One Parameter Elliptic Motions in Three-Dimensional Space

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.

Keywords:

Kinematics, elliptical motion one-parameter motion,

PDF

___

[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).

International Electronic Journal of Geometry-Cover

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2008
Yayıncı: Prof.Dr. H.Hilmi Hacısalioğlu

Arşiv