Scientific American handy book of facts and formulae

Preface

WHEN a receipt or a table of weights and measures is wanted in a hurry there is generally a trip to a library and a search through old or indifferent authorities before the matter desired is secured. Each year the ''Scientific American" receives 15,000 letters of inquiry and the query editor with a staff of four highly trained specialists, Engineers, Electricians, Chemists and all-around technicians deal with this enormous mass of correspondence. The reading of this vast number of letters shows what people really w^ant to know. Very generally the inquiries are inspired by a desire to improve themselves in their trade or profession, a most laudable desire, and assistance is freely afforded. It is on the basis of actual knowledge of what over 200,000 men really want that the present volume has been compiled largely from the successes which are the literary property of the publishers. Years of effort and considerable iums of money have been spent in securing the information which is aow presented in a form which is so usable and portable that even the enormous sales of the ''Scientific American Reference Book" and the "Scientific American Cyclopedia of Formulas" will be eclipsed. It is hoped that the usefulness of this little volume will obtain in the shop, the amateur's workshop and the home. It is essentially a book for men but if its success warrants it_, possibly a book of "Household" formulas may follow in due time.

Chapter I. Mechanical Movements

TOOTHED GEAR.

1. Spur Gears. — The ordinary form of toothed- wheel. The smaller of two intermeshing gear-wheels whether a spur- or bevelwheel is called a Pinion.

2. Gear with Mortised Teeth.— This is what is ordinarily known as a Cog-wheel among machinists. The wheel is. ordinarily made of iron and the teeth of wood. j.^.-j^T^.^ Gear.— The face of this gear is divided mto sections with the teeth of the different sections arranged in steps; that is one in advance of the other. Step gear-wheels are useful in. heavy machinery as they give a practically continuous bearing between the'intermeshing teeth of the gear-wheels.

4. Oblique Toothed Gear.— The teeth are cut diagonally across the working face of the wheel so as to give the gear-wheel a side thrust. In a double oblique toothed-gear, usually called a V-toothed gear, the thrust in one direction is neutralized by an equal thrust in the opposite direction. As in the stepped-gear it gives a continuous bearing of the teeth. ^

5 Internal or Annular Gear.— The teeth are formed on the inner periphery of a ring This type of gear is used in heavy machinery, because it offers a greater hold for the teeth of the driving pinion. There is less sliding friction between the teeth than in the usual outside spur-gear and pinion.

6. Star Wheel Gears.— The teeth are so formed as to permit an appreciable separation of the gear-wheels without preventing them from properly meshing one with the other. 1 hese gears are used on wringing machines, etc.

7 Elliptical Gears.— Due to their elliptical form, while the driving-gear rotates at constant speed, the other gear will be rotated at a variable speed. That is, its motion will tirst be accelerated and then retarded They are used in some machines to produce a slow powerful stroke followed by a quick return.

8. Angular Gears.— These gears have a rectangular form and, as in the elliptical gears, they serve to transform uniform rotary movement into variable rotary movement. However this movement is more jerky than that produced by elliptical gears. Angular gears are very seldom used.

.9. Lantern Gear.— The teeth consist of pms which he parallel with the axis of the gear-wheel, and are secured at their ends in two disks or gear heads. The pins are so spaced as to mesh with the teeth of a spur-gear, the lantern-gear permits limited sliding movement of the spur-gear along its axis. It can be very cheaply made, but is used chieflv tor light work, such '~-' ' ■ as clock mechanism, etc.

10. Crown GEAfe.— The teeth project pci^ pendicularly from a side face of the wh. instead of lying in the plane of the whe When in mesh with the teeth of a spur-g( or a lantern-gear, it forms a cheap method transmitting power from one shaft to anotl lying at right angles thereto. Crown ge; are useful for light work, and were comm in old clock mechanisms. They used to known as Contrate wheels.

11. BsyEL Gears. — The ordinary gear 1 transmitting power from one shaft to s other at an angle thereto. When the whe are of the same size and operate on shaf lying at an angle of 45 degrees, one with t other, they areicalled Miter gears.

