An invariant approach for curvature analysis of conjugate surfaces

Mechanism and Machine Theory

Volumn 64, Issue , 2013, Pages 175-199

  Wang, Peng ^a   Zhang, Yidu ^a  

^a BEIHANG UNIVERSITY   (China)

Author keywords

Curvature tensor; Local synthesis; Rotation tensor; Spiral bevel gears; Theory of gearing

Indexed keywords

CONJUGATE SURFACES; CURVATURE TENSORS; LOCAL SYNTHESIS; MATRIX COMPUTATION; REFERENCE COORDINATE SYSTEM; SPIRAL BEVEL GEARS; THEORY OF GEARING; TOOTH CONTACT ANALYSIS;

MATRIX ALGEBRA; POINT CONTACTS; TENSORS;

BEVEL GEARS;

EID: 84874928835     PISSN: 0094114X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmachtheory.2013.01.014     Document Type: Article

References (40)

1. A. Dyson A General Theory of the Kinematics and Geometry of Gears in Three Dimensions 1969 Clarendon Press Oxford
2. M.L. Baxter Second order surface generation Industrial Mathematics 23 1974 85 106
3. F.L. Litvin Theory of Gearing, NASA Reference Publication 1212 1989 NASA Washington
4. F.L. Litvin, and Y. Zhang Local Synthesis and Tooth Contact Analysis of Face-milled Spiral Bevel Gears, NASA Contractor Report 4342 1991 NASA Washington
5. F.L. Litvin, and A. Fuentes Gear Geometry and Applied Theory Second Edition, 2004 Cambridge University Press New York
6. X.C. Wang, Third Order Contact Analysis and Optimal Synthesis of Spiral Bevel and Hypoid Gears, Ph.D. Dissertation, Xi'an Jiaotong University, Xi'an, 1985 (in Chinese).
7. X.C. Wang, and S.K. Ghosh Advanced Theories of Hypoid Gears 1994 Elsevier Amsterdam
8. D.R. Wu, and J.S. Luo A Geometric Theory of Conjugate Tooth Surfaces 1992 World Scientific Singapore
9. X.T. Wu Principle of Gearing Second Edition, 2009 Xi'an Jiaotong University Press Xi'an (in Chinese)
10. Y.P. Zhao, W.J. Wei, and X.Z. Dong Some problems on the 2DOF theory of gearing Mechanism and Machine Theory 43 2008 1024 1037
11. X.Z. Dong Design and Manufacture for Epicycloidal Spiral Bevel and Hypoid Gears 2003 China Machine Press Beijing (in Chinese)
12. X.Z. Dong, H.T. Li, and W.J. Wei Two Degree-of-Freedom Theory of Gearing with Applications 2011 China Machine Press Beijing (in Chinese)
13. D.B. Dooner Kinematic Geometry of Gearing Second Edition, 2012 John Wiley & Sons
14. F. Di Puccio, M. Gabiccini, and M. Guiggiani Alternative formulation of the theory of gearing Mechanism and Machine Theory 40 2005 613 637 (Pubitemid 40422846)
15. F. Di Puccio, M. Gabiccini, and M. Guiggiani Comparison of different methods in gear curvature analysis using a new approach Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science 219 2005 1279 1294 (Pubitemid 43000807)
16. F. Di Puccio, M. Gabiccini, and M. Guiggiani Generation and curvature analysis of conjugate surfaces via a new approach Mechanism and Machine Theory 41 2006 382 404 (Pubitemid 43144489)
17. F. Di Puccio, M. Gabiccini, and M. Guiggiani An invariant approach for gear generation with supplemental motions Mechanism and Machine Theory 42 2007 275 295 (Pubitemid 46136462)
18. J. Angeles Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms 2007 Springer
19. B. Siciliano, and O. Khatib Springer Handbook of Robotics 2008 Springer
20. J.M. Selig Geometric Fundamentals of Robotics Second Edition, 2004 Springer
21. D.Z. Xiao, and A.T. Yang Kinematics of three dimensional gearing Mechanism and Machine Theory 24 1989 245 255
22. D.B. Dooner On the three laws of gearing Journal of Mechanical Design 124 2002 733 744
23. M. Griffis A study of curvature for single point contact Mechanism and Machine Theory 38 2003 1391 1411
24. J. Phillips General Spatial Involute Gearing 2003 Springer Verlag New York
25. M. Gabiccini A twist exponential approach to gear generation with general spatial motions Mechanism and Machine Theory 44 2009 382 400
26. P. Wang, Y. Zhang, and J. Deng Curvature analysis of conjugate surfaces via a tensor approach 9th International Conference on History of Mechanical Technology and Mechanical Design, ICHMTMD 2012, March 23, 2012-March 25, 2012 2012 Trans Tech Publications Tainan, Taiwan
27. M.P. Do Carmo Differential Geometry of Curves and Surfaces 1976 Prentice Hall Englewood Cliffs
28. D.R. Wu Differential Geometry Fourth Edition, 1981 Higher Education Press Beijing (in Chinese)
29. D.B. Dooner On the invariance of gear tooth curvature Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science 220 2006 1083 1096 (Pubitemid 44501577)
30. D.L. Wang, J. Liu, and D.Z. Xiao A unified curvature theory in kinematic geometry of mechanism Science in China, Series E: Technological Sciences 41 1998 196 202
31. J.G. Simmonds A Brief on Tensor Analysis 1994 Springer-Verlag
32. K.Z. Huang, M.D. Xue, and M.W. Lu Tensor Analysis Second Edition, 2003 Tsinghua University Press Beijing (in Chinese)
33. L.P. Lebedev, M.J. Cloud, and V.A. Eremeyev Tensor Analysis with Applications in Mechanics 2010 World Scientific Singapore
34. N. Chen Curvatures and sliding ratios of conjugate surfaces Journal of Mechanical Design 120 1998 126 132 (Pubitemid 128652150)
35. N. Ito, and K. Takahashi Differential geometrical conditions of hypoid gears with conjugate tooth surfaces Journal of Mechanical Design 122 2000 323 330
36. C. Chen Mathematical model of curvature analysis for conjugate surfaces with generalized motion in three dimensions Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science 215 2001 487 502
37. D.B. Dooner, and M.W. Griffis On spatial Euler-Savary equations for envelopes Journal of Mechanical Design 129 2007 865 875 (Pubitemid 47316492)
38. J.R. Ruíz-Tolosa, and E. Castillo From Vectors to Tensors 2005 Springer Berlin
39. H. Cheng, and K.C. Gupta An historical note on finite rotations Journal of Applied Mechanics 56 1989 139 145
40. J. Angeles The angular-acceleration tensor of rigid-body kinematics and its properties Archive of Applied Mechanics 69 1999 204 214