Kinematic geometry of gearing (2^nd Ed.)

Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure, the author has also completely reworked the ‘3 laws of gearing', the first law re-written to better parallel the existing ‘Law of Gearing” as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relation between gear sizes, and the 3rd law completely reworked from its original form to uniquely describe a limiting condition on curvature between gear teeth, with new relations for gear efficiency are presented based on the kinematics of general toothed wheels in mesh. There is also a completely new chapter on gear vibration load factor and impact. Progressing from the fundamentals of geometry to construction of gear geometry and application, Kinematic Geometry of Gearing presents a generalized approach for the integrated design and manufacture of gear pairs, cams and all other types of toothed/motion/force transmission mechanisms using computer implementation based on algebraic geometry.

CHAPTER 1: INTRODUCTION TO THE KINEMATICS OF GEARING

1.1 Introduction

1.2 An Overview

1.3 Nomenclature and Terminology

1.4 Reference Systems

1.5 The Input/Output Relationship

1.6 Rigid Body Assumption

1.7 Mobility

1.8 Arhnold-Kennedy Instant Center Theorem

1.9 Euler-Savary Equation for Envelopes (correct!, use arc-lengths)

1.10 Conjugate Motion Transmission

1.10.1 Spur gears

1.10.2 Helical and crossed axis gears

1.11 Contact Ratio

1.11.1 Transverse contact ratio

1.11.2 Axial contact ratio

1.12 Backlash

1.13 Special Toothed Bodies

1.13.1 Micro gears

1.13.2 Nano gears

1.14 Non - Cylindrical Gearing

1.14.1 Hypoid gear pairs

1.14.2 Worm gears

1.14.3 Bevel gears

1.15 Non-Circular Gears

1.15.1 Gear and cam nomenclature

1.15.2 Non-working profile

1.15.3 Rotary/translatory motion transmission

1.16 Schematic Illustration of Gear Types

1.17 Mechanism Trains

1.17.1 Simple drive trains

1.17.2 Epicyclic gear trains

1.17.3 Circulating power

1.17.4 Harmonic gear drives

1.17.5 Non-circular planetary gear trains

1.18 Summary

Part II

CHAPTER 2: KINEMATIC GEOMETRY OF PLANAR GEAR TOOTH PROFILES

2.1 Introduction

2.2 A Unified Approach to Tooth Profile Synthesis

2.3 Tooth Forms used for Conjugate Motion Transmission

2.3.1 Cycloidal tooth profiles

2.3.2 Involute tooth profiles

2.3.3 Circular-arc tooth profiles

2.3.4 Comparative evaluation of tooth profiles

2.4 Contact Ratio

2.5 Dimensionless Backlash

2.6 Rack Coordinates

2.6.1 The basic rack

2.6.2 The specific rack

2.6.3 The modified rack

2.6.4 The final rack

2.7 Planar Gear Tooth Profile

2.8 Summary

CHAPTER 3: GENERALIZED REFERENCE COORDINATES FOR SPATIAL

GEARING-THE CYLINDROIDAL COORDINATES

3.1 Introduction

3.2 Cylindroidal Coordinates

3.2.1 The special features of cylindroidal coordinates

3.2.2 The benefits of cylindroidal coordinates

3.3 Homogeneous Coordinates

3.3.1 Homogeneous point coordinates

3.3.2 Homogeneous plane coordinates

3.3.3 Homogeneous line coordinates

3.3.4 Homogeneous screw coordinates

3.4 Screw Operators

3.4.1 Screw dot product

3.4.2 Screw reciprocity

3.4.3 Screw cross product

3.4.4 Screw intersection

3.5 The Generalized Equivalence of the Pitch Point - The Screw Axis

3.5.1 The theorem of three axes

3.5.2 The cylindroid

3.5.3 Cylindroid intersection

3.6 The Generalized Pitch Surfaces - The Axodes

3.6.1 The theorem of conjugate pitch surfaces

3.6.2 The striction curve

3.6.3 The hyperboloid of osculation

3.7 The Generalized Transverse Surface

3.8 The Generalized Axial Surface

3.9 Summary

CHAPTER 4: DIFFERENTIAL GEOMETRY AND THE TOOTH SPIRAL

4.1 Introduction

4.2 The Curvature of a Spatial Curve

4.3 The Torsion of a Spatial Curve

4.4 The First Fundamental Form

4.5 The Second Fundamental Form

4.6 Principle Directions and Principle Curvatures

4.7 Torsure of a Spatial Curve

4.8 The Cylindroid of Torsure

4.9 Ruled Surface Trihedrons

4.10 Formulas of Fernet-Serret

4.11 Coordinate Transformations

4.12 Characteristic Lines and Points

4.13 Summary

CHAPTER 5: ANALYSIS OF TOOTHED BODIES FOR MOTION GENERATION

5.1 Introduction

5.2 Spatial Mobility...

David B Dooner, University of Puerto Rico-Mayagüez, Puerto Rico and Ali A Seireg, University of Wisconsin at Madison and University of Florida at Gainesville, USA
David B Dooner is a Professor in the Department of Mechanical Engineering at the University of Puerto Rico-Mayagüez. He received his doctorate from the University of Florida at Gainesville in 1991 where he remained as a Post-Doctoral Fellow from 1991-1994. He worked at the General Motors Gear Center in 1989 and was a visiting scientist at the Mechanical Sciences Research Institute of the Russian Academy of Sciences in Moscow in 1992.