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TECHNICAL PAPERS

Nonintrinsicity of References in Rigid-Body Motions

[+] Author and Article Information
S. Stramigioli

Faculty of Electrical Engineering, Drebbel Institute, P.O. Box 217, NL-7500 AE Enschede, The Netherlandse-mail: S.Stramigioli@ieee.org

J. Appl. Mech 68(6), 929-936 (Apr 25, 2001) (8 pages) doi:10.1115/1.1409937 History: Received May 19, 2000; Revised April 25, 2001
Copyright © 2001 by ASME
Topics: Motion , Space
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References

Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, UK.
Lipkin, H., 1985, “Geometry and Mappings of Screws With Applications to the Hybrid Control of Robotic Manipulators,” Ph.D. thesis, University of Florida.
Lipkin,  H., and Duffy,  J., 1985, “The Elliptic Polarity of Screws,” ASME J. Mech., Transm., Autom. Des., 107, pp. 377–387.
Lipkin,  H., and Duffy,  J., 1988, “Hybrid Twist and Wrench Control for a Robotic Manipulator,” ASME J. Mech. Des., 110, pp. 138–144.
Olver, P. J., 1993, Applications of Lie Groups to Differential Equations, Vol. 107 (Graduate Texts in Mathematics) 2nd Ed., Springer-Verlag, New York.
Gilmore, R., 1974, Lie Groups, Lie Algebras, and Some of Their Applications, John Wiley and Sons, New York.
Murray, R. M., Li, Z., and Shankar Sastry, S., 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.
Stramigioli, S., Maschke, B., and Bidard, C. 2000, “Hamiltonian Formulation of the Dynamics of Spatial Mechanisms Using Lie Groups and Screw Theory,” Proceedings of the Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball H. Lipkin, ed., Cambridge University Press, Cambridge, UK.
Selig, J. M., 1996, Geometric Methods in Robotics (Monographs in Computer Sciences), Springer-Verlag, New York.
Maschke, B. M. J., 1996, Modeling and Control of Mechanisms and Robots, World Scientific, Singapore, pp. 1–38.
Stramigioli, S., 2001, Modeling and Interactive Mechanical Systems: A Coordinate Free Approach, Springer, Berlin.
Karger, A., and Novak, J., 1978, Space Kinematics and Lie Groups, Gordon and Breach, New York.
Herve,  J. M., 1999, “The Lie Group of Rigid Body Displacements, a Fundamental Tool for Mechanism Design,” Mech. Mach. Theory, 34, pp. 719–730.
Abraham, R., and Marsden, J. E., 1994, Foundations of Mechanics, 2nd Ed., Addison-Wesley, Reading, MA.
Samuel, P., 1988, Projective Geometry (Undergraduate Texts in Mathematics, Readings in Mathematics), Springer-Verlag, New York.

Figures

Grahic Jump Location
An example of a two-dimensional Euclidean system
Grahic Jump Location
Maps between Euclidean spaces
Grahic Jump Location
Compatibility of the kinematic state
Grahic Jump Location
Commutation diagram of the intrinsic left translations
Grahic Jump Location
Commutation diagram of the intrinsic right translations
Grahic Jump Location
tij=ddt(hij(t)∘hji(0))|0
Grahic Jump Location
tji=ddt(hji(t)∘hij(0))|0
Grahic Jump Location
tii,j=ddt(hji(0)∘hij(t))|0
Grahic Jump Location
tjj,i=ddt(hij(0)∘hji(t))|0
Grahic Jump Location
The complete commutation diagram
Grahic Jump Location
The Lie group commutation diagram

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