J 135? I42I 7- 0.89 *3H !45s 9 i 3 6f 144! 8" 137? 1 44 A 71 0.9 i38| i 4 6| 8f 138I 146I 7! !39! 146] 7 0.91 1 40 -\ 148A 8 141 148J 7! J 4i| 148 6^ 0.92 142-I 150J 7! H3i i5°s (>l !43g 149; 6J o-95 150I 156! 6 5 I 5 1 i 156A 5.5 r 5*i 156^ 4| (RANK AND PISTON CO N N E CTION. 63 STROKE TABLE. CRANK ANi (FOR ORDINARY COl . 1 Piston Position. (Stroke = unity.) RATIO 1 : &L RATIO 1 : 6. RATIO 1 : t>.!. Forward Return. Diff. Forward Return. Diff. Forward Return. Diff. deg. <*&-. deg. deg. deg. 3i 70 6,4 635 69! 6| o-333=l 66^ 74| 7;' 67 b 74l 7i 6 7 | 74 6^ o-375=| 7i§ 79i 7i 7iia 79s 75 7 2 ' 79s 7 0.4 74i 82.1 8 74| 82 { 7 J 75 82 7 o-45 8o| 88| «* 80A 88 7? 8o| 87? 7 0.5 =£ 85s 94i 81 86] 92 93] 75 86| 9 2 1 93s 99i 7i 7 o-55 9ig 99! 8| 99' 7-5 0.6 97A io 5' 8 97 4 3 105! 75 98 105 7 0.625=1 1 00 \ io8| 7s 1 oof 108^ 75 ioo| !07s 7 , 0-65 103' mj It I03I IIO? 7A 104 IlOf 6? o.666=| io 5' H3s 7s 1051 112I 7i 106 II2| 62 0.68 107] 1 14| 7A 107! "4i 7 1071 II4J 6.1 0.7 109I H7-] 7i no 116JJ 64 no] n6| 6| 0.71 in n8| 7^ IIX 4 ii8| 61 111A "7^ 6| o-73 ri 3i I20| 7? "3b I20| bj ii4s I2o| 61 °-75 =| 0.76 116J ii7| I2 3J 12 : 4b 7 7 n6| 1231 I24I 61 n6| I22| I24J 6| 6 ii7? 6,1 0.77 H9s 126 6; 119I I2 5f 6^ "9s I2 5^> 5s 0.78 I20.\ 127I 6| 120; 127 H 121 126^ 5^ 0.79 122 I28A 6A 122] 128I 6,5 1 22 A 1281 5s" 0.8 12 3] 130 6A 123! £2 9 | 6| I23s I2 9 g 5' 0.81 125 1314 6} I25fi I3IB 6 i-5; : r 3oI 5A 0.82 126^ ^i 3 61 126I T 3 2 i 5? 127 !3 2 ! S[ 0.83 I2SI 1344 6s 1283 i33s 5 5 128! 1334 5? 0.84 I29| i35s 6 I30 T 35i 55 13° ,- 1351 5s 0.85 131" i37i " I3 1 " 137 51 13 !| 136^ 5 0.86 J 33' 138! 5l 133! 138.1 5} I33A I38I 43 0.87 134! 140] 5A 135 140^ 5k < I 354 1 140 4! o.875=I I35l !4ig ^ 3 I36 140^ 44 136,. 140 j 4§ 0.88 !3 6 s 142 51 136^ 141 1 4; 137 141* 4l 0.89 I38.I i43s Si 138! 143^ 4? 138, i43i 4A 0.9 1 40^ 145' 4j I40V i45l 4i i 4 o| 145 4.! 0.91 I 4 2g 147] 4^ I4- 7 4 H7g 4l H3 i47 4 0.92 I44g !49s 4j 145 149 4 i45i 149 3 s °-95 i52| 155.-; 3l 152^ I55s; 1 ! 1 3g ; 1522 1554 2i E C C E X TRIC AND VALVE Co N N E CTION, 65 Referring to this Ratio column in the Stroke Table we obtain :■ Crank angle of the forward stroke for the 0.65 position 12|°. Crank angle of the return stroke for the 0.65 position 22 \ . Difference between the return and forward = 9 j-°. = 1221 • SECOND EXAMPLE. Stroke of piston =45 inches. Ratio of crank to rod=l : 6 J. Forward stroke crank angle=131]°. Return stroke crank angle =134f°. What locations will the piston occupy for these angles ? From the Stroke Table we learn that : — 131 \ J forwards piston location of 0.85 the stroke and 134f° return = piston location of 0.83 the stroke — consequently: 45" x 0.85 = 38 \ inches from commencement of forward stroke. 45"x0.83=37f " " " return ECCEXTEIC AXD VALVE COXXECTIOX. The principle of this connection has already been illus- trated by Fig. 4, its standard motion in Fig. 5, but as the latter rarely occurs in practice it becomes necessary to study the former with reference to its influence on the events of the valve motion. It has been observed that the combination is nothing more nor less, than that of a small crank with a long connecting rod, the valve will therefore move in precisely the same manner as the piston, and will have in its progress from one extremity of the travel to the 60 LEXGTII OF ECCEXTEIC PwOD. opposite, like irregularities, differing only in degree. In other words, when the eccentric arrives at the positions for cut-off and lead, the valve will "be drawn beyond its time position— measured towards the eccentric — by a distance dependent on the ratio between the throw of the eccentric and the length of its rod. Since this difficulty is corrected by lengthening the rod, it follows that the width of the port opening in one stroke, will slightly exceed that in the other. This is practically the only effect produced by the use of the true eccentric connection ; although strictly speak- ing there is besides a slight difference in the equality of the exhaust closure, yet in no case does this become sufficient to affect the general action. Neither is the difference in the opening appreciable in stationary engines, for their ratio of eccentric throw to length of rod is usually that of 1 : 20 or 30, which gives a variation too small to influence the general admission of the steam. It does not come within the province of this work to introduce and explain The Indicator* — that most valued friend of the Engineer, whose card ever furnishes clear and indubitable proof of the character, time and correlation of the various events taking place within the cylinder, but the Author cheerfully testifies to its many excellencies and commends it to the Reader. * For a complete analysis of this instrument, its practical operation, etc., the reader is referred to Mr. Charles T. Porter's Treatise on the Richard's Steam Indicator, enlarged by F. W. Bacon, M. E., and published by D. Van Nostrand, New York. PART IV. LINK MOTIONS. LINK MOTION. The various mechanical devices embraced under this general term, have many strong points of resemblance and subserve a common object. By means of them, the Engi- neer is able at will to change the direction of the crank ro- tation, with only the loss of the time required for overcom- ing the momentum of the moving parts, and developing the like in a reverse direction. More than this simple result was not contemplated in the original discovery of the link. Subsequently, however, it was found to be capable of regu- lating the cut-off of the steam, so that the power could always be adjusted to the work required. This feature greatly enhanced its value, and placed the engine under the complete control of the operator. The extreme simplicity of the parts of the link motion, has enabled it to contend successfully with all rivals, and at the present day it remains in substantially its primitive form. It is applied principally to locomotive and marine engines, where the power demanded is quite variable, and the motion at one time direct, at another reverse. The designs may be divided into four classes : I. The shifting link motion. II. The stationary link motion. III. The Allan link motion. IV. The Walschaert link motion, 70 SHIFTING LINK MOTIONS, The first form was invented by Mr. Howe, in 1843, and applied to the locomotives of Messrs. Robert Stephenson & Co. It is in fact the representative link motion, which, ex- cepting slight modifications in the mode of suspension, remains unchanged by the accnmnlated experience of a quarter of a century. Simultaneous with the appearance of this motion was that of the second, the discovery of Mr. Daniel Gooch. It accomplishes perfectly analogous results, and has met with much favor throughout Great Britain and the Continent. The "Allan" combines the characteristic features of the Howe and Gooch link motions in such a manner that the parts are more perfectly balanced, consequently it dis- penses with the counter weight or spring peculiar to the former of these motions. The Walschaert motion is extensively applied in Bel- gium, but probably will not receive much attention from locomotive Engineers, beyond the limits of that Kingdom, unless future designers succeed in reducing the number of its connections. It is proposed to confine our investigation to the shifting link motion, to develop the general laws governing its ac- tion amid varied conditions, to present graphic methods for determining the proportions of the parts, and briefly to point out the general application of the same to the link motions of the other three Classes. SHIFTING LINK MOTIONS. A link, operated by two fixed eccentrics, forms when properly suspended an exact mechanical equivalent of the movable eccentric. Unlike the latter, however, its motion is SHIFTING LINK MOTIONS. 71 capable of an accurate adjustment, which practically nulli- fies the effect of irregularities in cut-off and exhaust closure, attributable to the angularity of the main connecting rod. The general form in which its parts are arranged in American locomotive practice, is clearly shown in Fig. 22. Upon the main shaft are keyed the forward and backing eccentrics, with their centres at F and B, so located as to secure the most appropriate angular advance. Then- straps are bolted to the eccentric rods, and these in turn are pinned to the "link." The slide valve is attached by its stem to one of the rocker arms, and a "block" sur- rounds the pin of the opposite arm, which fits the main link and slides freely therein. The centre of the link is spanned by a plate called the " saddle," on which is formed the pin or stud that supports the link and eccentric rods. This pin is embraced by a bar called the "hanger," or sometimes the suspending or the sustaining link, from its position and the service rendered to the motion. The former term is preferable on account of its conciseness, and can lead to no confusion. The opposite extremity of the hanger is attached to one arm of the tumbling shaft. Both arms of this shaft are rigidly secured, and form upon it a "bell crank." The shaft itself freely oscillates on prop- erly supported bearings, but is limited in its motion by the action of the reversing rod. The link has been dropped into the full gear forward, thus throwing the entire influ- ence of the eccentric F upon the valve motion to the almost complete exclusion of that of its mate B. By drawing back the reversing rod and raising the link until the pin of the other eccentric rod is brought in line with the pin of the rocker arm, the link will be made to occupy a location ap- propriate to a negative crank movement (4th quarter, Pig. 9) and Intermediate suspensions will in like manner be pro- 72 SHIFTING LINK MOTIONS ductive of earlier cut-off and exhaust closures. In order to clearly demonstrate that such similarity exists between these motions, it will he necessary to reduce Fig. 22 to a skeleton form like Fig. 23, and follow the journey ings of the "link arc" throughout a complete revolution of the crank. Let the path of the main crank pin be represented by the circle E D in Fig. 23. This being divided into 12 equal parts, gives a sufficient number of positions for the purpose of tracing the motions of the link arc. The zero mil be known as position No. 1, the 180° as position No. 7, and so on. Within this circle describe the path of the eccentric centres by means of the circle F B If. This should first be divided into 12 equal parts, with F as the origin of one ec- centric's motion, and again into 12 other equal parts with B a*s an origin, so that when the crank moves from position No. 1 to 3 the new positions f 3 and b 2 of the two eccentrics may be instantly found, and the same with other locations. The original positions F and B are of course laid off with the angular advance due to the proposed maximum cut-off. At the distance C t from the centre of the shaft erect the perpendicular T t and locate T the fixed centre of the tum- bling shaft. T li will represent the arm which supports the link through its hanger and Ti 7i' W the arc described by this arm. A second perpendicular at the distance C A will contain the point K, the centre of the rocker shaft, whose arm R A sweeps the arc r A r. The motion of the upper arm, being merely the reverse of the lower, need not be considered, and so long as the angular advance is properly located no error can arise from the omission. In the mo- tion of the lower arm there are five locations of vital im- portance, viz : one at which the exhaust of the valve opens or closes, two appropr'ate to the lead at full gear of the 8 H I F T ING J. I N K M TI N 8 . 