12. Worm or Screw Gear.— An endU screw engages a spur-gear with spiral disposed teeth. The screw is called a won and the spur-gear a worm-wheel. A mu diminished but very JDowerful motion is coi municated from the worm to the worm-whe It is used in heavy machinery.

13. Curved Worm Gear.— The worki face of the worm is curved so that a numb of teeth will be in mesh with the won wl^el, thus giving greater strength. It is difficult matter to cut the thread of tl worm correctly owing to its varying pitc Ihe gear is called the saw-tooth gear whi the teeth and thread are V-shaped, as illt trated.

14. Spiral or Helical Gears— Tl teeth are spirally disposed on the working faces of the wheels so that they will transmit motion to shafts lying at right angles one with the other.

oulk ^""vf-^ P^^^^;— The gears rotate on shafts wnich he in different planes and at an angle with each other. The drawing shows a skew spur-gear meshing with a bevel-gear. Ihe same term would apply to 'two bevel gears lying in different planes and at angles to each other.

16. Rack and Pinion.— A spur-gear engages a toothed bar. Rectilinear motion is by this mechanism transformed to rotary motion or vice versa. It is quite common in heavy machinery to find a worm meshing with and driving a rack.

17. Spherical or Globoid Gear. — A spiral thread is cut on a spherical body and naeshes with the spiral teeth of the spur pinion. The latter is so mounted that it may be swung to different positions on the spherical gear, thus varying its speed of rotation.

18. Gear with Roller Teeth.— The teeth project from the flat face of the wheel, and consist of pins carrying rollers. This construction is used to reduce friction.

• : PjN Wheel. —The f^at face of the gear IS studded with pms which are adapted to

(Toothed Gears)

(Friction Gears)

mesh with slots formed in the edge of a oinion. The pinion is so mounted that it can be moved toward or from the center of the pin wheel to vary its speed of rotation. When the pinion is moved past the center of the pin wheel its direction of rotation is reversed.

20. Spiral Hoop Gear. — A spiral thread is formed on the flat face of the wheel and this meshes with a worm-wheel. The latter is moved forward one tooth at each complete rotation of the spiral hoop. This gives a powerful drive, though, of course, at a greatly diminished speed.

21. Intermittent Gear or Geneva Stop. — The driving-wheel is provided with a single tooth adapted to engage one of a series of notches in the other wheel. At each complete rotation of the driving-wheel the other wheel is moved forward one notch but no more, due to the concave space between the notches which fits tlosely against the circumference of the other wheel. In the Geneva stop one of these spaces is formed with a convex outline, as illustrated. When this space is reached both wheels are prevented from further rotation forward. The Geneva stop is used on watches to prevent winding up the main spring too tightly.

22. Intermittent Bevel Gear or Mutilated Gear. — The teeth are formed only at intervals on the face of the gears. The space between the teeth in the driving-gear is convex, and that between the teeth in the other gear is concave, so that when the teeth are not in mesh with each other these convex and concave portions fit into each other and prevent the driven gear from moving forwardunder its own momentum.

23. Variable Gears. — The gear wheels are made up of gear sectors of different radial length, which, produce suddenly varying motions of the driven gear due to the varying leverage between the wheels. The segments are arranged on different planes so as not to interfere one with the other.

24. Scroll Gears. — The gears have a scroll form which produces a gradually increasing or decreasing speed during each rotation. These gears are also called cam gears.

25. Elliptical Bevel Gears. — They produce variable motion of a shaft lying at right angles to the driving shaft. This gear is used on bicycles to give increased power on the downstroke of the pedal and a quick movement on the return.

26. Variable Pin Wheel. — A cone is provided with pins arranged spirally thereon, and these mesh with teeth formed on the other cone. When one cone is rotated at a constant speed the other moves with a graduallv increasing or decreasing speed during each rotation.

27. Cam-toothed Pinion. — The pinion consists of two oppositely disposed heartshaped teeth, mounted side by side, on a shaft. The gear-wheel with which they mesh has teeth alternately arranged on opposite side faces. Due to the form of the

Einion teeth, the gear-wheel is locked after eing moved forward by one tooth until the other tooth comes into mesh with a tooth on the other face of the wheel.

