Kinematic Differential Geometry and Saddle Synthesis of Linkages.

Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- Chapter 1 Planar Kinematic Differential Geometry -- 1.1 Plane Curves -- 1.1.1 Vector Curve -- 1.1.2 Frenet Frame -- 1.1.3 Adjoint Approach -- 1.2 Planar Differential Kinematics -- 1.2.1 Displacement -- 1.2.2 Centrodes -- 1.2.3 Euler-Savary Equation -- 1.2.4 Curvatures in Higher Order -- 1.2.5 Line Path -- 1.3 Plane Coupler Curves -- 1.3.1 Local Characteristics -- 1.3.2 Double Points -- 1.3.3 Four-bar Linkage I -- 1.3.4 Four-bar Linkage II -- 1.3.5 Oval Coupler Curves -- 1.3.6 Symmetrical Coupler Curves -- 1.3.7 Distribution of Coupler Curves -- 1.4 Discussion -- References -- Chapter 2 Discrete Kinematic Geometry and Saddle Synthesis of Planar Linkages -- 2.1 Matrix Representation -- 2.2 Saddle Point Programming -- 2.3 Saddle Circle Point -- 2.3.1 Saddle Circle Fitting -- 2.3.2 Saddle Circle -- 2.3.3 Four Positions -- 2.3.4 Five Positions -- 2.3.5 Multiple Positions -- 2.3.6 Saddle Circle Point -- 2.4 Saddle Sliding Point -- 2.4.1 Saddle Line Fitting -- 2.4.2 Saddle Line -- 2.4.3 Three Positions -- 2.4.4 Four Positions -- 2.4.5 Multiple Positions -- 2.4.6 Saddle Sliding Point -- 2.5 The Saddle Kinematic Synthesis of Planar Four-bar Linkages -- 2.5.1 Kinematic Synthesis -- 2.5.2 Crank-rocker Linkage -- 2.5.3 Crank-slider Linkage -- 2.6 The Saddle Kinematic Synthesis of Planar Six-bar Linkages with Dwell Function -- 2.6.1 Six-bar Linkages -- 2.6.2 Local Saddle Curve Fitting -- 2.6.3 Dwell Function Synthesis -- 2.7 Discussion -- References -- Chapter 3 Differential Geometry of the Constraint Curves and Surfaces -- 3.1 Space Curves -- 3.1.1 Vector Representations -- 3.1.2 Frenet Trihedron -- 3.2 Surfaces -- 3.2.1 Elements of Surfaces -- 3.2.2 Ruled Surfaces -- 3.2.3 Adjoint Approach -- 3.3 Constraint Curves and Surfaces -- 3.4 Spherical and Cylindrical Curves.

3.4.1 Spherical Curves (S-S) -- 3.4.2 Cylindrical Curves (C-S) -- 3.5 Constraint Ruled Surfaces -- 3.5.1 Constant Inclination Ruled Surfaces (C'-P'-C) -- 3.5.2 Constant Axis Ruled Surfaces (C'-C) -- 3.5.3 Constant Parameter Ruled Surfaces (H-C, R-C) -- 3.5.4 Constant Distance Ruled Surfaces (S'-C) -- 3.6 Generalized Curvature of Curves -- 3.6.1 Generalized Curvature of Space Curves -- 3.6.2 Spherical Curvature and Cylindrical Curvature -- 3.7 Generalized Curvature of Ruled Surfaces -- 3.7.1 Tangent Conditions -- 3.7.2 Generalized Curvature -- 3.7.3 Constant Inclination Curvature -- 3.7.4 Constant Axis Curvature -- 3.8 Discussion -- References -- Chapter 4 Spherical Kinematic Differential Geometry -- 4.1 Spherical Displacement -- 4.1.1 General Expression -- 4.1.2 Adjoint Expression -- 4.2 Spherical Differential Kinematics -- 4.2.1 Spherical Centrodes (Axodes) -- 4.2.2 Curvature and Euler-Savary Formula -- 4.3 Spherical Coupler Curves -- 4.3.1 Basic Equation -- 4.3.2 Double Point -- 4.3.3 Distribution -- 4.4 Discussion -- References -- Chapter 5 Discrete Kinematic Geometry and Saddle Synthesis of Spherical Linkages -- 5.1 Matrix Representation -- 5.2 Saddle Spherical Circle Point -- 5.2.1 Saddle Spherical Circle Fitting -- 5.2.2 Saddle Spherical Circle -- 5.2.3 Four Positions -- 5.2.4 Five Positions -- 5.2.5 Multiple Positions -- 5.2.6 Saddle Spherical Circle Point -- 5.3 The Saddle Kinematic Synthesis of Spherical Four-bar Linkages -- 5.3.1 Kinematic Synthesis -- 5.3.2 Saddle Kinematic Synthesis of Spherical Four-bar Linkages -- 5.4 Discussion -- References -- Chapter 6 Spatial Kinematic Differential Geometry -- 6.1 Displacement Equation -- 6.1.1 General Description -- 6.1.2 Adjoint Description -- 6.2 Axodes -- 6.2.1 Fixed Axode -- 6.2.2 Moving Axode -- 6.3 Differential Kinematics of Points -- 6.3.1 Point Trajectory -- 6.3.2 Darboux Frame.

6.3.3 Euler-Savary Analogue -- 6.3.4 Generalized Curvature -- 6.4 Differential Kinematics of Lines -- 6.4.1 Frenet Frame -- 6.4.2 Striction Curve -- 6.4.3 Spherical Image Curve -- 6.4.4 Connecting Kinematic Pairs -- 6.4.5 Constant Axis Curvature -- 6.4.6 Constant Parameter Curvature -- 6.5 Differential Kinematics of Spatial Four-Bar Linkage RCCC -- 6.5.1 Adjoint Expression -- 6.5.2 Axodes -- 6.5.3 Point Trajectory -- 6.5.4 Line Trajectory -- 6.6 Discussion -- References -- Chapter 7 Discrete Kinematic Geometry and Saddle Synthesis of Spatial Linkages -- 7.1 The Displacement Matrix -- 7.2 Saddle Sphere Point PSS -- 7.2.1 Spherical Surface Fitting -- 7.2.2 Saddle Spherical Surface -- 7.2.3 Five Positions -- 7.2.4 Six Positions -- 7.2.5 Multiple Positions -- 7.2.6 Saddle Sphere Point -- 7.3 Saddle Cylinder Point PCS -- 7.3.1 Cylindrical Surface Fitting -- 7.3.2 Saddle Cylindrical Surface -- 7.3.3 Six Positions -- 7.3.4 Seven Positions -- 7.3.5 Multiple Positions -- 7.3.6 Saddle Cylinder Point -- 7.3.7 The Degeneration of the Saddle Cylinder Point (R-S, H-S) -- 7.4 Saddle Constant Axis Line LCC -- 7.4.1 Ruled Surface Fitting -- 7.4.2 Saddle Spherical Image Circle Point -- 7.4.3 Saddle Striction Cylinder Point -- 7.4.4 Saddle Constant Axis Line -- 7.5 Degenerate Constant Axis Lines LRC and LHC -- 7.5.1 Saddle Characteristic Line LRC (R-C, R-R) -- 7.5.2 Saddle Characteristic Line LHC (H-C, H-R, H-H) -- 7.6 The Saddle Kinematic Synthesis of Spatial Four-Bar Linkages -- 7.6.1 A Brief Introduction -- 7.6.2 The Spatial Linkage RCCC -- 7.6.3 The Spatial Linkage RRSS -- 7.6.4 The Spatial Linkage RRSC -- 7.7 Discussion -- References -- Index -- EULA.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.