73 link, and two at which cut-off lakes place or the valve closes its ports. The 1st is evidently the normal position R A of the rocker, the 2d E d, R d\ that in which the rocker pin I- drawn aside a distance A d equal to the sum of the lap and lead, and the 3d R /, 11 /' corresponds with a removal A I equal to the lap. Hence, so far as the slide valve is concerned we can confine our attention to the mo- tion of the rocker arm pin upon the arc r r. The five posi- tions in question can be distinctly located by sweeping a circle d d ! , with a radius equal to the lap pins the lead of the valve, around the exhaust point A, and inscribing a second circle 1 1' with a radius equal to the lap of the valve. Then the four points in which these circles intersect the arc r r will give the 4 positions of the pin corresponding with the lead and cut-off positions of the valve, and the centre of these circles will give the exhaust closure positions. As these locations will be constantly referred to in the sequel, it should be remembered that the "lead circle'' d d' iixes those points on the arc r r which the pin of the rocker arm must occupy when the valve has a given lead ; and that the "lap circle" I V locates the positions of the same pin for the moments at which the steam ports are closed against the admission of steam to the cylinder. Our next duty will be to reduce the link to its simplest form. It appears on examination that the rocker pin is entirely subject, in its motion, to the guidance of the link arc, and that this arc swept with a radius C A is rigidly connected with three moving points, viz. the saddle pin, and the two eccentric rod pins. In following the motion of the link arc, the connection of the parts can best be maintained by the use of a template, cut from white holly veneer or other hard wood and shaped like L L in Fig. 23, upon which are 74 SHIFTING LINK MOTIONS. made V shaped incisions for locating the points /, S and b of the pins. We are now prepared to find position No. 1 of the link corresponding with No. 1 of the crank. Of course when the crank is at the zero the steam port should be opened an amount equal to the lead of the valve. The rocker arm therefore will occupy the position R d, and the point d lie in the link arc. Since the eccentric centres F, B are found in a line perpendicular to the central line of motion, and the eccentric rods are of equal length, the link must occupy a nearly perpendicular position. Place the template so that its arc coincides with the point d and mark the point /upon the paper, then the distance from F to f will equal the length of the eccentric rod. With this length as a radius describe about F as a centre the small arc / g, likewise with B as a centre describe the small arc b li. Apply the template to these arcs so that the points f and b shall be found in them and the point d on the link arc n c d, after which, draw the link arc on the paper and we obtain posi- tion No. 1 of the link. With the saddle pin S as a centre and the length of the hanger li S as a radius, the position T 7i of the tumbling shaft arm is readily found for full gear of the link and conversely the arc c S c is fixed along which the saddle pin must travel during the revolution of the crank. The preparatory stages of our solution are now complete, the link motion of Fig. 22 has been reduced to its skeleton form and the first position of the link located. Our next step is to follow the link arc during its jo jrneyings in a single revolution of the crank. Suppose dien, the crank is made to occupy position No. 2, the eccentrics will be carried forward from F and B to/' 2 b 2 . Since the length of their rods remains unchanged the arcs ./ g, b h, will be / >'//// v// /////' of', \fation SHIFTING LI.XK MOTIONS. Fig. 24. 75 "5t PIN± ( ENTRAi LINE OF MOTION 7 removed from their first position and the link template will follow them with its points h and /. The only restraint 7 7G SHIFTING LINK MOTIONS. upon the course of this template is that the point S must travel on the hanger arc c c. If therefore we describe new arcs about the centres / 2 b 2 , and adjust the template so that / and b shall be found in those arcs and S in the arc c c there will result a new link position with its arc standing like 2 2 in Fig. 24 and intersecting the rocker pin arc r r at a point Jc. But as the rocker pin necessarily follows the course of the link arc it will by this change be drawn aside from d to k, coisequently the steam port will be opened wider by the extent of the horizontal measurement of this distance. In like manner when the crank is carried to position No. 3 the link arc will be removed to 3 3 as in Fig. 24, and the rocker pin to V, producing thereby a still wider opening of the steam port. The same process applied to the remainder of the 12 crank positions will give the other locations of the link arc (as in Fig. 24) for the full gear of the link. Now observe that the link position 3 3 pro- duces the widest opening of the steam port, and as the crank advances to 4 and 5 this opening grows less and less, until between 5 and 6 the rocker pin reaches the point Z, where the steam is finally cut off. During its further progress expan- sion goes on and at last when A is attained the exhaust opens and the steam escapes. At position No. 7 (the 180° location of the crank) the link arc is brought again in con- tact with the lead circle and a like process is repeated throughout the return stroke. A duplicate set of link arc locations, might readily be obtained by raising the link to the full gear back position and a similar set for the mid gear, but an examin- ation of the one just found will develop the character of the motion. ADJUSTMENT OF LINK MOTIONS. Besides the qualities possessed in common by the two motions, the link has that of adjustability, a very impor- tant feature, and one which specially characterizes it. As the tendency of the connecting rod angularity in a direct acting engine is to produce a later cut-off on the forward stroke than the amount required, and since with the link the cut-off in either stroke depends on its degree of elevation or depression ; it follows that if we suspend the link in such a manner as to cause a suitable elevation for the for- ward stroke, the result will be a perfectly equalized motion for the gear in question. And again if the equalization be made applicable to all gears, then the link may be suspended at any point between the full forward and full back without an appreciable inequality appearing between the cut-offs or the exhaust closures of either stroke. But a practical difficulty here arises ; the link block moves upon a fixed arc r r while the link rises and falls, consequently for each revolution of the crank the link will slip back and forth a certain distance on its block. Should this slip be excessive in any particular gear and the engine run a long time in this gear, the faces of the link would become worn, u lost motion" would ensue and the delicate action of the parts would be destroyed. Hence in planning a serviceable link motion it is neces- 78 CONNECTION OF ECCENTRIC HODS. sary to reduce the slip of the link to its smallest value, con- sistent with the equalization of the motion, and in marine engines to even sacrifice the equality of the cut-offs to the reduction of the slip. In Fig. 24 the motion of the two fixed points (m and n) on the link have been traced in looped curves. The upper of these, shows to what extent the point m falls below and rises above the arc r r, giving a slip equal to the distance S plus S'. It is important to observe that the magnitude of the slip grows smaller and smaller as the link block draws nearer to the point of suspension, because this fact indicates that the stud of the saddle should be placed — when a minimum value of the slip is required at a certain point of suspen- sion — as nearly over such point as possible. COX^ECTIOISr OF ECCEISTTEIO RODS. The variable character of the lead opening in a shifting link motion depends upon the manner in which its eccen- tric rods are attached, and its magnitude depends on the length of those rods. The force of this remark will appear from an examination of Figures 26 and 27. In both instances, the eccentric centres lie between the centre of the shaft and the MnTc, while the latter for sake of simplicity has been made to act directly on the valve. The No. 1 position represents the mid gear, and No. 2 the full gear forward of the link. If under these conditions the eccentric rods be crossed as in Fig. 26 the lead opening will decrease from the full to the mid gear of the link, where the motion may even be without lead. But with the open rods of Fig. 27 the lead opening CONNECTION OF ECCENTRIC RODS. 79 Fig. 26. Fig. 27. increases from the full to the mid gear, and the rapidity of this increase, for a given link, depends directly upon the length of the rods ; hence with a given mid gear lead open- 80 COX SECTION OF ECCENTRIC EODS. ing that for the full gear will be determined mainly by this length. Excepting the case of valves having an independent cut-off (Part Y.) the rods are seldom crossed as in Fig. 26, yet there are good reasons for believing that many instances exist in which the arrangement might be adopted with good results. It is also possible, with such a motion, to stop the engine by placing the link in the mid gear ; but this can never be done with a motion like Fig. 27, whose valve is invariably opened a certain amount in the mid gear. The extremes of mid gear lead opening in loco- motive practice are J and ^ an inch, but the more common value is f inch ; while the full gear lead varies between ^ and T 3 e inch, governed principally by the length of the ec- centric rods. With the stationary link the lead opening remains un- altered by changes in gear ; so that if § inch be assumed as the proper amount for the full gears, the motion will retain this lead for all gears between these extremes and the mid gear. This peculiarity is not inherent with the stationary link, since many shifting link motions may be arranged with a Constant Lead for the various gears of one direction of the motion. Take, for example, the motion shown in Fig. 22, in which the angular advance of each eccentric equals 21° and the lead enlarges from J" in the full, to T % n in the mid gear. By imparting an angular advance of 31° to the eccentric F, while that of B remains unaltered, the lead opening becomes constant for all points between the full gear forward and the mid gear, and diminishes from j' - 6 - inch in the mid gear to J" in the full gear back. Vice versa for a change in the angular advance of the eccentric B. CONNECTION OF ECCENTRIC RODS. 81 PRACTICAL OBSERVATIONS. (based on fig. 22.) I. The tumbling shaft must be located at such a dis- tance above or below the central line of motion, that neither eccentric rod can strike against it when the link is moved from one full gear to the other. Special cases may arise that demand a curvature of the eccentric rod, but the prac- tice in general should be discountenanced. II. The hanger must be of such a length that the ex- tremity of the link will not conflict with the tumbling shaft arm in either forward or back gear. The length of the tum- bling shaft arm is usually equal to or greater than that of the hanger. III. If the link cannot be placed in full gear back, owing to the arrest of its tumbling shaft arm by the boiler or other opposing object, either the tumbling shaft must be removed and located below the link motion, or the rocker must be lengthened in order to depress the central line of motion and with it, the entire motion. When the latter ex- pedient is resorted to, a change should be made in the rela- tive positions of the rocker arms, for the purpose of pre- serving the identity of their motions. The proper inclina- tion W of the arms is found by describing a circle rttr (Fig. 28) tangent to the central line of the valve stem, or aline sufficiently above the same to equalize the vibration of the stem, and the central line of the motion. Radial lines from the points of tangency will then give the relative positions of the arms. This method of correction is preferable to the former in respect to the symmetry of the motion, because the greater the length of the rocker arm, the less will be the vibration of the valve stem, as well as the slip of the link block. 