Gear Geometry and Applied Theory (2nd ed)

This revised, expanded edition covers the theory, design, geometry and manufacture of all types of gears and gear drives. An invaluable reference for designers, theoreticians, students, and manufacturers, the second edition includes advances in gear theory, gear manufacturing, and computer simulation. Among the new topics are: new geometry for gears and pumps; new design approaches for planetary gear trains and bevel gear drives; an enhanced approach for stress analysis; new methods of grinding and gear shaving; and new theory on the simulation and its application. First Edition published by Pearson Education Hb (1994): 0-132-11095-4 Cover......Page 1 Half-title......Page 3 Title......Page 5 Copyright......Page 6 Contents......Page 7 Foreword......Page 14 Preface......Page 16 Acknowledgments......Page 17 1.1 HOMOGENEOUS COORDINATES......Page 19 1.2 COORDINATE TRANSFORMATION IN MATRIX REPRESENTATION......Page 20 Two Main Problems......Page 24 Employment of Additional Coordinate Systems......Page 30 1.4 ROTATIONAL AND TRANSLATIONAL 4 × 4 MATRICES......Page 32 1.5 EXAMPLES OF COORDINATE TRANSFORMATION......Page 33 Generation of Epicycloid......Page 42 Generation of Involute Curves......Page 43 Generation of a Cycloid......Page 45 1.7 APPLICATION TO DERIVATION OF SURFACES......Page 46 2.1 VECTOR REPRESENTATION......Page 51 2.2 MATRIX REPRESENTATION......Page 57 2.3 APPLICATION OF SKEW-SYMMETRIC MATRICES......Page 59 3.1 THE CONCEPT OF CENTRODES......Page 62 3.2 PITCH CIRCLE......Page 67 3.3 OPERATING PITCH CIRCLES......Page 68 3.4 AXODES IN ROTATION BETWEEN INTERSECTED AXES......Page 69 3.5 AXODES IN ROTATION BETWEEN CROSSED AXES......Page 70 3.6 OPERATING PITCH SURFACES FOR GEARS WITH CROSSED AXES......Page 74 4.1 PARAMETRIC REPRESENTATION......Page 77 4.3 TANGENT AND NORMAL TO A PLANAR CURVE......Page 78 Introduction......Page 86 Frenet Trihedron......Page 87 Curvature of curve represented by vector function r(s)......Page 89 Curvature of parametric curve represented by vector function r(θ)......Page 90 Modification of Eq. (4.4.31)......Page 92 Curvature of curves represented by explicit or implicit functions......Page 93 5.2 CURVILINEAR COORDINATES......Page 96 5.3 TANGENT PLANE AND SURFACE NORMAL......Page 97 5.5 EXAMPLES OF SURFACES......Page 100 Surface of Revolution......Page 101 Spherical Surface......Page 103 Cone Surface......Page 106 General Equations of a Helicoid......Page 108 Helicoid with Ruled Surface......Page 109 Relationship Between Helicoid Coordinates and the Surface Normal Projections......Page 112 Cross Section of a Helicoid......Page 113 Introduction......Page 115 Engineering Approach......Page 116 Particular Cases......Page 117 Planar Gearing......Page 118 6.2 BASIC KINEMATIC RELATIONS......Page 120 6.3 CONDITIONS OF NONUNDERCUTTING......Page 121 Classical Approach......Page 125 Engineering Approach (proposed by Litvin [1968, 1989])......Page 127 6.5 CONTACT LINES; SURFACE OF ACTION......Page 128 6.6 ENVELOPE TO FAMILY OF CONTACT LINES ON GENERATING SURFACE 1......Page 130 6.7 FORMATION OF BRANCHES OF ENVELOPE TO PARAMETRIC FAMILIES OF SURFACES AND CURVES......Page 132 Branches of Tooth Profiles in a Cycloidal Pump......Page 133 6.8 WILDHABER’S CONCEPT OF LIMIT CONTACT NORMAL......Page 136 Planar Gearing......Page 137 Spatial Gearing......Page 139 Introduction......Page 142 Equation of Meshing......Page 143 Conditions of Nonundercutting......Page 144 Basic Concept......Page 146 Worm-Gear Drive with CylindricalWorm......Page 148 Generation ofWorm by Peripheral Tool......Page 150 6.12 KNOTS OF MESHING......Page 152 6.13 PROBLEMS......Page 155 Space Curve Trihedron......Page 171 Frenet–Serret Equations......Page 174 Determination of and ... for a Curve Represented by r(s)\......Page 176 Determination of κo and τ for a Curve Represented by Vector Function r(phi)......Page 177 Determination of κo......Page 179 Structure of Spatial Curve at the Curve Point......Page 180 Equation of Osculating Plane......Page 181 Surface Curve Trihedron......Page 182 Determination of Derivatives ts , ds , ns......Page 183 Velocity and Acceleration......Page 185 Curvature of Spatial Curve......Page 188 Geodesic Curvature......Page 190 First Fundamental Form......Page 193 Interpretation of Fundamental Forms......Page 194 Determination of Normal Curvature......Page 195 Approach 1......Page 198 Rodrigues’ Formula......Page 200 Approach 2......Page 201 Particular Case 1......Page 203 7.6 EULER’S EQUATION......Page 206 7.7 GAUSSIAN CURVATURE; THREE TYPES OF SURFACE POINTS......Page 207 Hyperbolic Point......Page 211 Geodesic Line......Page 212 Surface Torsion as the Curve Torsion of a Geodesic Line......Page 214 Relations Between Surface Torsion and Surface Principal Curvatures......Page 216 Relation Between Surface Normal Curvatures and Torsions in Directions of t(1) and t(2) (Fig. 7.9.5)......Page 219 8.1 INTRODUCTION......Page 220 8.2 BASIC EQUATIONS......Page 221 8.3 PLANAR GEARING: RELATION BETWEEN CURVATURES......Page 222 Transformation of Translation into Rotation and Rotation into Translation......Page 226 Auxiliary Equations......Page 236 Basic System of Linear Equations......Page 238 Case 1......Page 240 Case 3......Page 243 Case 1......Page 244 Derivation of First Two Equations of System (8.5.4)......Page 245 Derivation of Third Equation of System (8.5.4)......Page 246 Case 2......Page 247 Particular Case......Page 248 8.6 DIAGONALIZATION OF CURVATURE MATRIX......Page 249 Basic Equation of Elastic Deformations......Page 252 Determination of Contact Ellipse......Page 254 9.1 INTRODUCTION......Page 259 9.2 PREDESIGN OF A PARABOLIC FUNCTION OF TRANSMISSION ERRORS......Page 260 Effect of Application of a Predesigned Parabolic Function of Transmission Errors......Page 261 Determination of Derivative m 21......Page 262 9.3 LOCAL SYNTHESIS......Page 263 Relation Between Directions of Paths of Contact......Page 264 Relations Between the Magnitude of the Major Axis of the Contact Ellipse, Its Orientation, and Principal Curvatures and Directions of Contacting Surfaces......Page 265 Conditions of Continuous Tangency......Page 267 Analysis of Meshing......Page 269 9.5 APPLICATION OF FINITE ELEMENT ANALYSIS FOR DESIGN OF GEAR DRIVES......Page 275 9.6 EDGE CONTACT......Page 278 Edge Contact of Gear Tooth Surfaces That Are Initially in Line Contact......Page 280 Edge Contact of Gear Tooth Surfaces That Are Initially in Point Contact......Page 282 10.1 INTRODUCTION......Page 285 Involute Curve Used for Spur Gears......Page 286 Extended and Shortened Involute Curves......Page 