Geometry of Surfaces

A Practical Guide for Mechanical Engineers

Inbunden, Engelska, 2013

AvStephen P. Radzevich,USA) Radzevich, Stephen P. (Principal Gear Engineer,Stephen P Radzevich

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Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problemsGeometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces.Geometry of Surfaces: A Practical Guide for Mechanical Engineers combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering. Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineeringCombines differential geometry and gearing theoryHighlights new developments in the elementary theory of enveloping surfacesEssential reading for researchers and practitioners in mechanical, automotive and aerospace engineering industries; CAD developers; and graduate students in Mechanical Engineering.

Produktinformation

Utgivningsdatum2013-02-01
Mått175 x 252 x 18 mm
Vikt544 g
FormatInbunden
SpråkEngelska
Antal sidor264
FörlagJohn Wiley & Sons Inc
ISBN9781118520314

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About the Author xiiiPreface xvAcknowledgments xviiGlossary xixNotation xxiIntroduction xxvPart I PART SURFACES 11 Geometry of a Part Surface 31.1 On the Analytical Description of Ideal Surfaces 31.2 On the Difference between Classical Differential Geometry and Engineering Geometry of Surfaces 61.3 On the Analytical Description of Part Surfaces 71.4 Boundary Surfaces for an Actual Part Surface 91.5 Natural Representation of a Desired Part Surface 111.6 Elements of Local Geometry of a Desired Part Surface 192 On the Possibility of Classification of Part Surfaces 272.1 Sculptured Part Surfaces 272.2 Planar Characteristic Images 332.3 Circular Diagrams at a Surface Point 422.4 One More Useful Characteristic Curve 53Part II GEOMETRY OF CONTACT OF PART SURFACES 553 Early Works in the Field of Contact Geometry 573.1 Order of Contact 573.2 Contact Geometry of Part Surfaces 593.3 Local Relative Orientation of the Contacting Part Surfaces 593.4 First-Order Analysis: Common Tangent Plane 643.5 Second-Order Analysis 653.6 A Characteristic Curve Irk (R ) of Novel Kind 754 An Analytical Method Based on Second Fundamental Forms of the Contacting Part Surfaces 795 Indicatrix of Conformity of Two Smooth Regular Surfaces in the First Order of Tangency 835.1 Preliminary Remarks 835.2 Indicatrix of Conformity for Two Smooth Regular Part Surfaces in the First Order of Tangency 875.3 Directions of Extremum Degree of Conformity of Two Part Surfaces in Contact 945.4 Asymptotes of the Indicatrix of Conformity CnfR (P1/P2) 975.5 Comparison of Capabilities of Indicatrix of Conformity Cnf R(P1/P2) and of Dupin Indicatrix of the Surface of Relative Curvature Dup (R) 985.6 Important Properties of Indicatrix of Conformity Cnf R(P/T ) of Two Smooth Regular Part Surfaces 995.7 The Converse Indicatrix of Conformity of Two Regular Part Surfaces in the First Order of Tangency 996 Plücker Conoid: More Characteristic Curves 1016.1 Plücker Conoid 1016.2 On Analytical Description of Local Geometry of a Smooth Regular Part Surface 1056.3 Relative Characteristic Curve 1127 Feasible Kinds of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency 1177.1 On the Possibility of Implementation of the Indicatrix of Conformity for the Purposes of Identification of the Actual Kind of Contact of Two Smooth Regular Part Surfaces 1177.2 Impact of Accuracy of the Computation on the Parameters of the Indicatrices of Conformity Cnf R(P1/P2) 1217.3 Classification of Possible Kinds of Contact of Two Smooth Regular Part Surfaces 122Part III MAPPING OF THE CONTACTING PART SURFACES 1318 R-Mapping of the Interacting Part Surfaces 1338.1 Preliminary Remarks 1338.2 On the Concept of R-Mapping of the Interacting Part Surfaces 1348.3 R-mapping of a Part Surface P1 onto Another Part Surface P2 1368.4 Reconstruction of the Mapped Part Surface 1408.5 Illustrative Examples of the Calculation of the Design Parameters of the Mapped Part Surface 1419 Generation of Enveloping Surfaces: General Consideration 1459.1 Envelope for Successive Positions of a Moving Planar Curve 1459.2 Envelope for Successive Positions of a Moving Surface 1499.3 Kinematic Method for Determining Enveloping Surfaces 1549.4 Peculiarities of Implementation of the Kinematic Method in Cases of Multi-parametric Relative Motion of the Surfaces 16410 Generation of Enveloping Surfaces: Special Cases 16710.1 Part Surfaces that Allow for Sliding Over Themselves 16710.2 Reversibly Enveloping Surfaces: Introductory Remarks 16910.3 Generation of Reversibly Enveloping Surfaces 18010.4 On the Looseness of Two Olivier Principles 197Conclusion 203APPENDICES 205Appendix A: Elements of Vector Calculus 207A.1 Fundamental Properties of Vectors 207A.2 Mathematical Operations over Vectors 207Appendix B: Elements of Coordinate System Transformations 211B.1 Coordinate System Transformation 211B.2 Conversion of the Coordinate System Orientation 222B.3 Transformation of Surface Fundamental Forms 223Appendix C: Change of Surface Parameters 225References 227Bibliography 229Index 233