Araştırma Makalesi
BibTex RIS Kaynak Göster

One Parameter Elliptic Motions in Three-Dimensional Space

Yıl 2021, Cilt: 14 Sayı: 2, 391 - 399, 29.10.2021
https://doi.org/10.36890/iejg.959634

Öz

Elliptical motions have been defined by three different right-handed coordinate systems. The motion of these coordinate systems depends on the time parameter which has great importance in robotics. In particular, it is used in a model of a robot arm manipulator to achieve high performance. Hence, we have expressed some theorems and results concerning this elliptical motion. Besides, the special cases of this motion have been discussed.

Proje Numarası

Yok

Kaynakça

  • [1] Abdel-Baky, R.A., Al-Ghefari, R.A.: On the One-parameter Dual Spherical Motions. Comput. Aided Geom. Design 28, 23–37 (2011).
  • [2] Chiacchio, P., Bouffard-Vercelli, Y., Pierrot, F.: Force Polytope and Force Ellipsoid for Redundant Manipulators. J. Field Robot. Syst. 14, Issue 8, 613–620 (1997).
  • [3] Eberly, D.H.: 3D Game Engine Design, Academic Press, San Diego, USA, (2001).
  • [4] Frahm, G., Junker, M., Szimayer, A.: Elliptical Copulas: Applicability and Limitations. Stat. Probab. Lett. 63 (3), 275–286 (2003).
  • [5] Güngör, M.A., Tosun, M.: One Parameter Dual Lorentzian Spherical Motions and Ruled Surfaces. Matematiche LXIII, 63–82 (2008).
  • [6] Güngör, M.A., Tosun, M.: One Parameter Lorentzian Motions in Lorentz 3-Space. Kragujevac J. Math. 31, 95–109 (2008).
  • [7] Jüttler, B.: An Osculating Motion with Second Order Contact for Spatial Euclidean Motions. Mech. Mach. Theory 32 (7), 843–853 (1997).
  • [8] Kim, S., Karrila, S.J.: Microhydrodynamics: Principles and Selected Applications. Dover Publications Inc., New York, USA (2005).
  • [9] Köse, Ö.: On the Dual Spherical Motions-II. Mech. Mach. Theory 17, 191–196 (1982).
  • [10] Mackey, D.S., Mackey, N., Tisseur, F.: G-reactors: Analogues of Householder Transformations in Scalar Product Spaces. Linear Algebra Appl. 385, 187–213 (2004).
  • [11] Massa, W.: Crystal Structure Determination (2nd ed.). Springer-Verlag, Berlin Heidelberg, Germany (2004).
  • [12] Müller, H.R.: Kinematik Dersleri. Ankara Üniversitesi Fen Fakültesi Yayınları 27, Ankara (1963).
  • [13] Özdemir, M.: An Alternative Approach to Elliptical Motion. Adv. Appl. Clifford Algebras 26, 279–304 (2016).
  • [14] Torge, W.: Geodesy (3rd edition). Walter de Gruyter, Berlin, Germany (2001).
  • [15] Tosun, M., Güngör, M.A., Hacısalihoğlu, H.H., Okur, I.: A Study on the One Parameter Lorentzian Spherical Motions. Acta Math. Univ. Comenianae LXXV (1), 85–93 (2006).
  • [16] Turhan, T., Yüksel, N., Ayyıldız, N.: On Pseudohyperbolic Space Motions. Turk J. Math. 39, 750–762 (2015).
  • [17] Wen, J.T., Wilfinger, L.S.: Kinematic Manipulability of General Constrained Rigid Multibody Systems. IEEE Trans. Robot. Autom. 15, Issue 3, 558–567 (1999).
  • [18] Yaylı, Y., Çalışkan, A., Uğurlu, H.H.: The E Study Maps of Circles on Dual Hyperbolic and Lorentzian Unit Spheres H0 2 and S2 1. Proc. Roy. Irish Acad. Sect. A 102A, 37–47 (2002).
Yıl 2021, Cilt: 14 Sayı: 2, 391 - 399, 29.10.2021
https://doi.org/10.36890/iejg.959634