288 Generation by a Rack-Cutter......Page 291 Design Parameters of Rack-Cutter......Page 293 Generation by Hob......Page 294 10.4 TOOTH ELEMENT PROPORTIONS......Page 296 Conditions of Nonundercutting......Page 298 Change of Gear Tooth Thickness and Dedendum Height......Page 301 10.6 RELATIONS BETWEEN TOOTH THICKNESSES MEASURED ON VARIOUS CIRCLES......Page 303 Line of Action......Page 305 Change of Center Distance......Page 306 Involute Profiles as Equidistant Curves......Page 307 Interference......Page 308 10.8 CONTACT RATIO......Page 310 10.9 NONSTANDARD GEARS......Page 312 Long–Short Addendum System......Page 313 Long–Short Addendum System: Computational Procedure......Page 314 General Nonstandard Gear System: Computational Procedure......Page 316 11.1 INTRODUCTION......Page 322 11.2 GENERATION OF GEAR FILLET......Page 323 Pseudohypocycloid......Page 325 Envelope to Family of Extended Hypocycloids......Page 326 Internal Gear Involute Profile......Page 327 Nonundercutting by Axial Generation......Page 329 Two-Parameter Generation......Page 330 Axial Assembly......Page 332 Radial Assembly......Page 333 Nomenclature......Page 334 12.2 CENTRODES OF NONCIRCULAR GEARS......Page 336 12.3 CLOSED CENTRODES......Page 341 Modification of Elliptical Centrode......Page 344 12.5 CONDITIONS OF CENTRODE CONVEXITY......Page 347 12.6 CONJUGATION OF AN ECCENTRIC CIRCULAR GEAR WITH A NONCIRCULAR GEAR......Page 348 12.7 IDENTICAL CENTRODES......Page 349 12.8 DESIGN OF COMBINED NONCIRCULAR GEAR MECHANISM......Page 351 12.9 GENERATION BASED ON APPLICATION OF NONCIRCULAR MASTER-GEARS......Page 353 12.10 ENVELOPING METHOD FOR GENERATION......Page 354 Generation by a Rack-Cutter: Relations Between Motions......Page 356 12.11 EVOLUTE OF TOOTH PROFILES......Page 359 12.12 PRESSURE ANGLE......Page 362 Gear Centrode......Page 363 Equations of Centrode Tangency......Page 364 Computational Procedure......Page 365 APPENDIX 12.B: DISPLACEMENT FUNCTIONS FOR GENERATION BY SHAPER......Page 366 13.2 GENERATION OF CYCLOIDAL CURVES......Page 368 Extended Epicycloid......Page 372 13.4 CAMUS’ THEOREM AND ITS APPLICATION......Page 373 Tooth Addendum–Dedendum Profiles......Page 374 Watch Gearing......Page 376 13.5 EXTERNAL PIN GEARING......Page 377 Conjugation of Tooth Profiles......Page 378 Equation of Meshing......Page 379 Gear 2 Tooth Profile......Page 381 Rack-Cutter Tooth Profile......Page 382 Applied Coordinate Systems......Page 383 Line of Action......Page 384 Basic Idea......Page 385 Relation Between Gear Tooth Numbers......Page 386 13.8 ROOT’S BLOWER......Page 387 Conjugation of Profiles......Page 388 Applied Coordinate Systems......Page 389 Equation of Meshing; Line of Action......Page 390 Equations of Dedendum Curve Sigma 2 of Rotor 2......Page 392 14.2 GENERAL CONSIDERATIONS......Page 393 14.3 SCREW INVOLUTE SURFACE......Page 395 14.4 MESHING OF A HELICAL GEAR WITH A RACK......Page 400 Rack Surface Sigma r......Page 401 Interpretation of Sigma r......Page 402 Sections of Sigma r......Page 403 Lines of Contact on Sigma r......Page 405 Lines of Contact L1r on Surface Sigma 1......Page 406 Surface of Action......Page 407 Relations Between Design Parameters......Page 408 Equation of Meshing......Page 410 Derivation of Surface Sigma 2......Page 411 Surface of Action......Page 413 14.6 