Research article

Ruled surfaces with constant Disteli-axis

  • Received: 09 July 2020 Accepted: 03 September 2020 Published: 27 September 2020
  • MSC : 53A04, 53A05, 53A17

  • This work develops the kinematic-geometry for ruled surfaces by using the analogy with spherical kinematics. This provides the ability to compute set of curvature functions which define the local shape of ruled surfaces. Hence, the well known equation of the Plücker's conoid has been obtained and its kinematic-geometry are examined in details. Finally, a characterization for a line trajectory to be a constant Disteli-axis is derived, and investigated.

    Citation: Nadia Alluhaibi. Ruled surfaces with constant Disteli-axis[J]. AIMS Mathematics, 2020, 5(6): 7678-7694. doi: 10.3934/math.2020491

    Related Papers:

  • This work develops the kinematic-geometry for ruled surfaces by using the analogy with spherical kinematics. This provides the ability to compute set of curvature functions which define the local shape of ruled surfaces. Hence, the well known equation of the Plücker's conoid has been obtained and its kinematic-geometry are examined in details. Finally, a characterization for a line trajectory to be a constant Disteli-axis is derived, and investigated.


    加载中


    [1] R. A. Abdel-Baky, Inflection and torsion line Congruences, J. Geom. Graph., 11 (2007), 1-14.
    [2] R. A. Abdel-Baky, On the curvature theory of a line trajectory in spatial kinematics, Commun. Korean Math. Soc., 34 (2019), 333-349.
    [3] R. A. Abdel-Baky, R. A. Al-Ghefari, On the one-parameter dual spherical motions, Comput. Aided Geom. Design, 28 (2011), 23-37.
    [4] R. A.Abdel-Baky, F. R. Al-Solamy, A new geometrical approach to one-parameter spatial motion, J. Eng. Math., 60 (2008), 149-172.
    [5] R. A. Al-Ghefari, R. A. Abdel-Baky, Kinematic geometry of a line trajectory in spatial motion, J. Mech. Sci. Technol., 29 (2015), 3597-3608.
    [6] O. Bottema, B. Roth, Theoretical Kinematics, North-Holland Press, New York, 1979.
    [7] G. Figliolini, H. Stachel, J. Angeles, On Martin Disteli's spatial cycloidal gearing, Mech. Machine Theory, 60 (2012), 73-89.
    [8] G. Figliolini, H. Stachel, J. Angeles, A new look at the Ball-Disteli diagram and its relevance to spatial gearing, Mech. Machine Theory, 42 (2007), 1362-1375.
    [9] D. B. Dooner, M. W. Griffis, On spatial Euler-savary equations for envelopes, ASME J. Mech. Design, 129 (2006), 865-875.
    [10] A. Karger, J. Novak, Kinematics and Lie Groups, Gordon and Breach Science Publishers, New York, 1985.
    [11] H. Pottman, J. Wallner, Computational Line Geometry, Springer-Verlag, Berlin, Heidelberg, 2001.
    [12] H. Stachel, Instantaneous Spatial Kinematics and the Invariants of the Axodes, Institute fur Geometrie, TU Wien, Technical Report 34, 1996.
    [13] J. Tölke, Contributions to the theory of the axes of curvature, Mech. Machine Theory, 11 (1976), 123-130.
    [14] D. Wang, J. Liu, D. Xiao, A unified curvature theory in kinematic geometry of mechanism, Sci. China (Series E), 41 (1998), 196-202.
    [15] D. Wang, J. Liu, D. Xiao, Geometrical characteristics of some typical spatial constraints, Mech. Machine Theory, 35 (2000), 1413-1430.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2829) PDF downloads(108) Cited by(10)

Article outline

Figures and Tables

Figures(7)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog