Geometry of surfaces : a practical guide for mechanical engineers /: a practical guide for mechanical engineers. ([2020])

• Record Type: Book
• Further Information: Note: Stephen P. Radzevich.
• Authors: Radzevich, S. P (Stepan Pavlovich)
• Contents: Intro; Preface; Acknowledgements; Introduction; Contents; About the Author; Notations; Part Surfaces; 1 Geometry of a Part Surface; 1.1 On Analytical Description of Perfect Surfaces; 1.1.1 General Form of Representation of Smooth Regular Part Surfaces; 1.1.2 Essentials of Piecewise Approximation of Sculptured Part Surfaces; 1.1.3 Algebraic and Geometric Form; 1.1.4 Significance of the Unit Tangent Vectors; 1.2 On the Difference Between "Classical Differential Geometry" and "Engineering Geometry of Surfaces"; 1.3 On the Analytical Description of Part Surfaces 1.4 Boundary Surfaces for Actual Part Surface1.5 Natural Representation of Desired Part Surface; 1.5.1 First Fundamental Form of a Desired Part Surface; 1.5.2 Second Fundamental Form of a Desired Part Surface; 1.5.3 Illustrative Example; 1.6 Elements of Local Geometry of Desired Part Surface; 1.6.1 Unit Vectors of Principal Directions at Point on Part Surface; 1.6.2 Principal Curvatures at Point of Part Surface; 1.6.3 Other Parameters of Part Surface Curvature; References; 2 On a Possibility of Classification of Part Surfaces; 2.1 Sculptured Part Surfaces 2.1.1 Local Patches of Perfect Part Surfaces2.1.2 Local Patches of Real Part Surfaces; 2.2 Planar Characteristic Images; 2.2.1 Dupin Indicatrix; 2.2.2 Curvature Indicatrix; 2.2.3 Circular Chart of Curvature Indicatrices for Local Patches of Smooth Regular Part Surfaces; 2.3 Circular Diagrams at a Surface Point; 2.3.1 Circular Diagrams; 2.3.2 Circular Chart of Circular Diagrams for Local Patches of Smooth Regular Part Surfaces; 2.4 One More Useful Characteristic Curve; References; Contact Geometry of Part Surfaces; 3 Early Works in the Field of Contact Geometry of Surfaces 3.1 Order of Contact3.2 Contact Geometry of Part Surfaces; 3.3 Local Relative Orientation of Contacting Part Surfaces; 3.4 First-Order Analysis: Common Tangent Plane; 3.5 Second-Order Analysis; 3.5.1 Comments on Analytical Description of Local Geometry of Contacting Surfaces Loaded by a Normal Force: "Hertz Proportional Assumption"; 3.5.2 Surface of Normal Relative Curvature; 3.5.3 "Dupin Indicatrix" at a Point of Surface of Relative Normal Curvature; 3.5.4 Matrix Representation of Equation of "Dupin Indicatrix" at a Point of Surface of Relative Normal Curvature 3.5.5 Surface of Relative Normal Radii of Curvature3.5.6 Normalized Relative Normal Curvature; 3.5.7 Curvature Indicatrix of Surface of Relative Normal Curvature; 3.6 A Characteristic Curve mathfrakRK (R) of a Novel Kind; References; 4 An Analytical Method Based on the Second Fundamental Forms of Contacting Part Surfaces; Reference; 5 Indicatrix of Conformity at Point of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency; 5.1 Preliminary Remarks; 5.2 "Indicatrix of Conformity" at Point of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency
• Edition: Second edition
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (313 pages)
• Subjects: 516.3024/621; Mechanical engineering -- Mathematics; Surfaces (Technology) -- Mathematical models; Geometry, Differential; Electronic books
• Languages: English
• ISBNs: 9783030221843; 3030221849
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.