The Kinematics of Machinery

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The Kinematics of Machinery : Outlines of a Theory of Machines  (1876) 
by Franz Reuleaux, translated by Alexander Kennedy
London : Macmillan (1876). Scanned in July 2007 by the University of Toronto for the Internet Archive.

THE

KINEMATICS OF MACHINERY.


OUTLINES

OF A

THEORY OF MACHINES.


BY

F. REULEAUX,

Director of and Professor in the Königlichen Gewerbe-Akademie in Berlin.
Member of the Königl. technischen Deputation für Gewerbe.


TRANSLATED AND EDITED BY

ALEX. B. W. KENNEDY, C.E.,

Professor of Civil and Mechanical Engineering in University College, London.


WITH NUMEROUS ILLUSTRATIONS.


London:

MACMILLAN AND CO.

1876.

[The Right of Translation and Reproduction is Reserved.]

LONDON:
R. CLAY, SONS, AND TAYLOR, PRINTERS,
BREAD STREET HILL,
QUEEN VICTORIA STREET

CONTENTS.

  Page
Preface v
Introduction 1
OUTLINES OF THE THEORY OF MACHINES.
Chapter I. General Outlines 29
§ 1. Nature of the Machine-Problem 29
2. The Science of Machines 36
3. General Solution of the Machine-Problem 41
Chapter II. Phoronomic Propositions 56
§ 4. Preliminary Remarks 56
5. Relative Motion in a Plane 57
6. Temporary Centre; the Central Polygon 60
7. Centroids; Cylindric Rolling 63
8. The Determination of Centroids 65
9. Reduction of Centroids 70
10. Rotation about a Point 76
11. Conic Rolling 77
12. Most general Form of the Relative Motion of Rigid Bodies 78
13. Twisting and Rolling of Ruled Surfaces 79
Chapter III. Pairs of Elements 86
§ 14. Different Forms of Pairs of Elements 86
15. The Determination of Closed Pairs 87
16. Motion in Closed Pairs 92
17. The necessary and sufficient Restraint of Elements 96
18. Restraint against Sliding 98
19. Restraint against Turning 103

§ 20. Simultaneous Restraint of Sliding and Turning 112
21. The Higher Pairs of Elements 115
22. Higher Pairs.—Duangle and Triangle 116
23. Point-paths of the Duangle relatively to the Equilateral Triangle 121
24. Point-paths of the Triangle relatively to the Duangle 125
25. Figures of Constant Breadth 129
26. Higher Pairs of Elements.—Equilateral Curve-triangle and Rhombus 131
27. Paths of Points of the Curve-triangle relatively to the Square 133
28. Paths described by Points of the Square relatively to the Curve-triangle 139
29. Higher Pairs of Elements:—other Curved Figures of Constant Breadth 139
30. General Determination of Profiles of Elements for a given Motion 146
31. First Method.—Determination of the Profile of one Element,
that of the other being arbitrarily assumed
148
32. Second Method.—Auxiliary Centroids 152
33. Third Method.—Profiles described by Secondary Centroids 155
34. Fourth Method.—Point-paths of Elements used as Profiles 156
35. Fifth Method.—Parallels or Equidistants to the Roulettes as Profiles 157
36. Sixth Method.—Approximations to Curved Profiles by Circular Arcs. Willis's Method 160
37. Seventh Method. The Centroids themselves as Profiles of Elements 163
38. Generalisation of the foregoing Methods 164
Chapter IV. Incomplete Pairs of Elements 169
§ 39. Closure of Pairs of Elements by Sensible Forces 169
40. Force-Closure in the Rolling of Axoids 171
41. Flectional Kinematic Elements 173
42. Springs 176
43. Closure of a Pair of Elements by a Kinematic Chain 178
44. Complete Kinematic Closure of the Flectional Elements 183
Chapter V. Incomplete Kinematic Chains 186
§ 45. Dead Points in Mechanism,—their Passage by Means of Sensible Forces 186
46. Passage of the Dead Points by Chain-Closure 188
47. Closure of Kinematic Chains by Pairs of Elements 191

Chapter VI. Sketch of the History of Machine Development 201
§ 48. The Origin and Early Growth of Machines 201
49. The Development of the Machine from a Kinematic point of view 226
50. The Growth of Modern Machinery 232
51. The Present Tendency of Machine Development 242
Chapter VII. Kinematic Notation 247
§ 52. Necessity for a Kinematic Notation 247
53. Former Attempts 248
54. Nature of the Symbols required 251
55. Class or Name-Symbols 252
56. Form-Symbols 253
57. Symbols of Relation 255
58. Formulæ for simple Kinematic Chains and Mechanisms 258
59. Contracted Formulæ 263
60. Formulæ for Compound Chains 264
61. Formulæ for Chains containing Pressure-organs 268
62. Contracted Formluæ for Single Mechanisms 270
Chapter VIII. Kinematic Analysis 274
§ 63. The Problems of Kinematic Analysis 274
64. The "Mechanical Powers" or "Simple Machines" 275
65. The Quadric (Cylindric) Crank Chain 283
66. Parallel Cranks 287
67. Anti-parallel Cranks 290
68. The Isosceles Crank-train 292
69. The Cylindric Slider-crank Chain 294
70. The Isosceles Slider-crank Chain 302
71. Expansion of Elements in the Slider-crank Chain 304
72. The Normal Double Slider-crank Chain 313
73. The Crossed Slider-crank Chain 318
74. Recapitulation of the Cylindric Crank Trains 323
75. The Conic Quadric Crank Chain 327
76. Reduction of a Kinematic Chain 333
77. Augmentation of Kinematic Chains 341
Chapter IX. Analysis of Chamber-crank Trains 342
§ 78. Chaining of Crank Mechanisms with Pressure-Organs 342
79. Chamber-crank Trains from the Turning Slider-crank 344
80. Chamber-crank Trains from the Isosceles Turning Slider-crank 355