82 CONNECTION OF ECCENTKIC EODS. Fig. 28. ^^^m IV. So long as the angular advance of the eccentrics is laid off from a line at right angles to the central line of the link motion, the latter can be arranged at any inclination to the piston motion, withont affecting the action of the link. These central lines were made to coincide in Fig. 22, merely for the purpose of simplifying the investigation, whereas they might have formed with each other any angle what- ever (see Fig. 52, Part V). GENERA L 1) I M E N S I N S . 83 GEXEEAL DIMENSIONS. In ordinary locomotive practice the dimensions of the various parts range between the following extremes : Ratio of crank arm to connecting rod 1 : o] and 1 : 8. Travel of valve 4 to 6 inches. Maximum cut-off from f to 0.92 of the stroke (gene- rally =|). Mid-gear lead j" to §", usually the latter. Full gear (dependent on length of rods) ^" to T 3 6 ' f . Radius of link 3' 6" to 6 ft. Distance between eccentric rod pins 10" to 14". Pins back of link arc 2\ to 3 inches. Saddle-stud back of arc 0" to 1^ inches. Stud above central line of link 0" to 2±". Length of hanger 12 to 20 inches. Length of tumbling- shaft arm 14 to 22 inches. Length of rocker arm 8 to 11 inches. The following special dimensions, collated by the Master Mechanics' Associations, are indicative of the prevailing practice on thirty-five of the railroads of our country : Number of Roads and Class of Locomotives. Accomd. Roads use on their Express Pass, locomotives 5 4> ! 4 ' 5 5 5VS 4', 5 I 4' 4 Freight lecomotives. CD P *1 in. in. in. 1-10 % 1 % 1-16 1 1% yi V 1-10 y» 1-16 1-16 ',. 3-16 '. 1-10 1-16 1-16 l A 1-10 3-15 84 GEOMETRIC SOLUTION. GEIEEAL PRINCIPLES. OF THE GEOMETRIC SOLUTION. A cursory examination of the link motion might natu- rally lead to the conclusion— from the simplicity of the parts and the strong resemblance existing "between their ac- tion and the single eccentric' s — that the theory of the latter being perfectly comprehended, but little difficulty would attend the work of assigning proper proportions to the former. Such an inference, however, would not be strengthened by a closer inspection, much less sustained by an intelligent effort to accomplish a solution. The reason for this fact lies not only in the multiplicity of the parts, but also in the conflicting character of the elements that constitute a perfectly equalized link motion. The requirements of such a motion are— perfect equality of cut-off, of exhaust closure, lead opening and maximum port opening, together with absence of block slip, between the forward and return stroke of the piston for every sus- pension of the link from full gear forward to full gear back. Such theoretical excellence is absolutely impossible with the ordinary type of link motion, and efforts made to attain the same must necessarily result in failure. But good practical qualities may be obtained by sacri- ficing the non-essential to the essential points of the mo- tion. The action of the connecting rod on a link motion, may justly be compared to the distorting effect of pressure exerted upon one point of a symmetrical india-rubber ball, producing thereby a temporary concavity. This it is true can be removed by an even application of additional pres- sure to the adjoining parts, but the ultimate effect will be a bulging out of the central portion, and the symmetry can GEO M ETHIC SOLUTION. OO alone be restored by withdrawing all pressure. Just so with the link motion, the angularity of the rod tends to ren- der one or more events of the motion unequal in the oppo- site strokes of the piston, and should it appear more desira- ble to preserve certain ones of these than others, we must purchase their equality at the expense of the latter. Re- ducing the angularity of course diminishes its disturbing effect, hence in departments like locomotive engineering, where much attention is bestowed on the equalization of the motion, crank and connecting rod ratios of 1 : 7 or 8 obtain ; while in marine engineering ratios of 1 : 4 or 5 are common. The subject of preserving the equalities of cut-off and exhaust closure at the expense of lead and port openings has been considered already. It will only be necessary to examine it here with reference to the mid gear. At this point the port and lead openings attain their minimum value, which being much less than the 0.6 or 0.9 port open- ing required for perfect admission, tends to reduce the pres- sure of the steam by wire-drawing, and if these openings vary, unequal powers will be applied in opposite strokes. Consequently the mid gear, lead and port openings must have equal values in both strokes, however irregular they may be in the full gears. No fixed limit can be assigned to the slip of the link on its block, but the amount allowa- ble under different conditions will readily be determined by the judgment of the Engineer. In every case, the main ob- ject is to reduce the slip to a minimum value for that gear in which the engine will be most frequently operated. GEOMETRIC SOLUTION, LINK No. I In designing an engine, as a general thing, no particular part can be isolated, its proportions assigned, and its details worked out regardless of the conditions inevitably imposed upon it by the character of the adjoining parts ; but rather, trial dimensions must be affixed, their adaptability tested and modified by circum- stances, and finally all must be — ■ unfolded and developed in per- fect harmony. When the sub- ject of scheming the link motion comes in order, we find that pe- culiarities of detail have already fixed the ratio of the crank arm to the connecting rod, have pointed out a convenient location for the rocker shaft and have more or less circumscribed the boundaries of the entire motion. Since methods of construction are always most intelli- 88 LINK NO. I. gibly presented when tlie mind is able to follow their ope- ration in the solution of a practical example, we will take for illustration of our method the following dimensions : Ratio of crank to connecting rod— 1 : 7J-. Eccentric circle diameter=5J inches. Maximum cut-off=0.92 stroke. Rocker from shaft = 49 \ inches. c. to c. of eccentric pins =13 inches. Pins back of link arc =3 inches. Mid-gear lead = | inch. To find lap, full-gear lead, point ol suspension of link and location of tumbling shaft. Spread upon a long drawing board, or table, two sheets of paper large enough to contain figures similar to 29 and 31 when drawn on the Full Scale. The one will be used for locating the various important positions of the eccentric centres ; the other, for the journeyings of the link and its point of suspension, their centres should therefore be sepa- rated by the proposed distance between the shaft and rocker. Stretch a fine thread tightly across both papers in order to locate the right line ECDA, which constitutes the Central line of Motion* Describe about the point C as a centre the eccentric circle EFD, with a radius equal to the throw of the eccen- tric. Then, with the points of intersection E and D as centres describe with an assumed radius equal arcs inter- secting at Gr and H and erect the perpendicular Gr C H to represent the neutral positions of the eccentrics. From this * The use of the T square should be avoided in all of the constructions. LIXK X<> 89 line lay off an angular advance appropriate to the desired cut-off. This may be found in the subjoined Table : Cut-; Angular nice. Return Stroke M iximum 1 ul 1 >ff Angle. 0-75 = 1 28 degTces. 124 degrees. 0.8 25 « 130 " 0.84 22 " 136 " o.875 = I 20 140 " 0.9 17 « 146 0.92 16 148 « ! In the present case the advance equals 16°, which laid off, by means of a protractor, from the line C Gr, determines the position F of the forward motion eccentric when the crank stands at the zero. In like manner B might be found, but it will always prove more convenient and accurate to take in a pair of dividers the distance between F and the point of intersection of the circle with the line Gr C and then prick off from the line G H the points I), f, B. AVe thus obtain the two positions F and B of the forward and back- ing eccentrics when the crank stands at the zero, as well as their new ones/ and b for the 180° location of the crank. It is well known that the inequality of the crank angles attains its maximum value at the J stroke of the piston, hence the importance of examining the link motion with special reference to the J stroke c nt-off. Although appropr i a t< k angles for the crank have been furnished in the Stroke Table, it is thought best for facility of reference to here reproduce them in a more compact form. 90 L I X K X . I Crank Angles for Half-Stroke Position of the Piston. Ratio of Crank to Connecting Rod. Forward Stroke. Return Stroke. i : 4 82I degrees. 