GENERALIZED SCREW TRANSFORMATION AND ITS APPLICATIONS IN ROBOTICS

Year 2015, Volume: 4 Issue: 2, 81 - 88, 14.09.2015

Mehdi Jafari

Abstract

The workspace of the robots can be expressed in terms of the Clifford algebra of the dual quaternions. In this paper, after a review of some basic properties of the generalized dual quaternions we shall use them to kinematical modeling of the robotics in a generalized space.

Keywords

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GENERALIZED SCREW TRANSFORMATION AND ITS APPLICATIONS IN ROBOTICS

Abstract

The workspace of the robots can be expressed in terms of the Clifford algebra of the dual quaternions. In this paper, after a review of some basic properties of the generalized dual quaternions we shall use them to kinematical modeling of the robotics in a generalized space

Keywords

Dual Generalized Quaternion , Robotic , Screw Motion

References

• Agrawal O. P., (1987). Hamilton Operators and Dual-Number-Quaternions in Spatial
• Kinematics, Mechanism and Machine Theory, 22(6), 569-575. Ata E., Yayli Y., (2008). Dual Unitary Matrices and Unit Dual Quaternions, Differential
• Geometry-Dynamical System, 10, 1-12. Bayro-Corrochano E., Kahler D., (2000). Motor Algebra Approach for Computing the Kinematics of Robot Manipulators, Journal of Robotic Systems, 17(9), 495-516.
• Clifford W., (1873). Preliminary Sketch of Biquaternions. Proc. of London Math. Soc., 10, 381-3
• Flaut C., (2001). Some Equations in Algebras obtained by the Cayley-Dickson Process. An.
• Şt. Univ. ovidius constanta, 9(2), 45-68. Funda J., (1988). A Computational Analysis of Line-Oriented Screw Transformation in
• Robotics, University of Pennsylvania, New York. Funda J., Paul R.P., (1999). A Computational Analysis of Screw Transformation in
• Robotics, IEEE Transactions of Robotics and Automation, 6(3), 348-356. Gu Y., Luh J.Y.S., (1987). Dual-number Transformation and Its Applications to Robotics.
• IEEE journal of Robotics and Automation, 3(6), 615-623. Guggenheimer H.W., (1963). Differential Geometry, McGraw-Hill book company, Inc., New York.
• Han D., Wie Q., Li Z., (2008). Kinematic Control of Free Rigid Bodies Using Dual
• Quaternions, International Journal of Automation and Computing, 05(3), 319-324. Heard W. B., (2006). Rigid Body Mechanics, Mathematics, Physics and Applications,
• WILEY-VCH verlag GmbH & Co. KGaA, Weinheim. Kim J.H., KumarV.R., (1990). Kinematics of Robot Manipulators via Line
• Transformations, Journal of Robotic System, 7(4), 649-674. Kula L., Yayli Y., (2006). Dual Split Quaternions And Screw Motion In Minkowski 3
• Space, Iranian journal of Sci.& Tech., Transaction A, 30(3), 245-258. Jafari M., Yayli Y., (2013). Rotation in Four Dimensions via Generalized Hamilton
• Operators, Kuwait journal of science, 40(1), 67-79. Jafari M., (2012). Generalized Hamilton operators and their Lie groups, PhD thesis,
• Ankara University, Ankara, Turkey, Jafari M., Yayli Y., (2011). Hamilton Operators and Generalized Quaternions, 8th
• Geometry Conference, Antalya, Turkey. Jafari M., Yayli Y., (2011). Homothetic motions at E . International Journal 4 αβ
• Contemporary of Mathematics Sciences. 5(47), 2319-2326.
• Jafari M., Yayli Y., (2010). Dual Generalized Quaternions in Spatial Kinematics. 41st
• Annual Iranian Math. Conference, Urmia, Iran. Jafari M., Yayli Y., (2015). The E. Study Maps Of Circle On Dual Elliptical Unit Sphere 2 D
• E .Accepted the paper for publication in Bitlis Eren university jouranal of science. Jafari M., (2013). The E. Study mapping for directed lines in 3-space E . The First 3 αβ
• Regional Conference Mathematics & Statistics, Payame Noor university, Urmia, Iran. McCarthy J.M., (1986). Dual Orthogonal Matrices in Manipulator Kinematics,
• International journal Robotics Research, 5(2), 45-51. Mortazaasl H., Jafari M., Yayli Y., (2012). Some Algebraic Properties of Dual Generalized
• Quaternions Algebra, Far East journal of Mathematical science, 69(2), 307-318. Pennock G.R., Yang A.T., (1985). Application of Dual Number Matrices to the Inverse
• Kinematics Problem of Robot Manipulators, Journal Mechanisms Transmissions and Automat Design, 10(7), 201-208. Pottman H.,Wallner J. ,(2000). Computational Line Geometry, Springer-Verlag, New York.
• Sahu S., Biswal B.B., Subudhi B., (2008). A Novel Method for Representing Robot
• Kinematics Using Quaternion Theory, IEEE Sponsored Conference On Computational Intelligence, Control And Computer Vision In Robotics & Automation. Study E., (1891). Von Den bewegungen und umlegungen, Mathematische Annalen 39: 441- 5
• UGurlu H. H., Caliskan A., (1996). The Study Mapping for Directed Space-Like and Time
• Like in Minkowski 3-space R. Mathematical & Computational App., 1, 142-148. Mathematical & Computational App., 1, 142-148. 1 Veldkemp G.R., (1976). On the use of Dual Numbers, Vectors and Matrices in
• Instantanouse Spatial Kinematics, Mechanism and Machine Theory, 11, 141-156. Yang A.T., Freudensterin F., (1964). Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms. ASME journal of applied Mechnics, 86(2), 300-308.