A fully reversed (FR) sequence of rotations is defined as a series of rotations of a free rigid body about its body-fixed axes such that the rotation about each axis is fully reversed at the end of the sequence. Due to the non-commutative property of finite rigid body rotations, an FR sequence can effect non-zero changes in orientation of the rigid body even though the net rotation about each axis is zero. The FR sequences are useful for attitude maneuvers of miniature spacecraft that use elastic deformation-based microactuators and for other airborne or neutrally buoyant underwater vehicles where actuations effecting orientation change are restricted. This paper considers the kinematics of six-rotation FR sequences and discusses if each of them is capable of producing any desired change in orientation. It is concluded that out of a total of 24 six-rotation sequences, 12 are capable of this but not the remaining 12. The results are proved using mathematical formalism and are also interpreted using numerical computations and graphical visualization.
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July 2004
Technical Papers
Analysis of Fully Reversed Sequences of Rotations of a Free Rigid Body
Sung K. Koh,
Sung K. Koh
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104
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G. K. Ananthasuresh,
G. K. Ananthasuresh
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104
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Christopher Croke
Christopher Croke
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104
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Sung K. Koh
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104
G. K. Ananthasuresh
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104
Christopher Croke
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 2003; revised November 2003. Associate Editor: G. R. Pennock.
J. Mech. Des. Jul 2004, 126(4): 609-616 (8 pages)
Published Online: August 12, 2004
Article history
Received:
June 1, 2003
Revised:
November 1, 2003
Online:
August 12, 2004
Citation
Koh , S. K., Ananthasuresh, G. K., and Croke, C. (August 12, 2004). "Analysis of Fully Reversed Sequences of Rotations of a Free Rigid Body ." ASME. J. Mech. Des. July 2004; 126(4): 609–616. https://doi.org/10.1115/1.1758249
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