28. Bevel Scroll Gear. — The gear-wheel consists of a bevel spiral scroll which meshes with a bevel pinion. As the spiral scroll rotates it causes the pinion to slide forward on its shaft, and thus varies its speed.

FRICTION GEAR.

29. Flat-faced Friction Gear. — A common type of friction gear. The wheels are usually faced with rubber or leather to increase the frictional hold between the wheels. One of the wheels is journaled in bearings which can be adjusted toward the other wheel so as to increase the frictional engagement.

30. Grooved Friction Gear, — The faces of the wheels are grooved so as to increase the bearing surface. The best results are obtained by pressing the wheels but slightly into engagement with each other, as this produces little loss of power by friction,

31. Adjustable Friction Pinion. — The pinion is formed of a disk of rubber or other flexible material held between two washers. When these washers are tightened ■ together they press out the rubber between them, crowding it into closer contact with the Vgroove of the gear with which it engages.

32. Beveled Friction Gear. — Two cohe frustums are used to convey motion from one shaft to another at right angles thereto.

33. Friction Drums. — The drums have concave faceS which permit them to transmit motion one to the other while lying at an acute angle with each other. - ^

34 to 40. Variable Speed Friction Gear. — 34, a pinion, engages the flat face of the friction disk. Variable motion is produced by moving the pinion across the face of the disk. When the center of the disk ir. reached no motion is transmitted. Beyond the center the direction of motion transmitted is reversed. 35, Motion is transmitted from one friction disk to another lying parallel, but not in alignment therewith, through an intermediary pinion,. This pinion can be moved vertically to engage different points on the friction disks, and thus produce any desired variation in the speed transmitted. 36, Two convex friction disks are so arranged that one may be swung through an angle bringing different points on its surface into contact with the face of the other disk. In this manner the speed of the motion transmitted is varied. This gear is used on sewing-machines,:.' 37. Two parallel friction disks are each jjrovided with an annular concavity. Motion is transmitted from one disk to the other by a friction pinion mounted between the disks, and so arranged that it can be rotated to engage different points on the surfaces of the concavities, thereby varying the speed transmitted. 38, A cone with concave face is engaged by a pinion which may be swung about a center to engage different points on the face of the cone. 39. Two cones with concave faces are mounted on shafts running at right angles to each other. Motion is transmitted from one cone to the other through a friction pinion mounted to swivel so as to engage different points on the faces of the cones. 40. Two friction cones are moimted on parallel shafts, and between them runs a friction pinion having two faces, one engaging the upper cone and the other engaging the lower cone. This provides a broad bearing surface. The pinion may be moved to different positions along the faces of the cones, and thereby produce changes in the speed.

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Copyright, 1904, uy Munn &. Co.

CHAIN GEAR.

41. Sprocket Wheel. — The wheel is provided with teeth adapted to fit in between the links of a chain. The chain may be of the ordinary oval welded link type or of the flat riveted type used on bicycles.

42. Link-belt Wheel. — ^The chain is made up of square links which are engaged by ratchet-shaped teeth on the chain wheel.

43. Pocket Wheel. — The wheel is formed with pockets into which the links of the chain are adapted'to fit.

44. SiDE-TOOTHED Wheel. — The wheel is formed with two sets of teeth between which the chain travels. The teeth bear against the ends of the outer links of the chain.

45. Side and Center Toothed Chain Wheel. — This wheel is similar to that shown in Fig. 44, but has in addition a row of teeth along the center which bear against the center link of the chain.

46. Toothed-link Chain and Wheel. — The links are formed with projecting teeth which fit into notches on the rim of the chain

47. "Silent" Chain and Wheel. — Tkis is a special type of chain in which each link is formed with a tooth at each end. The teeth of adjacent links coact to completely fill the spaces between the teeth of the chain wheel. The construction is such as to produce a noiseless operation of the chain gear even at high speeds.

