Noncircular Gears: Design and Generation
, by Faydor L. Litvin , Alfonso Fuentes-Aznar , Ignacio Gonzalez-Perez , Kenichi Hayasaka- ISBN: 9780521761703 | 0521761700
- Cover: Hardcover
- Copyright: 9/14/2009
Foreword | p. xi |
Preface | p. xiii |
Acknowledgments | p. xv |
Introduction to Theory of Gearing, Design, and Generation of Noncircular Gears | p. 1 |
Historical Comments | p. 1 |
Toward Design and Application of Noncircular Gears | p. 6 |
Examples of Previous Designs | p. 6 |
Examples of New Designs | p. 11 |
Developments Related with Theory of Gearing | p. 14 |
Centrodes of Noncircular Gears | p. 18 |
Introduction | p. 18 |
Centrode as the Trajectory of the Instantaneous Center of Rotation | p. 20 |
Concept of Polar Curve | p. 21 |
Derivation of Centrodes | p. 21 |
Tangent to Polar Curve | p. 22 |
Conditions for Design of Centrodes as Closed Form Curves | p. 24 |
Observation of Closed Centrodes for Function Generation | p. 27 |
Basic and Alternative Equations of Curvature of Polar Curve | p. 27 |
Conditions of Centrode Convexity | p. 30 |
Evolutes and Involutes | p. 31 |
Introduction and Terminology | p. 31 |
Determination of Evolutes | p. 33 |
Local Representation of a Noncircular Gear | p. 36 |
Pressure Angle | p. 37 |
Elliptical Gears and Gear Drives | p. 40 |
Introduction | p. 40 |
Basic Concepts | p. 40 |
Ellipse Parameters | p. 40 |
Polar Equation of an Ellipse | p. 41 |
External Elliptical Gear Drives | p. 43 |
Basic Equations | p. 43 |
Conventional Elliptical Gear Drives | p. 45 |
Centrodes and Transmission Function | p. 45 |
Influence of Ellipse Parameters and Design Recommendations | p. 47 |
Gear Drive with Elliptical Pinion and Conjugated Gear | p. 52 |
External Gear Drive with Modified Elliptical Gears | p. 53 |
Modification of the Ellipse | p. 53 |
Derivation of Modified Centrode ?1 | p. 55 |
Derivative Functions m 21 (I)(?1) and m 21 (II) (?1) | p. 55 |
Relation between Rotations of Gears 1 and 2 | p. 55 |
Derivation of Centrode ?2 | p. 56 |
External Gear Drive with Oval Centrodes | p. 57 |
Equation of Oval Centrode | p. 57 |
Derivative Function m21(?1) | p. 58 |
Relation between Rotations of Gears 1 and 2 | p. 58 |
Transmission Function ?2(?1) | p. 60 |
Design of Noncircular Gears with Lobes | p. 60 |
Design of Gear Drives with Different Number of Lobes for Pinion and Gear | p. 63 |
Transmission Function of Elliptical Gears as Curve of Second Order | p. 65 |
Functional of Identical Centrodes | p. 66 |
Generation of Planar and Helical Elliptical Gears | p. 71 |
Introduction | p. 71 |
Generation of Elliptical Gears by Rack Cutter | p. 71 |
Generation of Elliptical Gears by Hob | p. 79 |
Generation of Elliptical Gears by Shaper | p. 86 |
Examples of Design of Planar and Helical Elliptical Gears | p. 90 |
Planar Elliptical Gears | p. 90 |
Helical Elliptical Gears | p. 92 |
Design of Gear Drives Formed by Eccentric Circular Gear and Conjugated Noncircular Gear | p. 94 |
Introduction | p. 94 |
Centrodes of Eccentric Gear Drive | p. 94 |
Equations of Mating Centrodes | p. 94 |
Curvature of Centrode a2 and Applications | p. 96 |
Generation of the Noncircular Gear by Shaper and Hob | p. 101 |
Generation of Noncircular Gear by a Noneccentric Shaper | p. 101 |
Generation of the Noncircular Gear by a Hob | p. 105 |
Generation of the Eccentric Gear Providing Localized Contact | p. 112 |
Design of Internal Noncircular Gears | p. 115 |
Introduction | p. 115 |
Derivation of Centrodes | p. 115 |
Preliminary Considerations of Kinematics of Internal Gear Drive | p. 115 |
Basic Equations of Centrodes | p. 116 |
Design of Centrodes ?1 and ?2 as Closed-Form Curves | p. 118 |
Examples of Design of Internal Noncircular Gear Drives | p. 118 |
Gear Drive with Elliptical Pinion | p. 118 |
Gear Drive with Modified Elliptical Pinion | p. 120 |
Gear Drive with Oval Pinion | p. 121 |
Gear Drive with Eccentric Pinion | p. 123 |
Generation of Planar Internal Noncircular Gears by Shaper | p. 126 |
Conditions of Nonundercutting of Planar Internal Noncircular Gears | p. 132 |
Approach A | p. 133 |
Approach B | p. 134 |
Numerical Example | p. 136 |
Application for Design of Planetary Gear Train with Noncircular and Circular Gears | p. 138 |
Introduction | p. 138 |
Structure and Basic Kinematic Concept of Planetary Train | p. 138 |
Planetary Gear Train with Elliptical Gears | p. 139 |
Planetary Gear Train with Noncircular and Circular Gears | p. 141 |
Transformation of Rotation into Translation with Variation of Gear Ratio | p. 143 |
Introduction | p. 143 |
Determination of Centrodes of Noncircular Gear and Rack | p. 144 |
Application of Mechanism Formed by a Noncircular Gear and Rack | p. 144 |
Tandem Design of Mechanisms for Function Generation and Output Speed Variation | p. 147 |
Introduction | p. 147 |
General Aspects of Generation of Functions | p. 152 |
Generation of Function with Varied Sign of Derivative | p. 153 |
Introduction to Design of Multigear Drive with Noncircular Gears | p. 156 |
Basic Functionals | p. 156 |
Interpretations of Lagrange's Theorem | p. 160 |
Illustration of Application of Lagrange's Theorem for Functional ?(a) = g2(gi(a)) | p. 161 |
Previous Solutions for ?(a) = f(f(a)) | p. 161 |
Computational Procedure for Functional (10.4.6) | p. 163 |
Design of Multigear Drive | p. 166 |
Basic Equations | p. 166 |
Design of Centrodes | p. 168 |
Design of Planar Linkages Coupled with Noncircular Gears | p. 171 |
Tandem Design of Double-Crank Mechanism Coupled with Two Pairs of Noncircuiar Gears | p. 171 |
Tandem Design of Slider-Crank Mechanism Coupled with Modified Elliptical Gears | p. 174 |
Preliminary Information | p. 174 |
Basic Ideas of Modification of Elliptical Centrodes | p. 174 |
Analytical Determination of Modified Elliptical Centrodes | p. 177 |
Numerical Examples | p. 179 |
Tandem Design of Scotch-Yoke Mechanism Coupled with Noncircular Gears | p. 180 |
Tandem Design of Mechanism Formed by Two Pairs of Noncircular Gears and Racks | p. 183 |
Generation of Function | p. 186 |
Additional Numerical Problems | p. 188 |
References | p. 201 |
Index | p. 203 |
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