97 J degrees. i : 4 ^ $3:i " 9 6J « i : 5 84J " 95,' " i:5} 84] " 95* " 1 : 6 855 " 94 ]. « 1 : 6A 85 1 " 94. ; " 1 : 7~ 8 5 3 " 94! " 1:7* 86 j " 93? " 1 : 8 86;; " 93s " If the ratio of crank to connecting rod be that of 1 : 1\ the two eccentrics will advance 86J° from F and B while the piston travels to its forward \ stroke location, and 93 f° frcm / and b for the return stroke. A very convenient way of locating these four points is to lay off from C F by means of a protractor, the point \ f distant 86£°, and f\ distant 93|° from /C. Then with a pair of dividers prick off these points at equal distances on the opposite side of E and D giving thereby the two other points \b and bh In the nomenclature here adopted the letter f refers to that eccentric which produces a forward or positive motion of the crank, while b always designates the eccentric for the back or reverse motion. When a fraction is prefixed to either of these letters, it signifies some forward stroke position of the piston with the link in the forward gear, but if it follows the letter a return stroke of the piston with the link in the same gear. Thus, tiie ^/'represents the position of the forward eccentric when the link is in the forward gear and the piston has advanced to its forward \ stroke location, and f\ represents the same when the piston has attained its \ stroke return position. Having accurately located these eight important positions [ratio , 1 7i .] FIGURE 29 Central line of ^Motion. figure: 30. Forward LINK NO. I. 91 of the eccentrics, we pass to the other sheet of paper and trace their influence on the proportions of the link attach- ments. Since the assumed distance of the rocker from the shaft is 49J" and the eccentric rod pins are withdrawn 3" back of the link arc, the length of each rod will equal 491"— 3" = 4<>[''. Adjust a pair of beam compasses to strike arcs of 46 \" radius. Step the needle point successively in the eight loca- tions of the eccentric' s centres just found, and sweep from the central line of motion the same number of indefinite arcs (as shown in Fig. 30) upon which the eccentric rod pins must inevitably travel for the four given positions of the crank arm. Next, from a piece of white holly veneer cut a template L (Fig. 32) having a link arc of 49 J" and with V incisions, 13" apart and 3" back of the arc to represent the location of the eccentric pins, and draw upon the same the three parallel lines f m,J S, b n ; making,/ S lie midway between/ and b as w T ell as perpendicular to a line joining these points. We are now prepared to trace the journeyings of the link arc. I. TO FIND THE MID-GEAK TEAVEL. For this purpose place the template in the mid gear positions ISTo. 1 and 2 (Fig. 31) with its eccentric pins on the arcs F, B, ./', &, and mark the points d', d 2 in which the link arcs intersect the central line of motion. Locate these points permanently by describing a circle through them, having its centre A in the central line. This point gives us the true location for the rocker shaft, the distance from the main shaft being equal to C A instead of 49 J '■'.'•• Through A. therefore, erect a perpendicular A R to the central line of motion and on it locate the centre R of the rocker shaft, * Their difference is always so trifling that the rocker box may readily be moved the proper amount and much difficulty of construction be thereby avoided. 92 LINK NO. I. II. To FIND THE LAP OF THE VALVE. From d) and d 2 lay off the mid-gear lead opening of | inch towards A, and permanently locate the positions thus found by sweeping about the centre A a second circle I V. But since the mid-gear travel invariably equals the sum of the laps plus the mid-gear lead openings, the diameter of the circle I V will equal the sum of the laps, consequently the simple lap of the valve must equal its radius A I or A l\ Fig. 32. The following Table will aid the designer in the selec- tion of a suitable lead oj)ening after the mid-gear travel has been determined. For since the value of the lead angle may range between about 30° and 40°, the widths of the openings will be those found in the Table. Of course much latitude is here allowed to the exercise of individual judg- ment, for the subject demands it. Observe, the larger trav- els are only found on marine engines : MID-GEAR DIMENSIONS. Mid-gear Travel. LEAD OPENING FOR A LEAD ANGLE OF SO . 35°. JfO . i inch. J inch. T 3 g inch. \ inch. t l a 3 " i it 5 a Itt Hi 4 1 6 o ~ " 1 u 3 « 7 « 2 4 8 1 6 r> 1 " 5 a 7 " 9 " 2tt 1 6 1 6 16 - a 3 « 1 << 11 cc 8 •> 1 6 -> 1 » 7 a 5 " 1 3 u O .' 1 6 8 ] 6 A " 1 a 1 1 u 1 5 " 4 1 1 o 1 6 III. TO FEND POSITION OF THE STUD FOE EQUAL CUT-OFFS AT THE \ STROKE OF THE PISTON. Place the template in position No. 3, with its eccentric pins on the forward ^-stroke elements \f\ &, and its link arc in contact with the lap or cut-off point I. Then mark upon the paper the position ,/ S occupied by its central line LINK X O . I . 9:] together with a portion of the link arc. Next, place the template in the position No. 4, with its pins on the arcs./' • , b i and link arc over the other cut-off point I', after which mark on the paper the second position, / S', of the link cen- tre line. Having decided to suspend the link centrally, the point of suspension must be found on the line,/ S, and con- sidering the manner in which it hangs from the tumbling shaft it is evident that for a short distance the stud will practically move along some straight line c c parallel to the central line of motion. The point of suspension therefore must reside in the central lines j S, / S f , must be equally remote from the link arcs and at such a distance that a line drawn through the two points will prove parallel to the cen- tral line of motion. The only two positions satisfying such conditions are S and S', found by trial distances laid off with a pair of dividers from the two link arcs. Having se- cured the proper distance for the stud, fix it permanently, by making a V incision in the link template ; for as our subsequent study of the link will be intimately associated with the motion of this point, it is important to be able to mark its position for other gears of the link. The inequality of the crank angles for different positions of the piston attains its maximum value at the \ stroke and gradually fades out at the extremities, and since we have equalized the cut-off for the \ stroke, it only remains to per- form the same office for the maximum cut-oft* before we practically equalize the motion for all intermediatt gears between the full and mid gears. Our next step, therefore, will be to return to Fig. 29 and map on it the four positions of the eccentrics for the maximum cut-off. The third col- umn of the Angular Advance Table gives the maximum cut-off angle for the return stroke, which in the present in- stance=148°, and the Stboke Table shows that the forward 94 LIXK X O . I . stroke angle is 4^° less than the return, or=143f°. With these angles known, the four positions for the maximum cut-off may be readily laid off with a protractor, but the nature of the case enables us to present a more rapid solu- tion. From C F (Fig. 33) lay off an angle of 143f°. This locates the forward eccentric position 0.92/ in the forward stroke. On the return stroke the same eccentric will be found at the old point b. Take the distance 0.92/' from/, in a pair of dividers and lay it off from b in order to find 0.92b. In like manner take that from/ to B and lay it off from B, giving thereby b 0.92 the last one of the four maxi- mum cut-off points sought. With these points as centres and the length of the eccentric rod as radius sweep indefi- LINK NO. I . 95 nite arcs (as shown in Figure 34), on which the link tem- plate may travel in the full gear. IV. TO LOCATE THE TUMBLING SHAFT FOR ACCOMPLISH- ING AN EQUALIZED CUT-OFF IN ALL GEARS. Slide the link template with its eccentric rod pins on the elements 0.92/; 0.92 b, until its link arc comes in contact with the lap or cut-off point I (position No. 5) and mark the point S 4 occupied by the stud. Again, slide the template on the return stroke elements /0.92 ; b 0.92 until its link arc is in contact with the other lap point V, and mark the stud position S 5 . Join the points S 4 S 5 by a line c 2 c% which is found to have an inclination to the central line of motion of about 5° instead of parallel- ism* as with c c. By projecting the eccentric position points to the oppo- site side of their circle, sweeping indefinite elementary arcs with the eccentric rod as radius, and applying to them the link template, a corresponding set of stud locations S 2 , S 3 , S 6 , S 7 (Fig. 35) may be found for equal cut-off in the back gear. But such efforts are uncalled for in the class of mo- tions just described, because their back motion will be a precise counterpart of their forward motion, consequently the latter may be reproduced from the former, as in Fig- ure So. Having thus determined 8 positions of the centre of sus- pension for equal \ strokes and maximum cut-offs, it only remains to sustain the hanger in such a manner that for the different elevations it will sweep arcs passing through all •of these points. Arcs of intersection formed with an as- sumed length of hanger as radius and these points as cen- * Parallelism might be secured by moving the stud S to within a distance t of the link arc (see Fig. W), but such a change would destroy the equality of the £ stroke cut-offs. 90 LINK NO. I. tres will locate the points li and h\ and in like manner the tumbling shaft arm will determine its centre of shaft T. * V. To FIND THE LEAD OF THE EOEWAED AND EETUEN STKOKES IN THE EULL GEAE. Having swept with the hanger an arc & c 2 (Fig. 36) upon which the stud travels in the full gear of the link, slide the template on the forward lead elements F, B, until its stud lies at S 7 in the full gear arc & c% and mark the point d in which the link arc then intersects the central line of motion. In like manner slide the template on the return stroke elements/', b, and mark the intersection d Q . The distances of these points from the lap circle will equal their respective leads. Thus in the forward stroke the lead equals I d in the full gear, but I dJ in the mid gear ; while V d s equals the lead opening of the full gear return stroke, but I' d 2 of its mid gear. In the present case both mid-gear leads were made equal to each other. Their slight variation in the full gear has absolutely no effect on the motion. YI. EXTEEME TEAVEL AND SLIP OF THE LINK. Referring to Fig. 34 we observe that the forward eccen- tric attains the extreme points of its throw at D and E on the central line of motion at which times the backing eccentric occupies the positions T and U. [The latter points may be laid off from D and E with a pair of divi- ders set to the distance F &.] By sweeping the elementary arcs of the eccentric rod pins for these points and adjusting the template thereto, we obtain the positions Nos. 9 and 10 * If the ratio of crank to connecting rod had been that of 1 : 5 or 6, the lines c 2 c 2 , c 3 c 3 would have had a greater inclination to the central line of motion, thereby removing h and h 3 to 7i 4 and //■>, and depressing the shaft to some im- practicable point T 2 , where it would have been brought in contact with the for- ward eccentric rod when the link was in the back gear. The proper adjust- ment for such a case will shortly receive our attention. M I' I F I C A T I o N S. 9t (Pig. 37) and are able to mark the extreme points Q, p, of the rocker arc which are separated by a horizontal distance equal to the extreme travel. For position No. 8 the fixed point m on the template attains its maximum elevation above the link arc, and now, at the extreme throw, its greatest depression below that arc. The maximum slip will consequently equal the distance from p to o on the link arc. This slip grows less and less the nearer the stud approaches the rocker pin, and if the intention should be to use the link principally in the \ gear this amount of slip would not prove detrimental. MODIFICATIONS. AVe have thus far, as concisely as possible, presented a geometric method for determining the proportions of all link motions, similar to those illustrated in Fig. 22. But its application cannot be considered universal, until certain expedients are explained, by which some of the results may be varied at will and also the motion corrected, when the ratio of crank to connecting rod is other than that of 1 : 1\. I. HOW TO REDUCE THE SLIP. In the link motion of Fig. 37 the greatest slip occurs in the full gear and the least in the mid gear. Now it fre- quently happens that after designing a motion the maxim um slip is too great for practical purposes and the query arises : what change should be made for effecting its reduction \ There are four varieties of alterations capable of accom- plishing this object, which we will here mention in the order of their relative efficiency. 