CONDITIONS OF NONUNDERCUTTING......Page 414 14.7 CONTACT RATIO......Page 416 14.8 FORCE TRANSMISSION......Page 417 14.9 RESULTS OF TOOTH CONTACT ANALYSIS (TCA)......Page 420 14.10 NOMENCLATURE......Page 421 15.1 INTRODUCTION......Page 422 15.2 AXODES OF HELICAL GEARS AND RACK-CUTTERS......Page 425 Pinion Parabolic Rack-Cutter......Page 426 Gear Rack-Cutter......Page 428 Generation of Sigma Sigma......Page 429 Necessary and Sufficient Conditions of Existence of an Envelope to a Parametric Family of Surfaces......Page 430 Representation of Envelope Sigma Sigma in Two-Parameter Form......Page 431 Meshing of Profile-Crowned Helicoids: Conceptual Considerations......Page 432 Algorithm of Analytical Simulation......Page 434 Application of a Plunging Disk......Page 437 Worm Installment......Page 442 Determination ofWorm Thread Surface Sigma w......Page 443 Profile Crowning of Pinion......Page 445 Double Crowning of Pinion......Page 447 15.7 TCA OF GEAR DRIVE WITH DOUBLE-CROWNED PINION......Page 448 Undercutting......Page 450 Pointing......Page 452 15.9 STRESS ANALYSIS......Page 453 Numerical Example......Page 457 16.1 INTRODUCTION......Page 459 Conceptual Considerations......Page 461 Analytical Determination of Line of Action of Crossed Helical Gears......Page 464 Case 1: Error γ of the Crossing Angle (Shaft Angle)......Page 466 Case 2: Error E of the Center Distance......Page 469 16.3 SIMULATION OF MESHING OF CROSSED HELICAL GEARS......Page 470 Numerical Example:Worm-Gear Drive......Page 472 Generation of a Helical Gear......Page 473 Generation of Conjugated Crossed Helical Gears......Page 474 Direction of Helices......Page 476 Canonical Design......Page 477 Numerical Example 1: Design of Standard Gears......Page 478 Numerical Example 2: Approach 1 for Design of Nonstandard Crossed Helical Gears......Page 480 Numerical Example 3: Approach 2 for Design of Nonstandard Crossed Helical Gears......Page 481 Numerical Example......Page 483 APPENDIX 16.A: DERIVATION OF SHORTEST CENTER DISTANCE FOR CANONICAL DESIGN......Page 485 APPENDIX 16.B: DERIVATION OF EQUATION OF CANONICAL DESIGN f (γo, αon, λb1, λb2) = 0......Page 490 APPENDIX 16.D: DERIVATION OF EQUATION (16.5.5)......Page 491 APPENDIX 16.E: DERIVATION OF ADDITIONAL RELATIONS BETWEEN αot1 AND αot2......Page 492 17.1 INTRODUCTION......Page 493 17.2 AXODES OF HELICAL GEARS AND RACK-CUTTER......Page 496 Mismatched Parabolic Rack-Cutters......Page 497 Pinion Parabolic Rack-Cutter......Page 499 Generation of Sigma Sigma......Page 500 Generation of Gear Tooth Surface Sigma 2......Page 501 Representation of Envelope Sigma Sigma in Two-Parameter Form......Page 502 17.5 TOOTH CONTACT ANALYSIS (TCA) OF GEAR DRIVE WITH PROFILE-CROWNED PINION......Page 503 Application of a Disk-Shaped Tool......Page 505 Worm Installment......Page 509 Determination ofWorm Thread Surface Sigmaw......Page 510 Profile Crowning of Pinion......Page 512 Double Crowning of Pinion......Page 514 17.8 TCA OF A GEAR DRIVE WITH A DOUBLE-CROWNED PINION......Page 515 Undercutting......Page 518 Pointing......Page 519 17.10 STRESS ANALYSIS......Page 520 Development of Finite Element Models......Page 521 Numerical Example......Page 523 18.1 INTRODUCTION......Page 526 Axodes......Page 528 Pitch Surfaces......Page 529 18.4 LOCALIZATION OF BEARING CONTACT......Page 