On the dual quaternion geometry of screw motions

[1]W. R. Hamilton, Elements of quaternions, I, II and III, Chelsea, New York, 1899.Search in Google Scholar

[2]H.H. Hacısalihoğlu, Motion geometry and quaternions theory, Faculty of sciences and arts. university of Gazi press, Ankara, 1983.Search in Google Scholar

[3]M. Nagaraj, K. Bharathi, Quaternion Valued Function of a Real Serret-Frenet Formulae, Indian J. Pure Appl. Math., 16 (7) (1985), 741-756.Search in Google Scholar

[4]V. Majernik, Basic space time transformations expressed by means of two component number systems, Acta Phys. Pol. A., 86 (1) (1994), 291-295.Search in Google Scholar

[5]V. Majernik, Quaternion formulation of the Galilean space time transformation, Acta Phy. Slovaca, 56 (1) (2006), 9-14.Search in Google Scholar

[6]Y. Yaylı, E. E. Tütüncü, Generalized Galilean transformations and dual quaternions, Scientia Magna, 56 (1) (2009), 94-100.Search in Google Scholar

[7]Z. Ercan, S. Yüce, On properties of the dual quaternions, European Journal of Pure and Applied Mathematics, 4 (2) (2011), 142-146.Search in Google Scholar

[8]L. Kula, Y. Yaylı, A commutative multiplication of dual number triplets, Dumlupınar University Journal of Science Institute, 10 2006.Search in Google Scholar

[9]O. Bottema, R. Roth, Theoretical kinematics, Amsterdam, 1979.Search in Google Scholar

[10]W. K. Clifford, Preliminary sketch of biquaternions, Proc. London Math. Soc. London, 1873.Search in Google Scholar

[11]E. Study, Geometry der dynamen, Leipzig, Druck und Verlag von B.G. Teubner, 1903.Search in Google Scholar

[12]B. Akyar, Dual quaternions in spatial kinematics in an algebraic sense, Turkish Journal of Mathematics, 32 (4) 2008.Search in Google Scholar

[13]M. Gouasmi, Robot kinematics using dual quaternions, IAES International Journal of Robotics and Automation, 2012.Search in Google Scholar

[14]DP. Han, Q. Wei, ZX. Li, Kinematic control of free rigid bodies using dual quaternions, Int. J. Autom. Comput., 5 (2008), 319-324.Search in Google Scholar

[15]A. Atasoy, E. Ata, Y. Yaylı, Y. Kemer, A new polar representation for split and dual split quaternions, Advances in applied cli ord algebras, 27 (3) (2017), 2307-2319.Search in Google Scholar

[16]M. Bekar, Y.Yaylı, Involutions in dual split-quaternions, Advances in applied cli ord algebras, 26 (2) (2016), 553-571.Search in Google Scholar

[17]E. Ata, Y. Yaylı, Dual quaternions and dual projective spaces, Solutions and Fractals, 40 (3) (2009), 1255-1263.Search in Google Scholar

[18]E. Ata, Y. Yaylı, Dual unitary matrices and unit dual quaternions, Di er. Geom. Dyn. Syst., 10 (2008), 1-12.Search in Google Scholar

[19]L. Kula, Y. Yaylı, Dual split quaternions and screw motion in Minkowski 3-space, Iran J. math. tech.trans., 30 (3) (2006), 245-258.Search in Google Scholar

[20]M.A. Güngör, M. Sarduvan, A note on dual quaternions and matrices of dual quaternions, Scientia Magna, 7 (1), 2011.Search in Google Scholar

[21]A. Dağdeviren, S. Yüce, Dual quaternions and dual quaternionic curves, Filomat, 33 (2019), 1037-1046.Search in Google Scholar

[22]G. Y. Şentürk, N. Gürses, S. Yüce, Algebraic construction for dual quaternions with GCN, Bitlis Eren University Journal Of Science, 11 (2) (2022), 586-593.Search in Google Scholar

[23]S. Yüce, On the E. Study maps for the dual quaternions, Applied Mathematics E-Notes, 21 (2021), 365-374.Search in Google Scholar

[24]L. Hao, W. Xiafu, Z. Yisheng, Quaternion-based robust attitude control for uncertain robotic quadrotors, Ieee Transactions On Industrial Informatics, 11 (2), 2015.Search in Google Scholar

[25]F. Mehdi, Z. Nadjet, St-A. Jonathan, A novel quantum model of forward kinematics based on quaternion/Pauli gate equivalence: Application to a six-jointed industrial robotic arm, Results in Engineering, 14 (2022), 100402.Search in Google Scholar

[26]J. Funda, R. P. Paul, A computational analysis of screw transformations in robotics, IEEE Transactions on Robotics and Automation, 6 (3) (1990), 348-356, doi: 10.1109/70.56653.Search in Google Scholar

[27]F. Torunbalcı Aydın, Dual Jacobsthal Quaternions, Communications in Advanced Mathematical Sciences, 3 (3) (2020), 130-142, 10.33434/cams.680381.Search in Google Scholar

[28]D. Güçler, N. Ekmekçi, Y. Yaylı, M. Helvacı, Obtaining the Parametric Equation of the Curve of the Sun’s Apparent Movement by Using Quaternions, Universal Journal of Mathematics and Applications, 5 (2) (2022), 42-50, doi:10.32323/ujma.1091832.Search in Google Scholar

[29]K. Eren, H. Kösal, Numerical Algorithm for Solving General Linear Elliptic Quaternionic Matrix Equations, Fundamental journal of mathematics and applications, 4 (3) (2021), 180-186, 10.33401/fujma.888705.Search in Google Scholar

[30]M. Jafarı, Matrix Formulation of Real Quaternions, Erzincan University Journal of Science and Technology, 8 (1) (2015), 27-37, doi: 10.18185/eufbed.99802.Search in Google Scholar

[31]S. Kızıltuğ, T. Erişir, G. Mumcu, Y. Yaylı, On the quaternionic osculating direction curves, International Journal of Geometric Methods in Modern Physics, 19 (4) (2022), 2230001.Search in Google Scholar

[32]G. Cerda-Morales, On fourth-order jacobsthal quaternions, Journal of Mathematical Sciences and Modelling, 1 (2) (2018), 73-79.Search in Google Scholar