Elements of machine construction and drawing: or, Machine drawing, with some elements of descriptive and rational cinematics

Front matter

COURSE IN DESCRIPTIVE GEOMETRY AND STEREOTOMY.

BY S. EDWARD WARREN, C.E.,

PROFESSOR OF DESCRIPTIVE GEOMETRY, ETC., IN THE RENS- SELAER POLYTECHNIC INSTITUTE, TROY, N. Y.

Introduction

General principles 1

Scales 2

Elements of projections 4

Constructions of the ellipse 10

Special definitions 12

Classification of Machines 13

Functional classification of mechanical organs 15

Geometrical classification of mechanical organs 19

Reduction of scales. . . .20

PART H.

Theorems, Problems, and Examples on Elements of Machines.

CLASS I.— SUPPORTERS.

SECTION I. — LOCAL SUPPORTERS. A— Point Supporters

PiUow Blocks.

EXAMPLE I.— A heavy pillow block 22

EXAMPLE II. —A Putnam pillow block 24

47. Heavy lines.

EXAMPLE III. —A French pillow block 25

CONTENTS.

EXAMPLE IV.— A locomotive main axle box 26

48. Shaft hangers.

EXAMPLE V.— A bracket hanger 28

EXAMPLE VI.— A self-oiling drop hanger 29

EXAMPLE VII.— Turbine and spindle footsteps 30

49. Cold rolled shafting.

B — Line Supporters.

EXAMPLE VIII. — Locomotive guide bars and cross head. 31

50 — Progressive forms of cross heads.

O— Surface Supporters.

a — Plane Supporters.

b — Developable Supporters.

EXAMPLE LX.— A local bed plate 34

D — Volume Supporters.

EXAMPLE X.— A locomotive cylinder 34

EXAMPLE XI. —A jet-condenser 36

EXAMPLE XIL— A surface-condenser 38

SECTION II.— GENERAL SuppoRTERa A— Point Supporters

B — Line Supporters.

53. Standards.

EXAMPLE XHL— The standard of a power hammer 39

54. Comparative examples.

C — Surface Supporters.

a — Plane Supporters.

55. Fra'mes.

EXAMPLE XTV.— Locomotive frames 45

b — Developable Supporters.

56. Beds.

EXAMPLE XV.— A prismatic beam-bed and pedestal 48

D — Volume Supporters.

EXAMPLE XVL— A tank bed-plate 49

EXAMPLE XVIL — Housing, or chambered frame, for a reversible rolling

. 51

CONTENTS. V

PAGE

EXAMPLE XVIII.— Housing for a rolling mill 54

EXAMPLE XTY, —A passenger car truck. Practical remarks 56

CLASS II — RECEIVERS.

A — Point Receivers.

B — Line Receivers.

C— Surface Receivers.

a — Plane Receivers.

EXAMPLE XX. — Locomotive piston ; with Roth's steam piston packing. . 63 EXAMPLE XXI.— Thirty-six, and fifty-four inch pistons 67-

b — Developable Receivers.

EXAMPLE XXII.— A Fourneyron wheel plan 68

c — Warped Receivers.

EXAMPLE XXIII. —A Jonval turbine wheel and bucket 71

d — Double Curved Receivers.

EXAMPLE XXIV.— The Swain central discharge wheel 75

CLASS HI — COMMUNICATORS.

A — Point Communicators.

EXAMPLE XXV.— Collins' shaft coupling 79

B — Line Communicators.

Band, Cord, and Chain Wheels.

THEOREM I. — A rotary motion of two parallel axes may be maintained indefinitely, and in one and the same direction for both, by a band passing directly around cylindrical pulleys in the same plane, on those axes ; but, if the band be crossed, the rotations will be in opposite directions ; but, in both cases, the ratio of the velocities

will be constant 81

THEOREM II. — A band should be crossed by giving it a half twist, in a plane perpendicular to that of the wheels which hold it : it should be shifted, laterally, by operating on its advancing side, and if applied to a cone-wheel, will work itself towards the larger end of

the cone 82

PROBLEM I. — To connect wheels lying in different planes, by a band ; when the intersection of their planes is also a common tangent to the two wheels 84

PROBLEM II.— To connect band wheels, in different planes, when the intersection of those planSs is not a common tangent to the wheels... 86

Vlli CONTENTS.

PAGH

PROBLEM VIII. — To find the radii of the tooth curves 147

PROBLEM IX. — To find centres for approximate involute teeth 148

EXAMPLE XXXIV.— To construct teeth having separate faces and flanks,

by the odontograph 149

EXAMPLE XXXV. — To construct approximate involute teeth by the odontograph 152

EXAMPLE XXXVI.— Projections of bevel gearing 153

c — Warped Communicators.