530 Shaper Tooth Surfaces......Page 533 Face-Gear Tooth Surface Sigma2......Page 535 18.6 CONDITIONS OF NONUNDERCUTTING OF FACE-GEAR TOOTH SURFACE (GENERATED BY INVOLUTE SHAPER)......Page 537 Directions for Computations......Page 539 18.7 POINTING OF FACE-GEAR TEETH GENERATED BY INVOLUTE SHAPER......Page 540 18.8 FILLET SURFACE......Page 542 Basic Concept......Page 543 Reference and Parabolic Rack-Cutters......Page 544 Shaper Tooth Surface......Page 545 Pinion Tooth Surface......Page 546 18.12 DESIGN RECOMMENDATIONS......Page 547 Applied Coordinate Systems......Page 549 Computational Procedure......Page 551 Results of Investigation......Page 552 Concept of GeneratingWorm......Page 553 Crossing Angle Between Axes of Shaper andWorm......Page 554 Determination ofWorm Surface Sigmaw......Page 555 Generation of Surface Sigma2 byWorm Surface Sigmaw......Page 556 Dressing of theWorm......Page 557 Numerical Example......Page 559 19.1 INTRODUCTION......Page 565 19.2 PITCH SURFACES AND GEAR RATIO......Page 566 Worm Pitch Diameter, Lead Angle, and Axial Pitch......Page 570 Relation BetweenWorm and Worm-Gear Pitches......Page 571 Radius ofWorm-Gear Operating Pitch Cylinder......Page 572 Relations Between Profile Angles in Axial, Normal, and Transverse Sections......Page 573 19.4 GENERATION AND GEOMETRY OF ZA WORMS......Page 575 Generation......Page 579 Representation of Generating Lines in Coordinate Systems Sa......Page 582 Note 1: Determination of Expressions for cos δ and sin δ......Page 583 Determination of ρ......Page 584 Equations of Surfaces ofWorm Thread......Page 585 Kinematic Interpretation of Surface Generation......Page 587 Particular Cases......Page 591 Surface Equations......Page 592 Methods for Generation......Page 596 Generation......Page 599 Worm Surface Equations......Page 600 Particular Case......Page 606 19.8 GEOMETRY AND GENERATION OF F-I WORMS (VERSION I)......Page 608 Installment of the Grinding Wheel for F-I......Page 609 Equations of Generating Surface Σc......Page 610 Lines of Contact onWorm Surface......Page 611 Method for Grinding......Page 615 Equation of Meshing......Page 617 19.10 GENERALIZED HELICOID EQUATIONS......Page 619 19.11 EQUATION OF MESHING OF WORM AND WORM-GEAR SURFACES......Page 621 19.12 AREA OF MESHING......Page 624 Introductory Remarks......Page 627 Application of Oversized Hob......Page 629 Worm Generation......Page 632 Worm-Gear Generation......Page 633 Worm-Gear Surface......Page 634 Unmodified and Modified Gearing......Page 635 20.3 WORM SURFACE EQUATIONS......Page 636 Unmodified Gearing......Page 638 Modified Gearing......Page 639 20.6 WORM-GEAR SURFACE EQUATIONS......Page 640 Unmodified Gearing......Page 641 Modified Gearing......Page 643 21.1 INTRODUCTION......Page 645 21.2 BASIC IDEAS OF THE DEVELOPED APPROACH......Page 646 Introduction......Page 651 Applied Coordinate Systems......Page 652 Head-Cutter Surfaces......Page 654 Equations of the Generated Gear Tooth Surface......Page 657 Equations of the Formate-Cut Gear Tooth Surface......Page 659 Head-Cutter Surfaces......Page 662 Families of Pinion Tooth Surfaces......Page 665 Equation of Meshing......Page 666 21.5 LOCAL SYNTHESIS AND DETERMINATION OF PINION MACHINE-TOOL SETTINGS......Page 667 Local Synthesis of Face-Milled Generated Spiral Bevel Gear