48. Detachable Toothed-link Belt and Wheel. — Each link is formed with a tooth, which meshes with the teeth of the chain wheel. The construction of each link is such that it may be readily slipped into or out of engagement with the next link of the chain,

ROPE GEAR.

49. V-PuLLEY. — The ordinary type of pulley for roimd ropes or cables. Owing to the V-shaped construction of the pulley groove, the rope wedges tightly into engagement with the pulley.

50. Pulley with Flexible Filling. — In order to secure frictional engagement of the cable with this pulley, the pulley groove is provided with rubber, leather, wooden, or other filling.

51. Pulley with Ribbed Groove. — In this construction of pulley the required grip is produced by forming ribs in the bottom of a pulley groove.

52. Pulley with Gripping Lugs. — The flanges of this pulley are formed with lugs which kink the rope or cable as shown, thus producing the required grip.

53. Rope Sprocket-wheel. — An old form of rope gear used in hoists and the hke.

54 and 55. Gripping Pulleys. — Gripping arms are provided which grip the cable at the point where the cable presses into the pulley. In 54 the gripping arms are wedged inward by the side walls of the pulley groove when pressed downward by the cable. These arms are normally h Id up by coil springs. In 55 the cable is gripped by the toggle movement of hinged clips placed at intervals along the periphery of the pulley.

56. Cable Sprocket-wheel. — The cable is provided with clamps which enter sockets formed in the cable wheel. This is a f9rm of cable gear commonly used at present m elevating and conveying machinery.

CLUTCHES.

57. Common Jaw Clutch. — One member of the clutch is mounted f o slide on a feathered shaft, and the other member which is connected with the machinery is normally stationary on this shaft. When the slidable member is moved forward the teeth on its forward edge intermesh with the teeth of the other member, setting the machinery in motion. The slidable member is moved forward by means of a forked lever which is hinged to a split collar mounted loosely between flanges on the clutch memben

58: Claw Clutch, — The slidable member of the clutch consists of a body portion with two claw arms which, when moved forward, are adapted to engage opposite sides of a bar on the other member of the clutch.

59. Lever Clutch. — The slidable member is provided with a lever loosely hinged to its forward end. The other member of the clutch consists of a disk formed with ratchet teeth on its face. These are engaged by the hinged arm when the shaft rotates in one direction, but the arm moves freely over them when rotated in the opposite direction.

60. Knee and Rose Clutch. — A crank arm is attached to the slidable member of the clutch, and engages a pin on an arm loosely hinged to the opposite member of the clutch.

61. Ratchet Clutch. — The clutch members are formed with ratchet teeth, so that when the motion of the driving shaft is reversed, the members will be disengaged.

62. Pin Clutch. — The slidable member is provided with radial arms formed with pins at their outer ends which are adapted to enter sockets formed along the periphery of a disk on the opposite member of the clutch.

63. Friction Disk Clutch. — The two clutch members are each formed w"ith disks preferably faced with rubber or leather, so that when pressed together their frictional engagement wOl cause a transmission of motion from the rotating disk to the other.

64. Friction Groove Clutch. — One of the clutch members is formed with a groove in its face to receive the lip of the other member which is cup-shaped. Both the lip and the side walls of the groove are slightly tapered to insure a close fit, even after the parts have been partly worn away by friction.

65. Stud Clutch. — Engagement between the two members of the clutch is effected by means of a stud on each disk adapted to enter a notch formed in the periphery of the opposing disk.

66. Friction Band Clutch. — One memt^r of the clutch consists of a pulley provided with a steel band which encircles and fits tightly on its periphery. The other member of the clutch consists of a lever provided with pins at its outer ends, which are adapted to engage the steel band. Since this band is not fastened to the pulley, any shock due to suddenly throwing the clutch members into engagement will be taken up by the steel band slipping on the face of the pulley,

67. Friction Cone Clutch. — The clutch is made up of two cones, one adapted to fit into the other. The frictional engagement causes one to drive the other.

68. Self-releasing Clutch. — The clutch disks are provided with inclined teeth, so that in case the resistance to the driven shaft in-

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Copyright, 1904, by Munn & Co.

