A Treatise on the Theory of Screws

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CUP 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
BIBLIOGRAPHICAL NOTES
510
104
532
106
537

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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...

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