98 MODIFICATIONS 1st. Increase the Angular Advance. 2d. lied nee the Travel. 3d. Increase the Length of the Unix. 4th. Shorten the Eccentric Hods. Any one or more of these agencies may be employed at the discretion of the designer and a more perfect motion be produced. Thns we conld diminish the slip to J of its pres- ent value, by either increasing the angular advance to 30°, or \)j reducing the travel to 4 inches. Of course any snch change involves an entire reconstruction of the motion in accordance with the principles already explained. II. HOW THE SLIP MAY BE DISTEIBUTED. Eeferring to Fig. 24 we observe that the general tendency of the fixed point m is to move in an arc the reverse of that pertaining to the rocker pin, while n traverses one more or less parallel. The maximum slip of the forward gear con- sequently exceeds that of the back gear. These quantities can be equalized in great measure by placing the stud, not on the central line j S between/ and &but, upon some parallel line nearer tof than to b, usually from 2 to 2% inches above j S. In such case the proper location for the stud is found by first drawing such a suspension line upon the link tem- plate, then sliding the template to the positions Nos. 3, 4, 5 and 6 for the forward motion, and locating the line in question at each of these positions. Make similar locations (found with the proper arcs) for the back motion. Finally locate the stud for the full gear forward in such a manner that the line c 2 c 2 joining its points shall be parallel to the central line of motion. Two or three trials may be neces- sary before a suitable height for the suspension line above j S is obtained. This mode of suspension is frequently adopted on locomotive link motions. On the other hand, where no importance is attached to MODIFICATIONS. tlie accuracy of the back motion, the slip may be greatly diminished by inclining the rocker arms to each other (Fig. 28) so that the arc r r of the pin shall, instead of preserving a state of tangency to the central line of motion, intersect it in a similar manner to the path of the point, m, Fig. 24. This method can be employed with advantage in designing marine link motions. III. SlIOKT CONNECTING EODS. If the ratio of crank to connecting rod had been assumed at 1 : 4J instead of 7J, the position of the stud S found as before for equalized cut-off at the \ stroke, and the template slid to the positions 5 and 6, the change would have im- pressed on the line c 2 c 2 an inclination of 18° (instead of 5°) to the central line of motion. This would have rendered it impossible to equalize the motion in the ordinary way for more than one direction of the crank, without bringing the tumbling shaft and eccentric rods in conflict. But if the aim be simply to equalize the forward without regard to the back motion — a very common practice — no special difficulty will be experienced in hanging the tumbling shaft to even this case, for the point 7i s , Fig. 35, would then be left out of the account. There exists, however, a method of equalization which cor- rects the difficulty for both the forward and the back gears. It is clear that the tumbling shaft is employed most conven- iently and successfully, when it sustains the hanger in such a manner as to guide its vibrations in arcs practical! // par- allel to the central line of motion. Hence if we wish the link to conform with this condition it will be necessary to raise the template from position No. 6 of Fig. 34 to No. 11 of Fig. 38 in which the line c 2 c 2 becomes parallel to the central line of motion. This elevation moves the lap point V to I 2 giving thereby a smaller lap circle 1 1 2 from which to 100 :iodificatioxs. determine the lap, and at the same time increasing the lead opening of the return stroke. The position A of the rockei is thereby carried to a point a more remote from the shaft, and the lead opening of the return stroke in the mid gear becomes greater than that for the forward gear. But we have already seen that whatever inequalities of lead open- ing may arise in the full gear, none can be tolerated in the mid gear. Nor is there an occasion for their existence, be- cause the link arc may be struck with a shorter radius than the distance from the shaft to the rocker and all such inequalities be entirely eliminated. Take in a pair of compasses, the radius A d' of the mid- gear travel and strike the circle rZ 4 d 5 about the new position a of the rocker. To this the link arc must be tangent when the template is placed at the mid-gear position No. 1 and 2. Bring the template to position No. 2, mark the fixed points m and n of the full gears on the paper, and then search for a radius, having its centre in the central line of motion, whose arc shall embrace the three points m, d~°, n. In the present extreme case the radius equals 41 J" against 49J" employed with the ratio of 1 : 7J. The two little cuts V and Z, Fig. 39, illustrate the character of the lead openings before and after the change of the link arc radius. Having thus determined the true radius for the link arc a new template should be constructed, and all the locations made which are appropriate to the template positions Nos. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, under the new conditions, just as though no previous investigation had taken place. The result will be a motion capable of ready suspension from a tumbling shaft, with perfectly equalized cut-offs, with port openings varying to a slight extent in the full Central Line of Motion FIGURE 39 MODIFICATIONS. 101 gears but precisely equal in the mid gear, with a forward stroke lead opening increasing from I d (Fig. Z; in the full to I d x in the mid gear, and with a return stroke lead, open- ing gradually from I 2 d B in the full to I 2 d 5 in the mid gear. Both these lead openings will be exactly equal to each other in the latter gear. It will be observed that all the inequal- ities of the motion are thus brought in the full gears, the very position where their influence is the least injurious. Of course it is not pretended that great inequalities of port openings are admissible in the full gears, unless the smallest of these openings shall exceed the 0.6 or 0.9 area (mentioned on page 23), in which case the magnitude of their diiference becomes a matter of little importance, be- cause the wide opening will then admit no more steam than the narrow. But since the 0.6 or 0.9 area must be reached before the mid gear is attained, where the areas become equal, it is desirable to have as little irregularity in the other openings as possible. In reference to the lead opening, it is not unusual in lo- comotive " stationary -link " motions to give a constant lead of | inch, where one increasing from ^g" or an |" in the full gear to §" in the mid, would be employed under like circumstances for a shifting link motion, and so far as can be discovered both motions are productive of equally good results. Hence we fail to perceive the force of objections so frequently urged against a slightly irregular lead, but believe that within proper limits resort should be had to this most efficient means for correcting the inequalities due to a short connecting rod. The recommendation, however, must be qualified for marine engines, whose more massive reciprocating parts require equal admissions for bringing them smoothly to a state of rest at the extremities of the stroke. For all such it is better to equalize the lead open- 102 MODIFICATIONS. ings, at least in the Ml gear, and as far as practicable the cut-offs for the same, paying hut little attention to the back gear. It has doubtless been observed that throughout the pre vious investigation no allusion has been made to the equal- ity of the exhaust closure, and no direct effort put forth for its conservation. The omission was intentional, simply be- cause the very process of equalizing the cut-off incidentally accomplished this object. In proof of which, it is only ne- cessary to consider that the neutral position (A) or exhaust- closure point lies exactly midway between the cut-off points 7, 7'. so that if the motion be corrected for the latter when these are near each other, it must become practically per- fect for the former. But if the maximum cut-off should take place at about the f stroke of the piston, the lap points I and V would be widely separated, and probably give rise to a marked inequality of the exhaust closure at the mid gear. Since irregularities of closure and release produce a greater impression on the motion when they occur at the mid rather than at the full gear of the link, and since it is possible by means of inside lap and clearance to correct them for either of these gears, it will be well to determine the extent of the inequality for the mid gear, and regulate accordingly the position of the exhaust chamber with ref- erence to the edges of the valve. To determine this correc- tion, bring the link template to one set of the half- stroke elements (Fig. 32) and slide it thereon until the link arc stands over the exhaust-closure point A (or a, as the case may be). Mark the position of the stud S, and through this point draw a line parallel to the central line of motion. Next move the template on the other set of ^ stroke ele- ments until the stud reaches the line just determined. Mark the point in which the link arc now intersects the cen- MODIFICATIONS. 103 tral line of motion, and measure the distance of such inter- section from A. The required correction will be \ of this quantity. If the point falls on the forward side of the valve stroke it indicates that the exhaust chamber must be moved bodily this amount tow aids the forward edge F (Fig. 11) ; but if on the back, towards the back edge N. IT. ECCENTBIC ROD PINS BACK OF LINK ARC. Judging from the frequency with which mistakes are made in the location of the eccentric rod pins, one is apt to conclude that most Designers regard their arrangement as a mere matter of caprice, and as having little or no bearing on the symmetry of the motion. This, however, is by no. means the case, for each combination has its own appropri- ate method of attachment. A connection of the pins back of the link arc is best suited to a motion like that of Fig. 22, because it tends to liasten the speed of the rocker pin in the forward stroke, an object usually accomplished by raising the link at the expense of slip. The upper part of Fig. 34 has been reproduced in Fig. 40 for the purpose of explaining this peculiarity of Link No. 1. By erecting perpendiculars to the central line of motion through the cut-off points Z, Z', and by measuring from the same line, the respective distances of the eccentric rod pin/, for the 0.92 cut-off elements, we discover that the forward stroke distance T is much less than the return stroke E, and that if T was equal to R the rocker pin would be carried beyond /, thereby delaying the cut-off of the forward stroke which now it hastens. In reality the slip is avoided by elevating the eccentric rod pin instead of the link arc. The advantage gained by this feature is very great, for while it tends to equalize the motion it reduces the slip of the link and renders easy the work of suspension from a tumbling shaft. 