Kinematic Differential Geometry and Saddle Synthesis of Linkages

With a pioneering methodology, the book covers the fundamental aspects of kinematic analysis and synthesis of linkage, and provides a theoretical foundation for engineers and researchers in mechanisms design. The first book to propose a complete curvature theory for planar, spherical and spatial motion Treatment of the synthesis of linkages with a novel approach Well-structured format with chapters introducing clearly distinguishable concepts following in a logical sequence dealing with planar, spherical and spatial motion Presents a pioneering methodology by a recognized expert in the field and brought up to date with the latest research and findings * Fundamental theory and application examples are supplied fully illustrated throughout

Auteur

DELUN WANG, Dalian University of Technology, China WEI WANG, Dalian University of Technology, China

Texte du rabat
KINEMATIC DIFFERENTIAL GEOMETRY AND SADDLE SYNTHESIS OF LINKAGES With a pioneering methodology, this book covers the fundamental aspects of kinematic analysis and synthesis of linkages, and provides a theoretical foundation for engineers and researchers in mechanism design. The authors present, for the first time, both the kinematic geometry in differential geometry from planar motion to spherical and spatial motion, and the saddle kinematic synthesis of planar and spatial linkages by the best uniform approximation.

• The first book to propose the generalized curvature corresponding to binary links, and set up the unified curvature theory in kinematics based on centrodes (axodes).
• Describes the global geometrical properties of loci in discrete kinematics by the invariants of the constraint curves and ruled surfaces of binary links.
• Well-structured format with chapters progressing logically from planar to spherical and spatial motion.
• Presents a pioneering methodology by recognized experts in the field, updated with the latest research findings.
• Fundamental theory and application examples are supplied.
• Fully illustrated throughout. Kinematic Differential Geometry and Saddle Synthesis of Linkages is a ground-breaking and significant addition to the field of mechanism design. It is intended for graduate students, researchers, and design engineers in mechanical, aerospace, and automotive engineering.

Contenu
Preface ix

Acknowledgments xi

1 Planar Kinematic Differential Geometry 1

1.1 Plane Curves 2

1.1.1 Vector Curve 2

1.1.2 Frenet Frame 6

1.1.3 Adjoint Approach 10

1.2 Planar Differential Kinematics 14

1.2.1 Displacement 14

1.2.2 Centrodes 18

1.2.3 EulerSavary Equation 26

1.2.4 Curvatures in Higher Order 33

1.2.5 Line Path 42

1.3 Plane Coupler Curves 49

1.3.1 Local Characteristics 49

1.3.2 Double Points 51

1.3.3 Four-bar Linkage I 55

1.3.4 Four-bar Linkage II 61

1.3.5 Oval Coupler Curves 67

1.3.6 Symmetrical Coupler Curves 73

1.3.7 Distribution of Coupler Curves 75

1.4 Discussion 78

References 80

2 Discrete Kinematic Geometry and Saddle Synthesis of Planar Linkages 83

2.1 Matrix Representation 84

2.2 Saddle Point Programming 85

2.3 Saddle Circle Point 88

2.3.1 Saddle Circle Fitting 89

2.3.2 Saddle Circle 92

2.3.3 Four Positions 95

2.3.4 Five Positions 97

2.3.5 Multiple Positions 100

2.3.6 Saddle Circle Point 101

2.4 Saddle Sliding Point 106

2.4.1 Saddle Line Fitting 108

2.4.2 Saddle Line 109

2.4.3 Three Positions 111

2.4.4 Four Positions 114

2.4.5 Multiple Positions 116

2.4.6 Saddle Sliding Point 116

2.5 The Saddle Kinematic Synthesis of Planar Four-bar Linkages 120

2.5.1 Kinematic Synthesis 122

2.5.2 Crank-rocker Linkage 129

2.5.3 Crank-slider Linkage 139

2.6 The Saddle Kinematic Synthesis of Planar Six-bar Linkages with Dwell Function 145

2.6.1 Six-bar Linkages 146

2.6.2 Local Saddle Curve Fitting 149

2.6.3 Dwell Function Synthesis 150

2.7 Discussion 163

References 167

3 Differential Geometry of the Constraint Curves and Surfaces 171

3.1 Space Curves 171

3.1.1 Vector Representations 171

3.1.2 Frenet Trihedron 175

3.2 Surfaces 177

3.2.1 Elements of Surfaces 177

3.2.2 Ruled Surfaces 183

3.2.3 Adjoint Approach 186

3.3 Constraint Curves and Surfaces 192

3.4 Spherical and Cylindrical Curves 195

3.4.1 Spherical Curves (SS) 195

3.4.2 Cylindrical Curves (CS) 197

3.5 Constraint Ruled Surfaces 201

3.5.1 Constant Inclination Ruled Surfaces (CPC) 201

3.5.2 Constant Axis Ruled Surfaces (CC) 204

3.5.3 Constant Parameter Ruled Surfaces (HC, RC) 208

3.5.4 Constant Distance Ruled Surfaces (SC) 212

3.6 Generalized Curvature of Curves 214

3.6.1 Generalized Curvature of Space Curves 215

3.6.2 Spherical Curvature and Cylindrical Curvature 218

3.7 Generalized Curvature of Ruled Surfaces 224

3.7.1 Tangent Conditions 224

3.7.2 Generalized Curvature 225

3.7.3 Constant Inclination Curvature 227

3.7.4 Constant Axis Curvature 228

3.8 Discussion 228

References 230

4 Spherical Kinematic Differential Geometry 233

4.1 Spherical Displacement 233

4.1.1 General Expression 233

4.1.2 Adjoint Expression 235

4.2 Spherical Differential Kinematics 240

4.2.1 Spherical Centrodes (Axodes) 240

4.2.2 Curvature and EulerSavary Formula 245

4.3 Spherical Coupler Curves 257

4.3.1 Basic Equation 257

4.3.2 Double Point 257

4.3.3 Distribution 262

4.4 Discussion 263

References 266

5 Discrete Kinematic Geometry and Saddle Synthesis of Spherical Linkages 267

5.1 Matrix Representation 267

5.2 Saddle Spherical Circle Point 269

5.2.1 Saddle Spherical Circle Fitting 269 5.2.2 Saddle Spherical Circl...