Drives......Page 668 21.6 RELATIONSHIPS BETWEEN PRINCIPAL CURVATURES AND DIRECTIONS OF MATING SURFACES......Page 674 Meshing of Surfaces Σg and Σ2......Page 675 Meshing of Surfaces Σ2 and Σ1......Page 676 Procedure of Determination of kf , kh, and σ(12)......Page 677 Meshing of Surfaces Σ1 and Σp......Page 678 Applied Coordinate Systems......Page 679 Simulation Algorithm......Page 680 21.8 APPLICATION OF FINITE ELEMENT ANALYSIS FOR THE DESIGN OF SPIRAL BEVEL GEAR DRIVES......Page 683 21.9 EXAMPLE OF DESIGN AND OPTIMIZATION OF A SPIRAL BEVEL GEAR DRIVE......Page 684 21.10 COMPENSATION OF THE SHIFT OF THE BEARING CONTACT......Page 694 22.2 AXODES AND OPERATING PITCH CONES......Page 697 22.3 TANGENCY OF HYPOID PITCH CONES......Page 698 22.4 AUXILIARY EQUATIONS......Page 700 Tooth Longitudinal Shapes......Page 701 Sliding Velocity at the Pitch Point......Page 702 Derivation of Equations (22.5.1) and (22.5.2)......Page 703 Derivation of Equation (22.5.3) Case 1: Hypoid gear drive with face-milled teeth is considered......Page 704 Case 2: Hypoid gear drive with face-hobbed teeth......Page 705 Computational Procedure for Determination of γ1, γ2, and β2......Page 707 Gear Generation......Page 708 Pinion Generation......Page 710 Pinion Tool Surface Equations......Page 711 Equation of Meshing......Page 713 Pinion Tooth Surface......Page 714 Planetary Mechanisms of Figs. 23.2.1 (a) and (b)......Page 715 Planetary Mechanism of Fig. 23.2.2......Page 717 Planetary Mechanism of Fig. 23.2.3......Page 718 Bevel Gear Differential of Fig. 23.2.5......Page 719 Observation of Assigned Backlash Between Planet Gears [Litvin et al., 2002e]......Page 721 Relation Between Tooth Numbers of Planetary Train of Fig. 23.2.4......Page 722 Determination of m(k) , m(k) , δ (k) , and δ (k) (k = 1, . . . , n)......Page 724 23.4 PHASE ANGLE OF PLANET GEARS......Page 725 23.5 EFFICIENCY OF A PLANETARY GEAR TRAIN......Page 727 Modification of Geometry of Planet Gears......Page 729 Conventional Gear Drive......Page 730 Function of Transmission Errors of Sub-Gear Drives......Page 732 23.8 ILLUSTRATION OF THE EFFECT OF REGULATION OF BACKLASH......Page 734 24.2 GENERATION BY FINGER-SHAPED TOOL: TOOL SURFACE IS GIVEN......Page 736 Equation of Meshing......Page 738 Derivation of Generated Surface Σp......Page 739 24.3 GENERATION BY FINGER-SHAPED TOOL: WORKPIECE SURFACE IS GIVEN......Page 741 Equation of Meshing......Page 744 Generated Surface......Page 746 Equation of Meshing......Page 748 Determination of the Tool Profile......Page 749 25.1 INTRODUCTION......Page 752 25.2 TWO-PARAMETER FORM REPRESENTATION OF WORM SURFACES......Page 753 25.3 THREE-PARAMETER FORM REPRESENTATION OF WORM SURFACES......Page 755 ZN (Convolute)Worm......Page 756 ZI (Involute)Worm......Page 757 ZK (Klingelnberg)Worm......Page 758 F-I (Flender Version I)Worm......Page 759 F-II (Flender Version II)Worm......Page 762 26.1 INTRODUCTION......Page 764 Coordinate Systems Applied for “Phoenix” CNC machine......Page 765 Basic Principle of Execution of Motions......Page 766 Derivation of L(G) and (OtOp).........Page 768 Execution of Motions of CNC Machine......Page 769 Introduction......Page 770 Equation of Meshing Between Σt and Σg......Page 772 Determination of Generated Surface Σg......Page 777 Optimal Approximation of Generated Surface