104 MODIFICATIONS. In locomotive practice the distance of the pins' removal from the arc varies between 2\ and 3 inches. For marine work the limits are, in general terms, double these quan- tities. Fig. 40. ALD The principal fact to be borne in mind is that, within & aitable limits, the greater this distance the more readily can the motion be equalized. From the foregoing we perceive that Likk No. 1 is ap- propriate to a motion requiring acceleration for any cut-off point beyond tlie neutral position A, and having its small- est crank angles laid off between tlie link and centre of tin MODI F ICATIONS. 1 < >5 main shaft (as in Fig. 29). The four typical forms of such motions are here presented with a suitable arrangement of the parts, when the link is dropped in the full gear forward, for a positive motion of the crank. But if a negative mo- tion be demanded it is only necessary to transpose the en- tire motion so that the cylinder conies on the opposite side of the shaft, in other words to take the power off the oppo- site extremity of the shaft after first turning the engine end for end. It was remarked (page 61) that the crank angles of a bad-action engine are invariably the reverse of those com- mon to one of direct action ; hence, if we wish to preserve the identity of the motion in laying off a figure like 29 for such an engine, it will be necessary to locate the initial po- sitions F and B of the eccentrics opposite to those proper for a direct action, and apply thereto either of the two schemes offered in the Diagram. EXAMPLE. The following dimensions have been taken from a most successful freight engine ; their application will serve to familiarize the student with the principles of the foregoing method : 6 driving wheels, 57 inches diameter. Outside cylinders, 18 inches x 22 inches. Connecting rods 86 inches in length. Ports 15" in length; steam, If" wide; exhaust, 3". Diameter of eccentric circle=5 inches. Maximum cut-off=0.8 of stroke. Mid gear lead=fg inch. Booker from shaft =55 J inches. Length of rocker arms =9 inches, c, to c. of eccentric pins =13 inches. Tumbling shaft arm= 18 inches. Hanger =13 J inches. Pins back of arc = 3| inches. Required. — Radius of link, distance of point of sus- pension back of link arc, lap of valve, full gear lead, and location of the tumbling shaft. LINK No. II, C031MONLT known as the " Open Link," is specially adapted to cases in which the link acts directly on the valve stem without the intervention of a rocker, as peculiar to British practice. It differs from No. 1 in the location of its eccentric rod pins. These, instead of occupy, ing stations "back of the link arc, reside at points / and b beyond the extreme positions m and n of the link block. They conse- quently move a greater distance than the latter points, and in order to preserve the same travel of valve the eccentric circle must be enlarged. In locomotive practice the dis- tance between eccentric rod pins / and b varies from 16''' to 20". The diameter of the eccentric circle varies from 5J to 7 inches, and the working points m and n usually about 3" from the pins. The template for this form of link is illus- trated by Fig. 41. This link No. 2 is specially adapted to a motion re- quiring acceleration for any cut-off point beyond the neu- tral position A, and having its greatest crank angles laid off between the link and centre of the main shaft. It will be remembered that with Link No. 1 (Fig. 40) the smallest crank angles occupied such a station, and the eccentric pin LINK NO. II. 107 was elevated to the position ./', making the distance T Less than R. If, however, the greatest crank angles had occu pied this position, the element f would have been removed Fig. 41. B*0^ to some line/ 4 nearer the shaft, while the link wonld have been depressed and slip increased in the endeavor to make T=E. But the equality of these terms is established when the link arc passes through the centres of the eccentric rod pins ; hence, a "Box Link," having its pins over the work- ing points m and n, will be found better adapted to this position than Link No. 1, yet it only supplants the more readily-constructed open link, when it becomes important to retain the throw of the eccentric at its lowest limit. As with Link No. 1, so with No. 2, there are fonr 9 108 CONST R UCTIO.N. schemes to which the motion is peculiarly applicable. These are given in the accompanying Diagram for the posi- tive motion of direct and back-action Engines. As hereto- fore explained, their negative motion may be obtained by transposing the cylinder and link motion to the opposite side of the main shaft and taking off the power from the other extremity of the same. When, therefore, it has been decided that an engine shall have a direct or back-action arrangement of the connecting rod, the link to act through or without a rocker on its valve, and its forward motion to be positive or negative, then an appropriate arrangement of the link can be at once selected from these two diagrams, and the side of the shaft determined, on which the cylinder should be placed, to secure the desired crank motion when the link is dropped in the full gear forward. It should be observed here, that the lower part of the link is never used in a horizontal engine to impart a forward motion because the weight of the overhanging or sustained parts tends to render the motion unsteady. CONSTRUCTION To find approximately the throw of the eccentrics and their angular advance for a given travel of the valve, length of link and position of the working point. Describe about any point C (Fig. 42) on a vertical line F R a semi-circle E H with a diameter equal to the proposed travel of the valve ; from C lay off C P, the extreme dis- tance of the working point from the eccentric pin, also C S the J- length of the link. With S as a centre describe the arcs C /, P m, and b R. Suppose now the cut-off must take place at 0.78 of the stroke, then from the Travel Scale t O N S T RUC T I N . 109 \ve learn that the tri al angular advance shoul d be 28° . Lay off C B 28 from F C and produce tlie line D B pas Fig. 42. I2/j=CUT OFF. 0.78 STROKE. OR AM ADVANCE OF Z3° through the point of intersection B parallel to F R. Strike a trial eccentric circle j F K about the centre C. Take the distance between its two intersections D and F in a pair of dividers and lay it off twice from G, giving the point K. 110 APPLICATION OF LINK NO. II. Through K draw a line parallel to C R and determine its intersection b with the arc R b. Draw a right line through b and the extreme travel point m. If now / should Ibe found in the tangent line through j to the eccentric circle it would prove that the diameter of this circle had been assumed correctly. But if it falls without the assumed circle, this diameter must be increased. Conversely any point within requires a diminution of the same. Thus the point e indicates that the diameter of its circle j g k has been assumed too large. Having secured the correct diameter of the eccentric circle, join the points D and C by a right line and measure its inclination to the line F R. We thus obtain 19° the true angular advance of the eccentric for accomplishing the desired cut-off. The principle involved in this construc- tion is that when one eccentric produces its extreme throw D (Fig. 33) the other will be separated from its like position E by the horizontal distance of T, which always equals double the angular advance. Although this construction does not claim strict accuracy, it will be found to answer all practi- cal purposes. APPLICATION OF LINK NO. II. For illustrating the process of manipulation peculiar to this form of link, we will assume the following terms : Crank and rod ratio = 1 : 6 J. Cut-off at 0.8 of the stroke. Travel of valve =4§ inches. Yalve stem from shaft =5 ft. Distance between eccentric rod pins =18". Extreme working points, 3" from pins. Mid-gear lead openings | inch. •a APPLICATION OF LINK NO. II 111 By a construction like that of Fig. 42, an angular ad vanceof about 10 and eccentric circle of 6| inches diametei are found to conform with the above conditions. If now the connecting rod and link motion act direct!// on the pisfo m and valve the initial position of the motion will be that pre- sented in the first Figure of the application-, and the four starting points F, B,/, b, together with the four I stroke points of the eccentric circle, may be mapped in a similar manner to Fig. 29 ; while the four 0.8 cut-off points should be laid off by means of a protractor from the lines F C, B C,/C, and&C. Having mapped these twelve important positions and constructed a template like Fig. 41 the next step will be to follow the journeyings of the link arc and locate the tum- bling shaft in a manner precisely analogous to that pursued with Link No. 1 : " 1st. The mid-gear travel —d) d 2 . „. -. 2d. The lap A I for a given mid-gear lead. 3d. The position of the stud for equal J stroke cut-offs of the piston. This form of link is more generally suspended from the upper eccentric rod pin than from a point midway between the two, and has the tumbling shaft below the central line of motion ; but by marking the various locations of botli pins, as well as the centre line j\ we will be able to select the most appropriate of the three suspensions. Let us follow first the central suspension. We find that by locating the stud on the arc, the line c c of its motion. for the J stroke cut-off, becomes parallel to the central line of motion, a condition suited to ready suspension. But on 112 APPLICATION OF LINK NO. II. dropping the template to the full gear cut-offs the stud as« sumes the positions S 4 S 5 , Fig. 43, whose line c 2 c 2 has sc great an inclination to the central line of motion, that it would be next to impossible to successfully hang it from a tumbling shaft and accomplish equal cut-offs in all gears. We must consequently resort to a change of link arc radius and unequal full gear leads (as in Figs. 38 and 39) in ordei to establish perfect equality. To do this, raise the link arc so that the stud shall occupy a location S 6 * thereby bringing & & more nearly to a state of parallelism with the central line of motion. Mark I 2 the new lap point ; strike a new lap circle I V with neutral position a, nearer to the main shaft, and about this point describe the mid -gear travel cir- cle giving new points d 4 d b through which the link arc must pass for the mid gear. Bring the template to position No. 2, as in Fig. 31, mark the eccentric pin points/ and b ; then search for a radius whose arc shall pass through the three points/, d'% I). This radius will always prove grealer than the distance from the centre of the shaft to the neutral po- sition A instead of