A Treatise on the Theory of ScrewsCUP Archive, 2006 - 544 Seiten |
Inhalt
CHAPTER I | 2 |
The canonical form of a Small Displacement | 5 |
Instantaneous Screws 7 Definition of the word Wrench | 6 |
Restrictions | 7 |
CHAPTER II | 15 |
The Virtual Coefficient 11 Symmetry of the Virtual Coefficient 12 Composition of Twists and Wrenches | 18 |
The Cylindroid | 20 |
General Property of the Cylindroid 15 Particular Cases 16 Cylindroid with One Screw of Infinite Pitch | 22 |
Intersecting Screws in a ThreeSystem | 210 |
CHAPTER XVI | 218 |
Applications of the TwoSystem | 225 |
Polar Screws | 226 |
Application of Eulers Theorem | 231 |
Impulsive Screws and Instantaneous Screws | 232 |
Impulsive Screws | 238 |
103 | 242 |
Form of the Cylindroid in general 18 The Pitch Conic 19 Summary | 22 |
CHAPTER III | 22 |
Reciprocal Cone | 23 |
PAGE 1 | 25 |
Locus of a Screw Reciprocal to Four Screws | 29 |
Screw Reciprocal to Five Screws | 30 |
CHAPTER IV | 31 |
Intensities of the Components | 32 |
The Intensity of the Resultant | 33 |
Coordinates of a Wrench | 34 |
Identical Relation | 35 |
The Virtual Coefficient | 36 |
6 | 37 |
The Canonical Coreciprocals | 38 |
A Screw of Infinite Pitch | 39 |
Indeterminate Screw | 40 |
A Screw at Infinity | 41 |
Transformation of Screw Coordinates | 42 |
Principal Screws on a Cylindroid | 43 |
CHAPTER V | 45 |
The Axis of Pitch | 46 |
The Distance between Two Screws | 47 |
7 | 48 |
8 | 49 |
9 | 50 |
10 | 51 |
11 | 52 |
Screw Coordinates | 57 |
15 | 58 |
17 | 60 |
CHAPTER VII | 69 |
An Algebraical Lemma | 75 |
Expression for Kinetic Energy | 80 |
Twist Velocity acquired by an Impulsive Wrench | 81 |
Kinetic Energy acquired by an Impulsive Wrench 92 Formula for a Free Body | 82 |
Lemma 94 Eulers Theorem 95 Coordinates in a Screw System | 83 |
The Reduced Wrench | 84 |
Coordinates of Impulsive and Instantaneous Screws 80 81 82 82 83 83 83 84 | 85 |
CHAPTER VIII | 87 |
The Potential 99 The Wrench evoked by Displacement | 88 |
Conjugate Screws of the Potential 101 Principal Screws of the Potential | 90 |
Coordinates of the Wrench evoked by a Twist | 91 |
Form of the Potential CHAPTER IX | 92 |
HARMONIC SCREWS 94 96 99 100 104 Definition of an Harmonic Screw | 94 |
Equations of Motion | 98 |
Discussion of the Results | 99 |
Remark on Harmonic Screws | 100 |
CHAPTER X | 101 |
18 | 102 |
CHAPTER XI | 107 |
Relation between Two Cylindroids | 108 |
Screws on One Line | 109 |
Displacement of a Point | 110 |
Equilibrium | 111 |
Particular Case | 112 |
Impulsive Forces | 113 |
Small Oscillations | 114 |
Property of Harmonic Screws | 115 |
The Ellipse of the Potential | 116 |
101 | 117 |
Harmonic Screws | 118 |
Reaction of Constraints | 119 |
19 | 120 |
Conjugate Screws of Inertia | 124 |
Impulsive Screws and Instantaneous Screws | 125 |
Two Homographic Systems | 126 |
21 | 127 |
22 | 128 |
Twist Velocity acquired by an Impulse | 129 |
24 | 131 |
A Special Case | 133 |
Another Construction for the Twist Velocity acquired by an Impulse | 134 |
Constrained Motion | 136 |
Energy acquired by an Impulse | 137 |
Eulers Theorem | 138 |
Principal Screws of the Potential | 140 |
102 | 141 |
Reciprocal Screws | 164 |
Relation between the Impulsive Screw and the Instantaneous Screw | 168 |
The Family of Quadrics | 174 |
71 | 185 |
Equilibrium of Four Forces applied to a Rigid Body | 186 |
Kinetic Energy acquired by an Impulse | 189 |
CHAPTER XV | 197 |
The Pitch Conics | 204 |
Analogy to Anharmonic Ratio | 266 |
78 | 267 |
Corresponding Screws defined by Equations | 272 |
The Dyname | 275 |
Property of the Pitches of Six Coreciprocals | 282 |
A Pitch Invariant | 290 |
Expression for the Kinetic Energy | 297 |
Case of a Constrained Rigid Body | 303 |
General Conditions of Chiastic Homography | 309 |
297 | 316 |
Cylindroid Reduced to a Plane | 319 |
A difficulty removed | 320 |
CHAPTER XXII | 322 |
One Pair of Impulsive and Instantaneous Screws | 323 |
An Important Exception | 325 |
A System of Rigid Bodies | 326 |