( shaft Couplings )

(Ratchet Movements)

creases beyond a certain degree, the clutch members will automatically move apart.

69. Cam Clutch. — One of the members is cup shaped, and within this the other member operates. The latter comprises a number of cam-shaped arms hinged to a body portion, and so arranged that when moved in one direction they will bind agamst the inner wall of the drum, but when moved in the opposite direction "they will be automatically disengaged therefrom.

70. V-GROovED Clutch. — The clutch disks are formed with annular V-grooves adapted to fit into each other, and thus increase the friction surface of the clutch members.

71. Expansion Clx tch. — The slidable member is provided with a number of movable ring segments connected by radial arms to the main body of the clutch and adapted to bear against the inner surface of the drum or cup which constitutes the other member of the clutch. When the slidable member is moved forward, by reason of the toggle action of the radial arms, the segments are brought into frictional engagement with the other member of the clutch.

72. CoiLr-GRip Clitch: — The movable member of the clutch is formed with a number of coils of steel in which there is a central conical opening. This is moved over the cone which constitutes the opposite member of the clutch, producing the required frictional engagement of the two members.

ANGLE SHAFT COUPLINGS AND UNIVERSAL JOINTS.

73. Crank and Hinged-pin Coupling. — A couplmg for shafts which lie at an angle to each oth^r. One shaft carries a hinged pin which fits into an opening in the outer end of a crank arm carried by the other shaft.

74. Double-sleeve Angle Coi fling. — Each shaft carries a crank arm provided with a pin at its outer end, which lies parallel with its respective shaft. The two pins enter a coupling device consisting of two sleeves integrally formed, but lying at an angle with each other which corresponds to the angle formed by the shafts. Through this double-sleeve coupling, motion is transmitted from one shaft to the other, the pins sliding back and forth in the sleeve openings.

75. Cross-bar Angle Coupling. — This is used for coupling two parallel but offset shafts. Each shaft carries a yoke piece provided with sleeves at its outer ends. The coupling member is a cross-shaped piece, its arms fitting into the sleeves of the yoke pieces, and permitting the necessary latere 1 play as the shaft rotates. This form of coupling is also applicable to shafts which lie at an angle with each other.

76. Pin and Slot CorPLiNC. — A crank pin ca.rried by one shaft engages a slot in a crank arm carried by the other shaft. The motion transmitted is variable, due to the fact that the leverage varies as the pin moves up and down in the slot.

77. Ring-Gtmbal Universal Joint. — The ends of the shafts are provided with yoke members whose arms are pivoted to a ring- ^imbal, the pivot pins of the two yoke pieces ^ying at right angles to each other. This coupling will communicate motion at any angle under 45 degs. For angles of over 45 degs. a double-Unk universal joint is used.

78. Double- LINK Universal Jointt. — A link forked at each end is hinged to two rings', which are mounted in the yoke pieces on the ends of the shafts. In place of rings cross pieces such as shown m the illustration are often used.

79. Hooke's Angular Coupling. — The shafts are connected by two double links which are arranged in the form of a parallelogram. Intermediate of the shafts the links are connected with ball-and-socket joints,

80. Ball-and-socket Universal Joint. — Socket pieces are secured to the ends of the shafts, and these are provided with metal bands which encircle the ball that constitutes the coupling member. The bands enter grooves in the ball which lie at right angles to each other.

81. "Almond" Angular Coupling. — A side view ol the coupling is shown at I and a plan view at 2. Between the shafts to be coupled is a fixed stud on which a bell crank is mounted to turn. The bell crank is permitted to slide axially on the stud. The bell crank is connected at the ends by ball- -and-socket joints with links attached to the

ends of the shafts. Now, as the power shaft rotates, rotary motion will be communicated to the other shaft through the bell crank, which will rock and also slide axially on the stud.

82. Flexible Shaft. — Two shafts are connected by a flexible shaft consisting of a coil spring, or a metal tube in which a helical sawslot has been cut. This flexible shaft will permit transmission of motion through a wide angular range.

