KINEMATIC GEOMETRY OF GEARING -- Contents -- Preface -- Part I FUNDAMENTAL PRINCIPLES OF TOOTHED BODIES IN MESH -- 1 Introduction to the Kinematics of Gearing -- 1.1 Introduction -- 1.2 An Overview -- 1.3 Nomenclature and Terminology -- 1.4 Reference Systems -- 1.5 The Input/Output Relationship -- 1.6 Rigid Body Assumption -- 1.7 Mobility -- 1.8 Arhnold-Kennedy Instant Center Theorem -- 1.9 Euler-Savary Equation for Envelopes -- 1.10 Conjugate Motion Transmission -- 1.10.1 Spur Gears -- 1.10.2 Helical and Crossed Axis Gears -- 1.11 Contact Ratio -- 1.11.1 Transverse Contact Ratio -- 1.11.2 Axial Contact Ratio -- 1.12 Backlash -- 1.13 Special Toothed Bodies -- 1.13.1 Microgears -- 1.13.2 Nanogears -- 1.14 Noncylindrical Gearing -- 1.14.1 Hypoid Gear Pairs -- 1.14.2 Worm Gears -- 1.14.3 Bevel Gears -- 1.15 Noncircular Gears -- 1.15.1 Gear and Cam Nomenclature -- 1.15.2 Rotary/Translatory Motion Transmission -- 1.16 Schematic Illustration of Gear Types -- 1.17 Mechanism Trains -- 1.17.1 Compound Drive Trains -- 1.17.2 Epicyclic Gear Trains -- 1.17.3 Circulating Power -- 1.17.4 Harmonic Gear Drives -- 1.17.5 Noncircular Planetary Gear Trains -- 1.18 Summary -- Part II THE KINEMATIC GEOMETRY OF CONJUGATE MOTION IN SPACE -- 2 Kinematic Geometry of Planar Gear Tooth Profiles -- 2.1 Introduction -- 2.2 A Unified Approach to Tooth Profile Synthesis -- 2.3 Tooth Forms Used for Conjugate Motion Transmission -- 2.3.1 Cycloidal Tooth Profiles -- 2.3.2 Involute Tooth Profiles -- 2.3.3 Circular-arc Tooth Profiles -- 2.3.4 Comparative Evaluation of Tooth Profiles -- 2.4 Contact Ratio -- 2.5 Dimensionless Backlash -- 2.6 Rack Coordinates -- 2.6.1 The Basic Rack -- 2.6.2 The Specific Rack -- 2.6.3 The Modified Rack -- 2.6.4 The Final Rack -- 2.7 Planar Gear Tooth Profile -- 2.8 Summary.

3 Generalized Reference Coordinates for Spatial Gearing-the Cylindroidal Coordinates -- 3.1 Introduction -- 3.2 Cylindroidal Coordinates -- 3.2.1 History of Screw Theory -- 3.2.2 The Special Features of Cylindroidal Coordinates -- 3.3 Homogeneous Coordinates -- 3.3.1 Homogeneous Point Coordinates -- 3.3.2 Homogeneous Plane Coordinates -- 3.3.3 Homogeneous Line Coordinates -- 3.3.4 Homogeneous Screw Coordinates -- 3.4 Screw Operators -- 3.4.1 Screw Dot Product -- 3.4.2 Screw Reciprocal Product -- 3.4.3 Screw Cross Product -- 3.4.4 Screw Intersection -- 3.4.5 Screw Triangle -- 3.5 The Generalized Equivalence of the Pitch Point-the Screw Axis -- 3.5.1 Theorem of Three Axes -- 3.5.2 The Cylindroid -- 3.5.3 Cylindroid Intersection -- 3.6 The Generalized Pitch Surface-Axodes -- 3.6.1 The Theorem of Conjugate Pitch Surfaces -- 3.6.2 The Striction Curve -- 3.7 The Generalized Transverse Surface -- 3.8 The Generalized Axial Surface -- 3.9 Summary -- 4 Differential Geometry -- 4.1 Introduction -- 4.2 The Curvature of a Spatial Curve -- 4.3 The Torsion of a Spatial Curve -- 4.4 The First Fundamental Form -- 4.5 The Second Fundamental Form -- 4.6 Principal Directions and Principal Curvatures -- 4.7 Torsure of a Spatial Curve -- 4.8 The Cylindroid of Torsure -- 4.9 Ruled Surface Trihedrons -- 4.10 Formulas of Fernet-Serret -- 4.11 Coordinate Transformations -- 4.12 Characteristic Lines and Points -- 4.13 Summary -- 5 Analysis of Toothed Bodies for Motion Generation -- 5.1 Introduction -- 5.2 Spatial Mobility Criterion -- 5.3 Reciprocity-the First Law of Gearing -- 5.4 The Line Complex -- 5.5 The Tooth Spiral -- 5.5.1 The Tooth Spiral Curvature -- 5.5.2 The Tooth Spiral Torsion -- 5.6 Tooth Spiral Angle-the Second Law of Gearing -- 5.6.1 The I/O Relationship -- 5.6.2 The Phantom I/O Relationship -- 5.7 Reduced Tooth Curvature-the Third Law of Gearing.

