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Kinematic Geometry of Gearing

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Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and... Weiterlesen
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Beschreibung

Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure’, cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the ‘3 laws of gearing’, the first law re-written to better parallel the existing ‘Law of Gearing” as pioneered by Leonard Euler, expanded from Euler’s original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relation between gear sizes, and the 3rd law completely reworked from its original form to uniquely describe a limiting condition on curvature between gear teeth, with new relations for gear efficiency are presented based on the kinematics of general toothed wheels in mesh.  There is also a completely new chapter on gear vibration load factor and impact.

Progressing from the fundamentals of geometry to construction of gear geometry and application, Kinematic Geometry of Gearing presents a generalized approach for the integrated design and manufacture of gear pairs, cams and all other types of toothed/motion/force transmission mechanisms using computer implementation based on algebraic geometry.



David B Dooner, University of Puerto Rico-Mayagüez, Puerto Rico and Ali A Seireg, University of Wisconsin at Madison and University of Florida at Gainesville, USA
David B Dooner is a Professor in the Department of Mechanical Engineering at the University of Puerto Rico-Mayagüez. He received his doctorate from the University of Florida at Gainesville in 1991 where he remained as a Post-Doctoral Fellow from 1991-1994. He worked at the General Motors Gear Center in 1989 and was a visiting scientist at the Mechanical Sciences Research Institute of the Russian Academy of Sciences in Moscow in 1992.

Autorentext
David B Dooner, University of Puerto Rico-Mayagüez, Puerto Rico and Ali A Seireg, University of Wisconsin at Madison and University of Florida at Gainesville, USA
David B Dooner is a Professor in the Department of Mechanical Engineering at the University of Puerto Rico-Mayagüez. He received his doctorate from the University of Florida at Gainesville in 1991 where he remained as a Post-Doctoral Fellow from 1991-1994. He worked at the General Motors Gear Center in 1989 and was a visiting scientist at the Mechanical Sciences Research Institute of the Russian Academy of Sciences in Moscow in 1992.

