Geometry of Surfaces

1. Front Matter

   Pages i-xxvi

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2. Part Surfaces

   1. Front Matter

      Pages 1-2

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   2. Geometry of a Part Surface

      • Stephen P. Radzevich

      Pages 3-34

   3. On a Possibility of Classification of Part Surfaces

      • Stephen P. Radzevich

      Pages 35-64

3. Contact Geometry of Part Surfaces

   1. Front Matter

      Pages 65-65

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   2. Early Works in the Field of Contact Geometry of Surfaces

      • Stephen P. Radzevich

      Pages 67-90

   3. An Analytical Method Based on the Second Fundamental Forms of Contacting Part Surfaces

      • Stephen P. Radzevich

      Pages 91-95

   4. Indicatrix of Conformity at Point of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency

      • Stephen P. Radzevich

      Pages 97-117

   5. “Plücker Conoid”: More Characteristic Curves

      • Stephen P. Radzevich

      Pages 119-136

   6. Possible Kinds of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency

      • Stephen P. Radzevich

      Pages 137-150

4. Mapping of Contacting Part Surfaces

   1. Front Matter

      Pages 151-151

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   2. ℝ-Mapping of Interacting Part Surfaces

      • Stephen P. Radzevich

      Pages 153-165

   3. Generation of Enveloping Surfaces: General Consideration

      • Stephen P. Radzevich

      Pages 167-189

   4. Generation of Enveloping Surfaces: Special Cases

      • Stephen P. Radzevich

      Pages 191-232

5. Back Matter

   Pages 233-303

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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 describes techniques in this volume based primarily on classical differential geometry of surfaces. He then transitions from differential geometry of surfaces to engineering geometry of surfaces, and examines how part surfaces are either machined themselves, or are produced by tools with surfaces that are precisely machined. The book goes on to explain specific methods, such as derivation of planar characteristic curves based on Plücker conoid constructed at a point of the part surface, and that analytical description of part surface is vital for surfaces machined using CNC technology, and especially so for multi-axes NC machines. Providing readers with a powerful tool for analytical description of part surfaces machined on conventional machine tools and numerically controlled machines, this book maximizes understanding on optimal treatment of part surfaces to meet the requirements of today’s high tech industry.

• Engineering geometry of surfaces
• contact geometry of surfaces
• indicatrix of conformity
• point of contact of two part surfaces
• condition of conjugacy of two part surfaces
• reversibly-enveloping surfaces
• conjugate surfaces

“The book ends with four appendices on the necessary mathematical background, a glossary, a rich bibliography, and an index. … it is an invaluable vade mecum for manufacturing engineers.” (Eleutherius Symeonidis, zbMATH 1492.53001, 2022)

• Southfield Innovation Center, Eaton Corporation, Southfield, USA

  Stephen P. Radzevich

Dr. Stephen P. Radzevich is a Professor of Mechanical Engineering, and a Professor of Manufacturing Engineering.  He received the M.Sc. (1976), the Ph.D. (1982), and the Dr.(Eng)Sc. (1991) – all in mechanical engineering.  Dr. Radzevich has extensive industrial experience in gear design and manufacture. He has developed numerous software packages dealing with CAD and CAM of precise gear finishing for a variety of industrial sponsors.  His main research interest is Kinematic Geometry of Surface Generation, particularly with the focus on (a) precision gear design, (b) high power density gear trains, (c) torque share in multi-flow gear trains, (d) design of special purpose gear cutting/finishing tools, (e) design and machining (finishing) of precision gears for low-noise/noiseless transmissions of cars, light trucks etc. Dr. Radzevich has spent about 40 years developing software, hardware and other processes for gear design an optimization. Besides his work for industry, he trains engineering students at universities and gear engineers in companies.  He authored and co-authored over 30 monographs, handbooks, and textbooks. The monographs entitled “Generation of Surfaces” (2001), “Kinematic Geometry of Surface Machining” (CRC Press, 2008), “CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach” (M&C Publishers, 2008), “Gear Cutting Tools: Fundamentals of Design and Computation” (CRC Press, 2010, 2^nd edition 2017), “Precision Gear Shaving” (Nova Science Publishers, 2010), “Dudley’s Handbook of Practical Gear Design and Manufacture” (CRC Press, 2012, 2^nd edition 2016), “Theory of Gearing: Kinematics, Geometry, and Synthesis” (CRC Press, 2012, 2^nd edition 2018), “Geometry of Surfaces: A Practical Guide for Mechanical Engineers” (2013) are among the recently published volumes.  He also authored and co-authored about 350 scientific papers and holds over 250 patents on inventions in the field, both, USA patents and International.

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