Öz

Destekleyen Kurum

Yok

Proje Numarası

Yok

Kaynakça

  • [1] Abdel-Baky, R.A., Al-Ghefari, R.A.: On the One-parameter Dual Spherical Motions. Comput. Aided Geom. Design 28, 23–37 (2011).
  • [2] Chiacchio, P., Bouffard-Vercelli, Y., Pierrot, F.: Force Polytope and Force Ellipsoid for Redundant Manipulators. J. Field Robot. Syst. 14, Issue 8, 613–620 (1997).
  • [3] Eberly, D.H.: 3D Game Engine Design, Academic Press, San Diego, USA, (2001).
  • [4] Frahm, G., Junker, M., Szimayer, A.: Elliptical Copulas: Applicability and Limitations. Stat. Probab. Lett. 63 (3), 275–286 (2003).
  • [5] Güngör, M.A., Tosun, M.: One Parameter Dual Lorentzian Spherical Motions and Ruled Surfaces. Matematiche LXIII, 63–82 (2008).
  • [6] Güngör, M.A., Tosun, M.: One Parameter Lorentzian Motions in Lorentz 3-Space. Kragujevac J. Math. 31, 95–109 (2008).
  • [7] Jüttler, B.: An Osculating Motion with Second Order Contact for Spatial Euclidean Motions. Mech. Mach. Theory 32 (7), 843–853 (1997).
  • [8] Kim, S., Karrila, S.J.: Microhydrodynamics: Principles and Selected Applications. Dover Publications Inc., New York, USA (2005).
  • [9] Köse, Ö.: On the Dual Spherical Motions-II. Mech. Mach. Theory 17, 191–196 (1982).
  • [10] Mackey, D.S., Mackey, N., Tisseur, F.: G-reactors: Analogues of Householder Transformations in Scalar Product Spaces. Linear Algebra Appl. 385, 187–213 (2004).
  • [11] Massa, W.: Crystal Structure Determination (2nd ed.). Springer-Verlag, Berlin Heidelberg, Germany (2004).
  • [12] Müller, H.R.: Kinematik Dersleri. Ankara Üniversitesi Fen Fakültesi Yayınları 27, Ankara (1963).
  • [13] Özdemir, M.: An Alternative Approach to Elliptical Motion. Adv. Appl. Clifford Algebras 26, 279–304 (2016).
  • [14] Torge, W.: Geodesy (3rd edition). Walter de Gruyter, Berlin, Germany (2001).
  • [15] Tosun, M., Güngör, M.A., Hacısalihoğlu, H.H., Okur, I.: A Study on the One Parameter Lorentzian Spherical Motions. Acta Math. Univ. Comenianae LXXV (1), 85–93 (2006).
  • [16] Turhan, T., Yüksel, N., Ayyıldız, N.: On Pseudohyperbolic Space Motions. Turk J. Math. 39, 750–762 (2015).
  • [17] Wen, J.T., Wilfinger, L.S.: Kinematic Manipulability of General Constrained Rigid Multibody Systems. IEEE Trans. Robot. Autom. 15, Issue 3, 558–567 (1999).
  • [18] Yaylı, Y., Çalışkan, A., Uğurlu, H.H.: The E Study Maps of Circles on Dual Hyperbolic and Lorentzian Unit Spheres H0 2 and S2 1. Proc. Roy. Irish Acad. Sect. A 102A, 37–47 (2002).
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Ayşe Zeynep Azak 0000-0002-2686-6043

Proje Numarası Yok
Yayımlanma Tarihi 29 Ekim 2021
Kabul Tarihi 18 Ekim 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 14 Sayı: 2

Kaynak Göster

APA Azak, A. Z. (2021). One Parameter Elliptic Motions in Three-Dimensional Space. International Electronic Journal of Geometry, 14(2), 391-399. https://doi.org/10.36890/iejg.959634
AMA Azak AZ. One Parameter Elliptic Motions in Three-Dimensional Space. Int. Electron. J. Geom. Ekim 2021;14(2):391-399. doi:10.36890/iejg.959634
Chicago Azak, Ayşe Zeynep. “One Parameter Elliptic Motions in Three-Dimensional Space”. International Electronic Journal of Geometry 14, sy. 2 (Ekim 2021): 391-99. https://doi.org/10.36890/iejg.959634.
EndNote Azak AZ (01 Ekim 2021) One Parameter Elliptic Motions in Three-Dimensional Space. International Electronic Journal of Geometry 14 2 391–399.
IEEE A. Z. Azak, “One Parameter Elliptic Motions in Three-Dimensional Space”, Int. Electron. J. Geom., c. 14, sy. 2, ss. 391–399, 2021, doi: 10.36890/iejg.959634.
ISNAD Azak, Ayşe Zeynep. “One Parameter Elliptic Motions in Three-Dimensional Space”. International Electronic Journal of Geometry 14/2 (Ekim 2021), 391-399. https://doi.org/10.36890/iejg.959634.
JAMA Azak AZ. One Parameter Elliptic Motions in Three-Dimensional Space. Int. Electron. J. Geom. 2021;14:391–399.
MLA Azak, Ayşe Zeynep. “One Parameter Elliptic Motions in Three-Dimensional Space”. International Electronic Journal of Geometry, c. 14, sy. 2, 2021, ss. 391-9, doi:10.36890/iejg.959634.
Vancouver Azak AZ. One Parameter Elliptic Motions in Three-Dimensional Space. Int. Electron. J. Geom. 2021;14(2):391-9.