Geometry of surfaces : a practical guide for mechanical engineers

Geometry of surfaces : a practical guide for mechanical engineers / Stephen P. Radzevich.

This updated and expanded edition presents a highly accurate specification for part surface machining. Precise specification reduces the cost of this widely used industrial operation as accurately specified and machined part surfaces do not need to undergo costly final finishing. Dr. Radzevich descr...

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Bibliographic Details
Main Author: Radzevich, S. P. (Stepan Pavlovich) (Author)
Format: eBook
Language:English
Published: Cham, Switzerland : Springer, [2020]
Edition:Second edition.
Subjects:
Mechanical engineering > Mathematics.
Surfaces (Technology) > Mathematical models.
Geometry, Differential.
Geometry, Differential
Mechanical engineering > Mathematics
Surfaces (Technology) > Mathematical models
Online Access:Click for online access
Table of 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 Surface; 1.5 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 Surfaces; 2.1.2 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 Contact; 3.2 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 Curvature; 3.5.6 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

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