Σg to Ideal Surface Σp......Page 778 Curvatures of Ground Surface Σg......Page 782 Numerical Example: Grinding of an ArchimedesWorm Surface......Page 784 27.2 PROBLEM DESCRIPTION......Page 787 Procedure of Computation......Page 789 Basic Equations......Page 791 Representation of the Unit Vectors of Wire Axes and the Shortest Distance Between the Axes of Two Wires......Page 792 Determination of the Overwire Measurement M......Page 794 Numerical Example: Measurement of Involute Helical Gear......Page 796 27.4 MEASUREMENT OF ASYMMETRIC ARCHIMEDES SCREW......Page 797 Numerical Example: Measurement of Asymmetric Screw......Page 799 28.1 INTRODUCTION......Page 800 28.2 OVERVIEW OF MEASUREMENT AND MODELLING METHOD......Page 801 28.3 EQUATIONS OF THEORETICAL TOOTH SURFACE.........Page 802 28.4 COORDINATE SYSTEMS USED FOR COORDINATE MEASUREMENTS......Page 803 28.5 GRID AND REFERENCE POINT......Page 804 28.7 MINIMIZATION OF DEVIATIONS......Page 805 References......Page 807 Index......Page 813 This revised, expanded, edition covers the theory, design, geometry and manufacture of all types of gears and gear drives. This is an invaluable reference for designers, theoreticians, students, and manufacturers. This edition includes advances in gear theory, gear manufacturing, and computer simulation. Among the new topics are: 1. New geometry for modified spur and helical gears, face-gear drives, and cycloidal pumps. 2. New design approaches for one stage planetary gear trains and spiral bevel gear drives. 3. An enhanced approach for stress analysis of gear drives with FEM. 4. New methods of grinding face gear drives, generating double crowned pinions, and improved helical gear shaving. 5. Broad application of simulation of meshing and TCA. 6. New theories on the simulation of meshing for multi-body systems, detection of cases wherein the contact line on generating surfaces may have its own envelope, and detection and avoidance of singularities of generated surfaces.

this Revision Creates The Standard Reference On The Theory, Design, Geometry, And Manufacture Of Gears.

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provides Grounding In Underlying Principles And Treats Important New Topics Such As Generation Of Gears With New Surface Topology By Application Of Cnc Machines, Minimization Of Deviations Of Real-tooth Surfaces, And Generation Of New Types Of Gears. Coverage Includes Coordinate Transformation, Relative Velocity, Centrodes, External And Internal Involute Gears, Noncircular Gears, Cycloidal Gearing, Double-circular Arc Helical Gears, Design Of Flyblades, And Overwire Measurements. Annotation C. Book News, Inc., Portland, Or (booknews.com)

"Revised and expanded, Gear Geometry and Applied Theory, 2nd Edition, covers the theory, design, geometry, and manufacture of all types of gears and gear drives. Gear Geometry and Applied Theory is an invaluable reference for designers, theoreticians, students, and manufacturers. This new edition includes advances in gear theory, gear manufacturing, and computer simulation."--Jacket A position vector in a three-dimensional space (Fig. 1.1.1) may be represented (i) in vector form as rm = OmM = xmim + ymjm + zmkm (1.1.1) where (im, jm, km) are the unit vectors of coordinate axes, and (ii) by the column matrix rm = [ ].