83. Linked Flexible Shaft. — The flexible shaft is made up of a series of links coupled together with universal joints. A coil. spring iits loosely over the links and prevents them from kinking. . This spring in turn is covered with a flexible tube. The shaft will transmit motion about almost any curve or angled It can be used for heavy work.

84. Right-angle Coupling. — The ends of the shafts are formed with heads in which are drilled a number of sockets. A series of rods, each bent to form a right angle, enter thesf; slots and form the coupling links between the shafts. As the shafts rotate these rods slide in and out of their sockets.

RATCHET MOVEMENTS.

85. The teeth of a ratchet wheel are en gaged by a pawl hinged to a rocking arm. The ratchet wheel is rotated only on the forward stroke of the arm.

86. A rocking lever carries two pawls, one on each side of its fulcrum. The wheel is rotated both by the downward and the return stroke of the lever; for while one pawl is rotating the wheel, the other swings to position to take a new hold on the ratchet wheel. The rotation of the ratchet wheel is thus kept nearly constant.

87. A ratchet crown-wheel or rag-wheel is engaged by pawls depending from two arms loosely pivoted on the axle of the ratchet-wheel. These two arms are connected by links to a common power arm. Rectilinear reciprocating movement of the latter in the fine of the arrow produces an almost Constant rotation of the ratchet-

I wheel.

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Copyii-ght, 1904, by Munn & Co.

(Ratchet Movements)

(Escapements)

88. The action of this ratchet mechanism is very similar to that shown in Fig. 86, except that the pawls are hooked and ratchet-wheel is rotated by an alternating pulling rather :than pushing action of the pawls.

89. This is a modification of the principle

{)ictured in Fig. 88, and shows a rocking ever with two pawls hinged thereon engaging a ratchet rack.

90. Another modification of the principle shown in 88. The rocking lever is mounted on a fixed stud and is provided at the center with a pin which enters a glot in a ratchet bar. The latter is formed with ratchet teeth on its opposite edges which are engaged by hooked pawls p.ivoted on the roicking lever. These pawls are cro.«!sed, as shown, so that they vvill be kept by gravity in constant engagement with the ratchet teeth. Now, when the lever is rocked the pawls will alternately act, to lift the ratchet bar.

91. A common construction used for rotating a ratchet-wheel against a spring resistance. A dog mounted on a fixed pivot drops by gravity or by spring pressure against the ratchet teeth and holds the wheel from turning while the pawl is being bwung back for a iresh hold on the ratchet-wheel.

92. This shows the method of rotating an ordinary spur gear-wheel by means of a pawl. The pawl is provided with a tooth at its outer end which fits between the teeth of the gear. The pawl is hinged to the lower arm of the bell-crank lever mounted on the gear shaft. The operating lever also mounted on this shaft is permitted a certain amount of play between two pins oh the shorter arm of the bell crank-lever. A rod connects the operating lever with the pawl. When the lever is raised it first lifts the pawl out of engagement with the gear, then, coming in contact with the upper pin on the bell crank-lever, it moves the pawl and bell crank back to the desired position. On lowering the operating lever the pawl is first brought into engagement with the gear and then the lower pin on the bell crank is encountered, and the gear is caused to rotate. This arrangement prevents wearing away of the teeth — a common defect in the ordinary type of ratchet mechanism.

93. The pawl is kept in contact with the ratchet-wheel by the weight of the lever on which it is formed. By pulling the rope attached to the end of the lever the pawl will be drawn out of engagement with the ratchet-wheel, and the latter will be turned by friction of the rope on the wheel hub.

94. A reversible spur-gear ratchet me-, chanism. Mounted on the shaft which carries the spur-gear is a bell crank-lever. This at one end carries a double-toothed

fiawl, one of which teeth meshes -with the eeth of the gear. The pawl is so shaped that it will withdraw the tooth from engagement with the gear teeth on the return stroke of the lever. When it is desired to reverse the direction of rotation, the pawl is moved over to the position shown in dotted lines, bringing its other tooth into engage- . ment with the gear reeth.

95. The ratchet-wheel is intermittently rotated by the oscillation of a lever which carries a spring-pressed pawl. On the upward stroke the ratchet is turned by the