Inhalt
Preface xiii

Part I FUNDAMENTAL PRINCIPLES OF TOOTHED BODIES IN MESH

1 Introduction to the Kinematics of Gearing 3

1.1 Introduction 3

1.2 An Overview 3

1.3 Nomenclature and Terminology 5

1.4 Reference Systems 8

1.5 The Input/Output Relationship 9

1.6 Rigid Body Assumption 11

1.7 Mobility 11

1.8 Arhnold-Kennedy Instant Center Theorem 14

1.9 Euler-Savary Equation for Envelopes 18

1.10 Conjugate Motion Transmission 19

1.10.1 Spur Gears 20

1.10.2 Helical and Crossed Axis Gears 21

1.11 Contact Ratio 22

1.11.1 Transverse Contact Ratio 24

1.11.2 Axial Contact Ratio 25

1.12 Backlash 25

1.13 Special Toothed Bodies 26

1.13.1 Microgears 28

1.13.2 Nanogears 28

1.14 Noncylindrical Gearing 29

1.14.1 Hypoid Gear Pairs 29

1.14.2 Worm Gears 30

1.14.3 Bevel Gears 32

1.15 Noncircular Gears 33

1.15.1 Gear and Cam Nomenclature 38

1.15.2 Rotary/Translatory Motion Transmission 39

1.16 Schematic Illustration of Gear Types 40

1.17 Mechanism Trains 40

1.17.1 Compound Drive Trains 41

1.17.2 Epicyclic Gear Trains 43

1.17.3 Circulating Power 49

1.17.4 Harmonic Gear Drives 50

1.17.5 Noncircular Planetary Gear Trains 51

1.18 Summary 52

Part II THE KINEMATIC GEOMETRY OF CONJUGATE MOTION IN SPACE

2 Kinematic Geometry of Planar Gear Tooth Profiles 55

2.1 Introduction 55

2.2 A Unified Approach to Tooth Profile Synthesis 55

2.3 Tooth Forms Used for Conjugate Motion Transmission 56

2.3.1 Cycloidal Tooth Profiles 56

2.3.2 Involute Tooth Profiles 59

2.3.3 Circular-arc Tooth Profiles 63

2.3.4 Comparative Evaluation of Tooth Profiles 64

2.4 Contact Ratio 65

2.5 Dimensionless Backlash 68

2.6 Rack Coordinates 69

2.6.1 The Basic Rack 71

2.6.2 The Specific Rack 76

2.6.3 The Modified Rack 77

2.6.4 The Final Rack 79

2.7 Planar Gear Tooth Profile 80

2.8 Summary 84

3 Generalized Reference Coordinates for Spatial Gearingthe Cylindroidal Coordinates 85

3.1 Introduction 85

3.2 Cylindroidal Coordinates 85

3.2.1 History of Screw Theory 87

3.2.2 The Special Features of Cylindroidal Coordinates 87

3.3 Homogeneous Coordinates 89

3.3.1 Homogeneous Point Coordinates 91

3.3.2 Homogeneous Plane Coordinates 92

3.3.3 Homogeneous Line Coordinates 93

3.3.4 Homogeneous Screw Coordinates 96

3.4 Screw Operators 99

3.4.1 Screw Dot Product 99

3.4.2 Screw Reciprocal Product 99

3.4.3 Screw Cross Product 101

3.4.4 Screw Intersection 102

3.4.5 Screw Triangle 103

3.5 The Generalized Equivalence of the Pitch Pointthe Screw Axis 104

3.5.1 Theorem of Three Axes 105

3.5.2 The Cylindroid 107

3.5.3 Cylindroid Intersection 108

3.6 The Generalized Pitch SurfaceAxodes 110

3.6.1 The Theorem of Conjugate Pitch Surfaces 115

3.6.2 The Striction Curve 116

3.7 The Generalized Transverse Surface 121

3.8 The Generalized Axial Surface 123

3.9 Summary 125

4 Differential Geometry 127

4.1 Introduction 127

4.2 The Curvature of a Spatial Curve 127

4.3 The Torsion of a Spatial Curve 129

4.4 The First Fundamental Form 130

4.5 The Second Fundamental Form 132

4.6 Principal Directions and Principal Curvatures 135

4.7 Torsure of a Spatial Curve 138

4.8 The Cylindroid of Torsure 142

4.9 Ruled Surface Trihedrons 148

4.10 Formulas of Fernet-Serret 150

4.11 Coordinate Transformations 151

4.12 Characteristic Lines and Points 158

4.13 Summary 159

5 Analysis of Toothed Bodies for Motion Generation 161

5.1 Introduction 161

5.2 Spatial Mobility Criterion 161

5.3 Reciprocitythe First Law of Gearing 164

5.4 The Line Complex 166

5.5 The Tooth Spiral 168

5.5.1 The Tooth Spiral Curvature 170

5.5.2 The Tooth Spiral Torsion 173

5.6 Tooth Spiral Anglethe Second Law of Gearing 174

5.6.1 The I/O Relationship 179

5.6.2 The Phantom I/O Relationship 181

5.7 Reduced Tooth Curvaturethe Third Law of Gearing 183

5.7.1 Absolute Tooth Curvature 187

5.7.2 Tooth Profile Modification 190

5.8 Classification of Gear Types 192

5.9 Contact Ratio 194

5.9.1 Transverse Contact Ratio 195

5.9.2...

Produktinformationen

Titel: Kinematic Geometry of Gearing
Autor:
EAN: 9781118385555
ISBN: 978-1-118-38555-5
Digitaler Kopierschutz: Adobe-DRM
Format: E-Book (epub)
Herausgeber: Wiley
Genre: Maschinenbau, Fertigungstechnik
Anzahl Seiten: 512
Veröffentlichung: 09.04.2012
Jahr: 2012
Auflage: 2. Aufl.
Untertitel: Englisch
Dateigrösse: 15.7 MB