# Index:The Kinematics of Machinery.djvu

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## 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."