The Geometrical Theory of Three Pairs of Screws | 330 |
Another Method | 332 |
Analogous Problem in a Threesystem | 334 |
Fundamental Problem with Free Body | 336 |
Freedom of the First or Second Order | 338 |
Freedom of the Third Order | 339 |
Freedom of the Fifth Order | 340 |
Principal Screws of Inertia of Constrained Body | 341 |
Third and Higher Systems | 342 |
Correlation of Two Systems of the Third Order | 344 |
A Property of Reciprocal Screw Systems | 347 |
Systems of the Fourth Order | 348 |
Systems of the Fifth Order | 350 |
Two Rigid Bodies | 351 |
CHAPTER XXIII | 355 |
A Differential Equation satisfied by the Kinetic Energy | 356 |
Another Proof of Article 303 | 357 |
Construction of Homographic Correspondents | 358 |
Geometrical Solution of the same Problem | 359 |
Coreciprocal Correspondents in Two Threesystems | 360 |
Impulsive and Instantaneous Cylindroids | 361 |
The Double Correspondents on Two Cylindroids | 363 |
A Property of Coreciprocals | 364 |
Instantaneous Screw of Zero Pitch | 365 |
CHAPTER XXIV | 367 |
The Graphic and Metric Elements | 368 |
The Definition of a Screwchain | 369 |
Freedom of the Second Order | 370 |
Homography of Screw Systems | 374 |
Freedom of the Third Order | 375 |
Freedom of the Fourth Order | 377 |
Freedom of the Fifth Order | 378 |
Application of Parallel Projections | 379 |
Properties of this correspondence | 383 |
Freedom of the Fifth Order | 384 |
Freedom of the Sixth Order | 386 |
Freedom of the Eighth and Higher Orders | 388 |
Twists on 6u+1 Screwchains | 390 |
Impulsive Screwchains and Instantaneous Screwchains | 392 |
The principal Screwchains of Inertia | 394 |
Conjugate Screwchains of Inertia | 396 |
Harmonic Screwchains | 397 |
CHAPTER XXV | 399 |
Different Properties of a Principal Axis | 400 |
A Property of the Kinetic Energy of a System | 401 |
The Identical Equation in Screwchain Coordinates | 403 |
The Converse Theorem | 404 |
Transformation of the Vanishing Emanant | 405 |
Generalization of the Eulerian Equations | 406 |
The Restraining Wrenchchain | 407 |
Physical meaning of the Vanishing Emanant | 408 |
The Accelerating Screwchain | 409 |
Accelerating Screwchain and Instantaneous Screwchain | 410 |
Conditions of a Permanent Screwchain | 411 |
Another identical Equation | 412 |
Different Screws on the same Axis | 414 |
The Geometrical Meaning of this Symmetric Function | 418 |
384 | 420 |
Application of the Theory of Emanants | 424 |
Three Degrees of Freedom | 426 |
394 | 432 |
401 | 441 |
Another Investigation of the possibility of Equally Graduated Ranges | 447 |
414 | 454 |
The Conception of Force in NonEuclidian Space | 480 |
Notes on various points | 496 |
510 | |
104 | 532 |
106 | 537 |
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Häufige Begriffe und Wortgruppen
a₁ acted amplitude axes axis belonging centre chord circle co-ordinates co-reciprocal coefficient common condition conic conjugate screws constant construction contains corresponding course cubic cylindroid defined denote determined diameter direction displacement Draw drawn ellipse equal equation equilibrium expression forces four freedom function geometrical give given given screw Hence homographic impulsive screw impulsive wrench infinite instantaneous screw intensity intersect kinetic energy known linear locus move objects obtain P₁ pair parallel pass perpendicular pitch plane position potential present principal screws problem proportional proved quantities ratio reciprocal reciprocal screws relation represented respect result rigid body rotation screw system screw-chain screws of inertia screws of reference shown suppose surface tangent theorem theory third order three-system twist velocity values whence zero zero pitch
Beliebte Passagen
Seite 512 - Treatise on the Theory of Screws (gr. 8°, 26 chapt., 544 p., 50 fig. and 3 plates; 18 sh.). Cambridge, University press, 1900. — Since the author's celebrated publication ,,The Theory of Screws: A study in the Dynamics of a Rigid Body...