EXAMPLE XXXVII. — The complete projections of a screw and nut 154

EXAMPLE XXXVIII.— The abridged drawing of screws 157

Uniform System of Screws 158

EXAMPLE XXXIX.— Endless screws and spiral gear 160

EXAMPLE XL. — Detailed construction of a tooth in spiral gearing 163

113. Manufacture of worm wheels 164

CLASS IV.— REGULATORS.

A — Point Regulators.

B — Line Regulators.

EXAMPLE XLL— A fly wheel 165

C — Surface Regulators.

Plane throttle valves. Single poppet valves. Cage valves. Cylindrical

throttle valves. Ball valves 167

D — Volume Regulators.

Cocks. Globe valves. Water gates 167

EXAMPLE XLII.— Chambered, or D locomotive slide valves; plain, and

anti-friction 169

EXAMPLE XLIII.— Tremain's balanced piston valve 171

EXAMPLE XLIV.— Balanced poppet valves. Data from practice 175

123. Examples of engine action 179

EXAMPLE XL V.— Richardson's locomotive and lock-up safety valve 180

EXAMPLE XLVI.— A double beat pump valve 183

EXAMPLE XL VII. —A Cornish equilibrium valve 185

EXAMPLE XLVIIL — Giffard's injector. 185

CLASS V.— MODULATORS.

A— Point Modulators.

Idler pulleys 190

B — Line Modulators.

Escapements. Band shifters. Clutches. Etc. 190

CONTENTS. IX

O— Surface Modulators, a — Plane Modulators.

PAGE

Variable crank 191

b — Developable Modulators.

Speed pulleys 193

THEOREM XXI. — If the band be crossed, it will be equally tight on

every pair of opposite pulleys 192

PROBLEM X. — To form a set of speed pulleys, to give a series of velocity ratios in geometrical progression 193

Cone pulleys. Dead Pulleys. Sectoral motions. Elliptic gears 195

c — Warped Modulators.

The helicoidal clutch 197

d — Double-curved Modulators.

Double-curved speed pulleys 198

CLASS VI.— OPERATORS.

A— Point Operators.

EXAMPLE XLIX.— Movable saw teeth 199

EXAMPLE L.— Lyall's positive motion shuttle 203

B — Line Operators.

Cutters (143) 209

O — Surface Operators, a — Plane Operators,

EXAMPLE LI.— Air pump bucket of a marine engine 209

b — Developable Operators, c — Warped Operators.

THE SCREW PROPELLER.

Preliminary remarks 210

Introductory geometrical principles 211

The helix and helicoid 212

Slip 217

Lateral slip 217

Negative slip 218

Irregular screws , 220

PROBLEM XI.— To construct a helix of uniform pitch and radius 221

PROBLEM XII. — To construct the projections of the common right helicoid, generated by the radius of a vertical cylinder 223

X CONTENTS.

PAGE

PROBLEM XIII. — To construct the projections of a common right helicoid, which is generated by the diameter of a vertical cylinder. 223

PROBLEM XIV. — Having given either projection of any element of a

helicoid, to find its other projection 224

PROBLEM XV. — To represent a common right helicoid by its helical

lines 224

PROBLEM XVI. — To construct the lines of a helicoid, made by its intersection with any plane parallel to its axis 225

PROBLEM XVII. — Having given either projection of any point upon a

helicoid, to find its other projection 226

PROBLEM XVIII. — To develope one or more given helices 226

PROBLEM XIX. — From the circular projection and development of a

helix, to construct its spiral projection 227

PROBLEM XX. — To construct a helicoid of axial expanding pitch, by

means of its helical lines 228

PROBLEM XXL — To develope the four helices last drawn 228

PROBLEM XXII. — To make the projections of a helicoid of radially

expanding pitch 229

PROBLEM XXIII. —To develope the helices shown in the last problem . 230 PROBLEM XXIV. — To construct the projections of the acting faces of

a four-bladed common screw propeller 231

EXAMPLE LIL— To represent variously limited propeller blades, with

their concentric and radial sections 232

Ideas expressed in modified forms of Screws 235

Historical note 236

EXAMPLE LHL— The screw of the " Dunderberg." 238

D — Volume Operators.

EXAMPLE LIV.— Andrews' centrifugal pump 240

Book II. Compound Elements, Or Sub-machines

SUPPORTERS.