5.7.1 Absolute Tooth Curvature -- 5.7.2 Tooth Profile Modification -- 5.8 Classification of Gear Types -- 5.9 Contact Ratio -- 5.9.1 Transverse Contact Ratio -- 5.9.2 Axial Contact Ratio -- 5.10 Spatial Backlash -- 5.11 Relative Displacements -- 5.11.1 The Sliding Velocity -- 5.11.2 The Rolling Velocity -- 5.11.3 The Pitch Line Velocity -- 5.12 Mesh Efficiency -- 5.13 Summary -- 6 The Manufacture of Toothed Bodies -- 6.1 Introduction -- 6.2 Manufacturing Background -- 6.2.1 Form-Type Fabrication -- 6.2.2 Generation-Type Fabrication -- 6.2.3 Spiral Bevel/Hypoid Gear Fabrication -- 6.2.4 Noncircular Gear Fabrication -- 6.3 Crossed Hyperboloidal Gears -- 6.4 Fabrication of Cutters -- 6.4.1 The Hyperboloidal Cutter -- 6.4.2 The Cutter Spiral Angle -- 6.4.3 The Face Spiral Angle -- 6.4.4 Cutter Constraints -- 6.4.5 Speed Ratio -- 6.4.6 Hyperboloidal Cutter Coordinates -- 6.5 Gear Cutting Machine Layout -- 6.6 The Envelope of the Cutter -- 6.6.1 The Equation of Meshing -- 6.6.2 Boolean Operations -- 6.7 Material Removal Rate -- 6.8 Surface Cutting Speed -- 6.9 Discretization Error -- 6.9.1 Scalloping -- 6.9.2 Tessellation -- 6.10 Inspection -- 6.11 Hyperboloidal Blank Dimensions -- 6.12 Summary -- 7 Vibrations and Dynamic Loads in Gear Pairs -- 7.1 Introduction -- 7.2 Excitations -- 7.3 Transmission Error -- 7.3.1 Static Transmission Error -- 7.3.2 Loaded Transmission Error -- 7.3.3 Dynamic Transmission Error -- 7.4 Fourier Transforms -- 7.5 Impact Loading -- 7.6 Mesh Stiffness -- 7.7 Inertial Properties -- 7.7.1 Center of Mass -- 7.7.2 Mass Moments of Inertia -- 7.8 Manufacturing Dynamics -- 7.9 Summary -- Part III THE INTEGRATED DESIGN AND MANUFACTURING PROCESS -- 8 Gear Design Rating -- 8.1 Introduction -- 8.2 Modes of Gear Failure -- 8.3 Reaction Loads -- 8.4 Gear Parameters for Specified Deflections -- 8.5 The Fillet Stress.