§ 81. Chamber-crank Trains from the Swinging-block 356
82. Chamber-crank Trains from the Turning-block 360
83. Chamber-crank Trains from the Swinging Slider-crank 371
84. Chamber-crank Trains from the Turning Double Slider-crank 374
85. Chamber-crank Trains from the Turning Cross-block 375
86. Chamber-crank Trams from the Lever-crank 378
87. Chamber-crank Trains from the Double-crank 382
88. Chamber Trains from Conic Crank Mechanisms 384
89. Chamber-gear from the Conic Turning Double-slider 386
90. Chamber-gear from the Conic Swinging Cross-block 391
91. Chamber-gear from the Conic Turning Cross-block 393
92. Review of the preceding Results 400
Chapter X. Analysis of Chamber-wheel Trains 402
§ 93. Chaining of Spur-Gearing with Pressure-Organs 402
94. The Pappenheim Chamber-wheels 403
95. Fabry's Ventilator 409
96. Root's Blower 411
97. Payton's Water Meter 414
98. Evrard's Chamber-wheel Gear 416
99. Repsold's Pump 417
100. Dart's or Behrens' Chamber-wheel Gear 420
101. Eve's Chamber-wheel Gear 422
102. Révillion's Chamber-wheel Gear 422
103. Other Simple Chamber-wheel Trains 424
104. Compound Chamber-wheel Gear 425
105. Epicyclic Chamber-wheel Gear 427
Chapter XI. Analysis of the Constructive Elements of Machinery 436
§ 106. The Machine as a Combination of Constructive Elements 436
107. Screws and Screwed Joints 438
108. Keys, Cutters, &c., and Keyed Joints 441
109. Rivets and Riveting, Forced or Strained Joints 443
110. Pins, Axles, Shafts, Spindles 444
111. Couplings 445
112. Plummer Blocks, Bedplates, Brackets and Framing 447
113. Ropes, Belts, and Chains 451
114. Friction-wheels; Belt and Rope-gearing 452
115. Toothed-wheels, Chain-wheels 453
116. Fly-wheels 453
117. Levers, Cranks, Connecting-rods 454

§ 118. Crossheads and Guides 454
119. Click-wheels and Gear 455
120. Reversed Motion in Free Click-trains 459
121. Ratchet-trains 461
122. Brakes and Brake-gear 467
123. Engaging and Disengaging Gear 468
124. Recapitulation of the Methods used for Stopping and Setting in Motion 472
125. Pipes, Steam and Pump-cylinders, Pistons and Stuffing-boxes 473
126. Valves 473
127. Springs as Constructive Elements 480
128. General Conclusions from the Foregoing Analysis 480
Chapter XII. The Analysis of Complete Machines 486
§ 129. Existing Methods and Treatment 486
130. The Tool 490
131. Kinematic Nature of the Tool 493
132. The Receptor 497
133. Kinematic Nature of the Complete Machine 502
134. Prime-movers and Direct-actors 505
135. The Principal Subdivisions of Complete Machines. Descriptive Analysis 510
136. Examples of the Descriptive Analysis of Complete Machines 516
137. The Relation of Machinery to Social Life 522
Chapter XIII. Kinematic Synthesis 527
§ 138. General Nature of Kinematic Synthesis 527
139. Direct Kinematic Synthesis 528
140. Indirect Kinematic Synthesis 529
141. Diagram of the Synthetic Processes 531
142. Synthesis of the Lower Pairs of Elements 532
143. The Simpler Higher Pairs 533
144. Synthesis of Toothed-wheel Pairs 535
145. Cam Pairs 537
146. Recapitulation of the Pairs of Rigid Elements 538
147. Pairs of Elements containing Tension-Organs 539
148. Pairs of Elements containing Pressure-Organs 542
149. Recapitulation of the Pairs containing Flectional Elements 544
150. Determination of the Simple Chains 545
151. The Screw Chain 546
152. Cylinder-Chains 549
153. Prism Chains 553
154. The Crossed and Skew Screw Chains 555
155. Substitution of Higher Pairs for Pairs of Revolutes 559
156. The Simple Wheel-chains 562
157. The Slider-cam Trains 563
158. Pulley Chains 565
159. Chains with Pressure-Organs 567
160. Compound Chains 569
161. Examples of Compound Chains 572
162. Closing Remarks 580
Notes 585
Alphabetical Index 615

ERRATA.

Page 47, line 8, after "mechanism" add "or train."

Page 66, line 5 from bottom, p. 67, line 13 from bottom, p. 68, line 2 from bottom, p. 77, line 13 from top, for "pole" read "instantaneous centre."

Page 77, lines 24 and 25 from top, and p. 78, line 2, for "polar" read "central."

Page 121, reference number at end of top line should be 15.

Page 145, line 7 from bottom, for "XII. 1" read "XII. 2."

Page 146, line 7 from top, for "XII. 2" read "XII. 1."

Page 205, after lower footnote add "R."

Page 216, Nos. 1 and 2, fig. 168, should be inverted.

Page 269, line 4 from bottom, in formula, for "P+" read "P+."

Page 291, line 2 from bottom, insert the sign Z in formula.

Page 294, line 4 from top, in formula, for "C″4" read "C″2."

Page 426, bottom line, in formula, for "±" read "+."

Page 429, line 10 from bottom, in formula, for "C′3" read " C″3."