EXAMPLE LV.— A compound chuck 245

COMMUNICATORS.

EXAMPLE LVI. — A beam-engine main movement 249

EXAMPLE LVII.— Wheeler's tumbling-beam engine 250

EXAMPLE LVIII.— An eight day clock train 252

Other trains 252'

Change wheels 256

THE SLIDE VALVE AND ITS CONNECTIONS.

General description of parts 257

General action . . 259

Modifications and adjustments 260

CONTENTS. XI

PAGE

Definitions ' 261

THEOREM XXII. — In either mode of connection the velocity of the

crank pin is uniform, and that of the piston is variable 268

THEOREM XXIII. — The piston positions, corresponding to crank pin positions, which are equidistant from the same dead-point are identical, for each connection separately. . r 264

THEOREM XXIV. — The segments of the double stroke are equal, in the direct connection, and the front one is the greater in the indirect

connection. Conversely, etc 264

Natnml zero paints of the piston and crank-pin motions, and segments of

the double stroke 265

THEOREM XXV. — The crank piston is ahead of the yoke piston during the stroke toward the shaft, and behind it during the opposite

stroke 266

THEOREM XXVI — The effect of a given angular advance of the eccentric will be to afford "admission" for a new stroke, "cut-off," " exhaust closure," and release, all at an equal number of degrees

before reaching a dead-point 267

THEOREM XXVII. — The effect of a given lap, alone, corresponding to an equal number of degrees from the zero diameter, is, to postpone admission for an equal number of degrees beyond the dead-point ; to produce cut-off at the same number of degrees beyond the dead-point ; with release and exhaust closure at the dead-point. 268 PROBLEM XXV. — To produce a cut-off at a given crank-pin position,

without preventing proper admission, etc 269

PROBLEM XXVI. — To determine the exhaust closure and release, for

the adjusted cut-off and admission 270

THEOREM XXVIII. — The travel of a valve, with lap, is the sum of twice

the lap, added to twice the steam port opening 270

THEOREM XXIX. — Inside lap prolongs expansion, and hastens compression ; while inside clearance hastens the release, and postpones the

beginning of compression 271

PROBLEM XXVII. — To determine the effect of the eccentric upon the

valve motion and to counteract it in part 272

Distribution of power. 273

Lead 273

PROBLEM XXVIII. — To provide a certain lead angle, without disturbance of the cut-off 274

PROBLEM XXIX.— To determine the effect of lead on exhaust closure,

release and travel 274

THEOREM XXX.— The angular advance, estimated from the zero radius hitherto taken, is equal to the sum of the lap and lead angles,

estimated from the same point 275

THEOREM XXXI. — When the steam port is open by the amount of the lead, the exhaust opposite port is open for exhaust by the amount

of the lap and lead 275

Port opening 276

Summary of elements 278

Xii CONTENTS.

PAGB

PKOBLEM XXX. — To reverse the motion of an engine. Drop hook. . . 280

EXAMPLE LIX.— A. Stephenson link motion 283

To find one position of the link 285

Data for finding any position of the link 2':' i

To adjust the model 287

Remarks and results * 2Q8

EXAMPLE LX.— Data of valve motions 290

I.— Of a 15" x 22" cylinder 290

II.— Of a 16" x 24" cylinder 291

III.— Of an 18" x 22" cylinder 291

Experimental determinations. 293

Setting the valve motion of a locomotive. 294

REGULATORS.

Governors.

Elementary Principles 297

EXAMPLE LXL— Chubbuck's fan throttle governor 300

EXAMPLE LXIL— The Huntoon oil throttle governor 302

EXAMPLE LXIIL— Wright's variable cut-off by the governor 304

EXAMPLE LXIV.— Babcock and Wilcox governor and variable cut-off. . . 307

Indicator diagrams 314

EXAMPLE LXV.— The Putnam Machine Co.'s variable cut-off 320

EXAMPLE LXVI.— The Rider cut-off 321

EXAMPLE LXVII.— Sibley and Walsh's water-wheel governor 322

MODULATORS.

EXAMPLE LXVIII.— Compound speed and feed motions 325

EXAMPLE LXIX.— Whitworth's quick-return motion 327

EXAMPLE LXX.— Mason's friction pulleys and couplings, or clutches 328

EXAMPLE LXXI. — Reversing gear for the compound Rolling-Mill Engine 332

EXAMPLE LXXIL— Bond's escapement, No. 2 334

EXAMPLE LXXHL— Bond's auxiliary pendulum gravity escapement 337