less, as found with Link No. 1. Having obtained a correct link arc, cut out a new tem- plate like Fig. 41 to represent it, and reconstruct the entire motion. The new radius will equal 5 ft. 7". The corrected lap =1^ inches. The lead for the forward stroke, increases from I to § in the mid gear, and from T 3 g to f for the return stroke. The lines of suspension pin motion c, d, c 2 , (f may converge, as in the present instance, towards some point beyond the link. In such case the tumbling shaft should be placed on the side of the convergence. If, however, the link is suspended by the upper eccen- tric rod pin, the forward gear paths of the suspension pin motion will be represented by the lines 7i, h\ and the tum- bling shaft will lie below the central line of motion ; but for Central Line of Moti FIGURE 43. hP8 APPLICATION OF LINK NO. II. 113 the lower eccentric rod pin, the lines will become e, t\ e\ and its tumbling shaft will stand above this line. The judgment of the designer will in every case decide to what extent the lead openings should vary in the full gears, what inequalities of cut-off are admissible, and whether or not the motion should be equalized simply for the forward without regard to the back gear. While attempting to analyze the pecidiarities ot various existing link motions, the investigator usually rinds that among other dimensions, only the lap and mid gear lead are given, and that no allusion is made to the angular advance, or to the maximum cut-off. To solve such cases, he is compelled to work the problem as it were, backwards. On the central line of motion he plots the lap and lead, as on Fig. 32, places the template in the Nos. 1 and 2 positions, as in Fig. 31, then with the length of the eccentric rod as a radius and the positions of the eccentric pins as centres, strikes in the direction of the shaft indefinite arcs, whose intersections with the eccentric circle give the points F, B, f, b, (equi-distant from the central line of motion) and from these the desired angular advance can readily be measured. BOX LIXK Although the mechanical construc- tion of this form of link is rather more difficult than that of No. 2, it serves the part of a good substitute when a short throw of the eccentric is required ; for with it the maximum travel of the valve always approximately equals the diameter of the eccentric circle. At times the box link can be em- ployed in positions appropriate to Link No. 1, but very rarely with those good results in respect to minimum slip which obtain with the former motion. On such occasions the stud usually lies — at some point beyond the link arc, de- termined by placing the link in the j stroke cut-off positions, Nos. 3 and 4, and plotting the centre liney as in Fig. 32. When, however, the box link is used in place of Link No. 2, the centre of suspension S generally falls within the link arc, or between it and the main shaft. The construction of these links varies ; in some instances the ribs are formed on the inside as represented, while in others, they are cast on the sliding block and overlap the link plates. STATIO^AEY LIISTK This form of connection between the valve and eccen- trics is specially applicable to those circumstances in which the former requires no rocker. The mutual relation oi the parts will be clearly perceived from an examination of Fig. 44 which illustrates one of the most successful methods of suspension. * The eccentrics stand in their usual location for a direct action motion. The main link is hung from a fixed point by a short bar called the " suspending link" and the link block connected with the valve stem through the " Radius Rod " m cV. By means of a reversing combination the block may be carried to any point between m the full gear forward and n the full gear back. But since the link arc is always struck with a radius equal to the length of the rod m d', having its centre at d 1 and d 2 in the central line of motion, when the crank occupies the zero or 180° location, it must be evident that the block can be moved from one full gear to the other without altering the position of the points d' or d\ consequently the lead opening will re- main constant throughout the motion Now it has been invariably the custom to simply define a station- ary link motion as "one in which the lead is constant" * For convenience of observation, the cross sections of the valve and seat have been revolved to a plane at right angles to their true position. 116 STATIONARY LINK. leaving it to be inferred that the angular withdrawal of tfe crank from its zero position at the moment of pre-admission must also be a constant quantity, whereas in reality thig lead angle increases just as much for a stationary link motion as for a shifting one. The only difference between the two is that the lead opening of the stationary link motion is more ample and the angle slightly greater, for all except the mid gear, than with the shifting link motion. But this distinction has been so clearly shown heretofore that further remark can scarcely be necessary. Unlike the shifting link motion, however, the lead opening is not dependent on the arrangement of the eccentric rods, for these may either be crossed or opened without altering the result. But for the purpose of meeting the other conditions of the motion an arrangement like Fig. 44 should be adopted. As a general thing more attention is paid to the equali- zation of the cut-off and reduction of the slip in the forward than in the back gear. For the accomplishment of this object, the centre of the link should be dropped below the central line of motion, the angular advance of the backing eccentric slightly reduced and the backing eccentric rod lengthened. The simplest method by which the student can obtain a clear idea of the action of the parts, in a stationary link motion, will be for him to take the dimensions of some suc- cessful motion, cut out a proper template for the link and trace its journey ings throughout the different gears in con- formity with principles already laid down for the shifting link motion. The following dimensions (in absence of others) will answer such a purpose : STATIONA R Y L I N K . 117 Diameter of piston =18 inches. Stroke = 24'' ; Connecting rod=91". Ratio =1 : 7-A. Throw of eccentrics=2§". Forward eccentric angular adv. =27£°. Rod=57§". Backing eccentric angular adv. =26'. Rod = 58". Eccentric rod pins 12 J" apart, 3" back of arc. Centre of suspension 1|" back of arc, 1|" below lire. Radius rod=37", Reversing link=ll|", Hanger=9". Tumbling shaft arm =18". Reversing pin 8" back of arc Lead=|", Steam port =2", Exhaust=3|". Maximum travel about 4| inches. The Stationary Link is seldom found in American practice from the fact that all modern locomotives are built with steam chests on top of their cylinders, instead of at the side. On stationary engines, the link and governor are occasionally used conjointly ; in such instances the station- ary link will be found best adapted to the requirements < I the case, because its radius rod imposes a far lighter duly upon the balls of the governor, than the shifting link villi its rods, hanger, and additional friction of eccentric straps. ALLAN LINK MOTION. The discovery of this motion was a natural sequence to the invention of the shifting and stationary links. By it a com- promise has been effected between the leading features of both motions, resulting in a more direct action and perfect balance of the parts together with a reduced slip of the link block. One mode of suspension, for the link in the full gear forward, appears in Fig. 45, in which the cross sections of the valve and its seat have been revolved for the purpose of more plainly exhibiting their relative positions. The locations of the point of suspension and attachments of the eccentric rod pins upon or back of the link arc are quite as variable for this, as for the shifting link motion ; and the requirements of the other details generally indicate whether the reversing shaft should be placed above or below the central line of motion. In proportioning the parts, the main object is to move the link and radius rod (when the crank stands at the zero or 180° locations) in such a manner that the link arcs peculiar to each motion shall always be tangent to each other. In this case all the locations of the link block will be found in one and the same straight line. This peculiar ity has given rise to the title "Straight Link" motion expressive of the form of the link. ALLAN LINK MOTION. 119 The radius rod and main link are supported by rods from the reversing shaft arms, and the inequality in the lengths of the latter, which is essential to a proper suspen- sion of the parts, incidentally tends to equalize the weights resting on the opposite sides of the reversing shaft, thus greatly facilitating a change of the motion from one full gear to the other. Well-schemed motions of this type practically preserve the characteristic feature of the stationary link, viz., a con- stant lead ; yet from the nature of the case they possess at times slight inequalities in one or both of the full gears. These, however, are quite insignificant for a relatively long radius rod and short travel. The ratio between the long and short arms of the re- versing shaft may be readily determined for any given travel, angular advance, length of eccentric rods, link and radius rod, by placing the template in the ISTo. 1 and 2 posi- tions (Fig. 31), marking the mid-gear travel d' d% sweeping indefinite arcs through these points with the radius rod, and drawing down the template, or centre of suspension, from S to S 8 until its straight line intersects these arcs in points m, m\ Then map the radius rod m d!, m 2 d 2 giving the points u, v) of the reversing rod pin above the central line of mo- tion. The centre I of the link arm pin must fall as much below the horizontal line through the reversing shaft E as S 2 does below S. In like manner the pin li of the other arm must rise as far above the horizontal as u does above the central line of motion. Finally, draw I li of length suf- ficient to accommodate the details of the shaft, and we have at once the proper dimensions for the reversing shaft arms. It should be observed that the tendency of m 2 is to drop below m and thus distort the motion, but this will be ob- viated if the two are brought into one horizontal line inter- 120 ALLAN LINK MOTION. mediate between such stations. The change will result in a slightly increasing lead, as is common with the shifting link motion. The following dimensions can be employed for an invea ligation of this class of motions : Diameter of cylinder =16". Stroke=24' ; Connecting rod=87" ; Ratio=l : 7|. Throw of eccentric =2|" ; Angular advance =26°. Eccentric rods=39^ inches. Radius rod =47", connected 7" back of link. Box link, suspended by stud at centre with eccentric rod phis 10" apart. Suspending rods both 18 ' long. Reversing lever, long arm = 6". Reversing lever, short arm=2|". Mid-gear lead = J inch. Steam port=lJ" ; Exhaust=2f. If the examiner desires to analyze any stationary or straight link motion already constructed, having a given lap and lead but no specified angular advance, he should work the problem backwards, as follows : First locate the four cardinal points d\ Z, 7', d\ and sweep their arcs with the radius rod ; then place the link in the positions Nos. 1 and 2, with the positions of the eccentric rod pins as centres and the length of the eccentric rod as a radius, sweep the four arcs, which must contain the points F, B, f, b, and describe through them the given eccentric circle, in such a manner that all the points of intersection will lie equally remote from the central line of motion. With these initial points determined, the investigation can proceed on th'^ principles already explained. WALSCHAEET LINK MOTION This device groups two perfectly distinct motions — the one derived from a single eccentric, the other from the cross- head of the piston rod — in such a manner that their combined effect is, when the parts are well proportioned, quite analogous to the motion obtained from the stationary link. From the nature of the connection between the cross- head and the valve-stem, the motion can be more readily applied to an outside cylinder engine than to an inside one. The eccentric usually assumes the form of a return crank from the main crank pin, as shown in Fig. 46. Its centre then is found on a line at right angles to the crank arm. The angular advance becomes equal to zero, and hence, so far as the link will be concerned, the valve can have neither lap nor lead. The link oscillates freely about a fixed axis, and its arc has a radius equal to the length of the radius rod. This rod is moved from one full gear to the other, in the usual manner, by means of a reversing shaft with arms. From the extremity of a short arm, rigidly bolted to the cross-head pin, extends a union bar which is pinned to one end of the combination lever. By the aid of this lever, the eccentric and cross-head motions are so combined, that the latter virtually restores the angu- lar advance discarded while locating the eccentric, and 122 WALSCHAEET L I X K MOTION. consequently enables the valve to possess both a constant lap and lead. The truth of this assertion will appear from an examina- tion of the lever elements (Fig. 47) for 12 locations of the crank arm. Fig. 47. 42. oj. tii2 cS^n r^ well as lead opening for neutralizing the effect of lost motion. 132 EQUALIZATION OF VALVE MOTION. In marine engines the cart-off valves act with their outer edges. The lap angle of the main valve is then taken at from 15° to 20 degrees, and the exhanst closure effected at about 0.9 the stroke, by simply raising the link, until the eccentrics have virtually an angular advance of 35 to 45 degrees ; in other words, by working the link in less than the full gear. The necessity of adjusting the eccentrics is thus obviated. When an engine is furnished with exhaust passages per- fectly distinct from those admitting the steam to the cylin- der, and the demands upon its power are quite uniform, the valves regulating the exhaust should be adjusted by the quantity of coal consumed. That is, the angular advance of their eccentric should, from time to time, be increased until at length the limit of greatest economy is attained. The result of course must not be judged by a computation of the indicator card, for that necessarily ignores the effect of the momentum of the reciprocating parts, since it mea- sures the power in the act of being applied and not subse- quently to the application, a distinction of great importance. EQUALIZATION OF VALVE MOTION. The cut-off being produced by a valve independent of that regulating the lead, its equalization may be accom- plished without any of the difficulties incident to a single eccentric motion, where the slightest change in either event is immediately felt by the other. The desired result is ap- proximately obtained for a single eccentric motion, by sim- ply lengthening the cut-off valve stem an amount depend- ent on the ratio existing between crank and connecting rod. CLEAKANCE. L33 If, however, the valve moves under fclie influence of a level attached to the reciprocating parts of the engine, as in Pig. 52, the motion will become equalized by virtue of the irreg- ularities thus introduced to the valve motion (a counterparl of those peculiar to the piston* and any slight inequalities of the main valve will he counteracted by a change in the length of the cut-off valve stem. The lead should be made equal for both faces of the main valve, and if neither the single eccentric nor link by which the latter is operated accomplishes an equalization of the exhaust closure, then a suitable amount of inside lap and clearance (as explained Part I) should be given to the exhaust edges of the valve face. The cut-off equality of the main valve, in itself con- sidered, is of little consequence, hence the link should be arranged to give the smallest amount of slip attainable with an equality of the lead, and the cut-off should be reg- ulated solely by the cut-off valves. CLE A EAKCE. This term is used to express, the extent of the space which exists between the piston at the extremity of its stroke and the valve face, or the cubic contents of the steam passage plus the unoccupied portion of the cylinder. Since for each stroke of the piston this space must be filled with steam, which in no way tends to improve the action of the parts, but rather increases the amount to be exhausted on the return stroke, it becomes desirable in long-stroke engines to locate the valve face as near the end of the stroke as possible, thus reducing the cubic contents of the passage and by its directness admitting the steam with a higher 134 F R I C T I O X . initial pressure than conld "be obtained through a more tor- tuous channel. A convenient method for accomplishing this result, is to separate the valve faces F and N by means of a stem, as shown in Fig. 50, and forming them either in the shape of a Fig. 50. ; letter Q laid on its side, or as small pistons. The former or D valve construction was much employed a few years since, but has been gradually supplanted by the more me- chanical arrangement of the piston valve. This, instead of being surrounded by packing in the valve case, carries its expansive packing in the same manner as an ordinary pis- ton. The steam is received either between the pistons, from a pipe P, giving the most direct admission to the cylinder, or externally from chambers e e. The parts surrounding the valves are well jacketed to prevent unequal expansion, and slight irregularities are compensated by the elasticity of the packing. FRICTION. The friction of a valve is quite independent of its surface, except so far as the latter may increase the area upon which the steam can exert an unbalanced pressure. REDUCTION IX TRAVEL 135 There are various expedients for relieving such rjressure. Two of these have been illustrated in Figs. 48 and 50. A third consists in casting a standard in the exhaust port on which is bolted a concave plate, scraped to a bearing upon the inner surface of the valve, and holes drilled through the top admit the steam under the valve, which tends to relieve the external pressure. Besides these devices the valve is frequently mounted on steel rollers about lj inches diame- ter resting on plates of the same metal, and thus the sliding converted into rolling friction. Heavy valves standing in a vertical position have additional rollers under their lower edge for supporting their great weight. EEDrCTIOX IjST TRAVEL. The work expended in friction depends directly upon the distance traversed by the valve. Hence, in marine en- gines every means possible should be employed to reduce this quantity to its minimum value. This object may be Fig. 51. attained by increasing the number of the steam ports two or three fold, so that \ or J of the travel will suffice to open the same extent of port area. For a reduction in the travel 136 L I N K A N D EECIPEOCATKXG of one-half, the parts are commonly arranged as shown in Fig. 51. In this the valve edges F and N are separated by a distance wide enough to admit two steam passages U, U, whose openings T T communicate with the inner ports but not with the exhaust. They are formed with a width equal to that designed for the port opening. The general propor- tions of such valves may be concisely expressed as follows : Total width of steam passage =2 S. Each port=S. Width of port opening =T. Exhaust port =4 S. Valve faces F and ]S"=S+lap of valve. Bridge W=4 travel + lap + T + f inch. Width of exhaust bridge B dependent on thickness of cylinder. Width of exhaust bridge b dependent on thickness of valve. Occasionally the travel is reduced still further by insert- ing a third port beyond the other two. When so arranged the outer faces F and N are extended and through them passages cut, which admit the steam to the cylinder, but remain closed during the period of exhaust ; consequently the two exhaust passages must be amply large to discharge the steam received through the three openings. LINK AND RECIPROCATING MOTION COMBINED. It was observed, while discussing the subject of link mo- tion, that the central line of motion might be inclined at any angle to that of the piston motion, without affecting the character of the valve action. Fig. 52 illustrates this pecu- MOTION COMBINED 13' liarity (for one position, namely, an angle of 75°) as applied to a back-action engine having an independent cut-off. The line E F represents the central line of the link motion, Fig. 52. AXIS OK CYLINDER and Gf H a line at right angles thereto from which are laid off the 15 degree angular advances of the eccentrics. The eccentric rods being crossed, the lead of course diminishes from the full to the mid gear of the link, but as this is only employed in the full or immediately adjacent gears, the re- duction proves advantageous, since it enables the engineer to stop his engine by placing the link in the mid gear (see Fig. 26). The cut-off valves are operated by a lever I J connected through the link J K with the pin K, which is secured to one of the piston rods or to the cross-head in a direct-action engine. This valve motion mistfit have been derived from an ec- 138 LINK AND RECIPROCATING MOTION. centric with its normal position in the line E F, and acting on the valve through the medium of a rocker. The general conditions governing the motion have already been ex- amined. There are numerous other positions in which the link may be placed, and many other plans for connection with the valve, but it is believed that the typical forms have been presented with sufficient care and accuracy to enable the designer by their aid to accomplish any desired result. It may prove a source of regret to some, that the numer- ous class of automatic cut-off gears, now so extensively applied to stationary engines, should have received no special attention in this Work. The Author however, has considered it most expedient to confine himself to general principles and to subjects requiring a solution in every day experience, leaving with those who hold such monop- olies, and who alone can make use of them, the onus of explaining their principles and advertising their points of excellence. Catalogue of the Scientific Publications of D. Van Nostrand Company, 23 Murray Street and 27 Warren Street, Mew Tork. ADAMS, J. W. Sewers and Drains for Populous Dis- tricts. 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