8.5.1 Discretization of Gear Tooth -- 8.5.2 Element Stiffness Matrix -- 8.5.3 Global Stiffness Matrix -- 8.5.4 Boundary Conditions -- 8.5.5 Nodal Strain -- 8.5.6 Nodal Stress -- 8.6 Inertial Stress -- 8.7 Contact Stress -- 8.8 Minimum Film Thickness -- 8.9 Wear -- 8.10 Friction Coefficient -- 8.10.1 Sliding Friction -- 8.10.2 Rolling Friction -- 8.11 Flash Temperature -- 8.12 Thermal Stress -- 8.13 Failure Analysis -- 8.13.1 Reliability Analysis -- 8.13.2 Fatigue Analysis -- 8.13.3 Cumulative Loading -- 8.14 Windage Losses -- 8.15 Optimization -- 8.16 Summary -- 9 The Integrated CAD-CAM Process -- 9.1 Introduction -- 9.2 Modular Components for Geometric Synthesis -- 9.2.1 The Motion Specification Module -- 9.2.2 The Tooth Parameters Module -- 9.2.3 The Gear Parameters Module -- 9.2.4 The Cutter Parameters Module -- 9.2.5 The Loading Parameters Module -- 9.2.6 The Material Specifications Module -- 9.2.7 The Lubricant Specifications Module -- 9.2.8 The Dynamic Factors Module -- 9.2.9 The Shaft Deflections Module -- 9.2.10 The Manufacturing Specifications Module -- 9.3 The Integrated CAD-CAM Process -- 9.4 Illustrative Example -- 9.5 Summary -- 10 Case Illustrations of the Integrated CAD-CAM Process -- 10.1 Introduction -- 10.2 Case 1 -- 10.3 Case 2 -- 10.4 Case 3 -- 10.5 Case 4 -- 10.6 Case 5 -- 10.7 Case 6 -- 10.8 Case 7 -- 10.9 Case 8 -- 10.10 Case 9 -- 10.11 Case 10 -- 10.12 Case 11 -- 10.13 Case 12 -- 10.14 Case 13 -- 10.15 Case 14 -- 10.16 Case 15 -- 10.17 Case 16 -- 10.18 Case 17 -- 10.19 Case 18 -- 10.20 Case 19 -- 10.21 Case 20 -- 10.22 Case 21 -- 10.23 Case 22 -- 10.24 Summary -- Appendix A Differential Expressions -- A.1 Derivatives of the Radius of the Axode -- A.2 Derivatives of the Included Angles -- A.3 Derivatives of the Generators -- A.4 Derivatives of the Pitch of the Instantaneous Twist.

A.5 Derivatives of the Parameter of Distribution -- A.6 Derivatives of the Striction Curve -- A.7 Manufacturing Expressions -- A.8 Derivatives of the Transverse Curve -- A.9 Derivatives of the Angle Between the Generator and the Transverse Curve -- A.10 Derivatives of the Spiral Angle -- A.11 Derivatives of the Input Trihedron of Reference -- A.12 Derivatives of the Cutter Parameters -- Appendix B On the Notation and Operations -- Appendix C Noncircular Gears -- C.1 Torque and Speed Fluctuations in Rotating Shafts -- C.2 2-Dof Mechanical Function Generator -- C.3 Steering Mechanism -- C.4 Continuously Variable Transmission -- C.5 Geared Robotic Manipulators -- C.6 Spatial Mechanism for Body Guidance -- C.7 Nonworking Profile -- C.8 Multiple Reductions -- Appendix D The Delgear© Software -- D.1 Installation -- Appendix E Splines -- E.1 Cubic Splines -- E.2 Natural Splines -- E.2.1 Derivatives -- E.3 NURBS -- Appendix F Contact Stress -- F.1 Introduction -- F.2 Background -- F.3 Material Properties -- F.4 Surface Geometry -- F.5 Contact Deformations -- F.6 Contact Area -- F.7 Comparison -- Appendix G Glossary of Terms -- Appendix H Equilibrium and Diffusion Equations -- H.1 Equilbrium Equations -- H.2 Diffusion Equation Formulation -- H.3 Expressions -- Appendix I On the Base Curve of Planar Noncircular Gears -- Appendix J Spatial Euler-Savary Equations -- J.1 Planar Euler-Savary Equations -- J.2 Hyperboloid of Osculation -- J.3 Spatial Euler-Savary Equations -- References -- Index.