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Orientation Kinematics

  • Reza N. Jazar

Abstract

Two parameters are necessary to define the direction of a line through O and one is necessary to define the amount of rotation of a rigid body about this line. Let the body frame B(Oxyz) rotate ϕ about a line indicated by a unit vector û with direction cosines u 1, u 2, u 3
$$ \hat u = u_1 \hat I + u_2 \hat J + u_3 \hat K $$
(3.1)
$$ \sqrt {u_1^2 + u_2^2 + u_3^2 } = 1. $$
(3.2)

Keywords

Rigid Body Transformation Matrix Coordinate Frame Rotation Matrix Euler Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Buss, S. R., 2003, 3-D Computer Graphics: A Mathematical Introduction with OpenGL, Cambridge University Press, New York.MATHGoogle Scholar
  2. Denavit, J., and Hartenberg, R. S., 1955, A kinematic notation for lowerpair mechanisms based on matrices, Journal of Applied Mechanics, 22(2), 215–221.MATHMathSciNetGoogle Scholar
  3. Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press, London U.K.MATHGoogle Scholar
  4. Mason, M. T., 2001, Mechanics of Robotic Manipulation, MIT Press, Cambridge, Massachusetts.Google Scholar
  5. Murray, R. M., Li, Z., and Sastry, S. S. S., 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, Florida.MATHGoogle Scholar
  6. Nikravesh, P., 1988, Computer-Aided Analysis of Mechanical Systems, Prentice Hall, New Jersey.Google Scholar
  7. Paul, B., 1963, On the composition of finite rotations, American Mathematical Monthly, 70(8), 859–862.MATHCrossRefMathSciNetGoogle Scholar
  8. Paul, R. P., 1981, Robot Manipulators: Mathematics, Programming, and Control, MIT Press, Cambridge, Massachusetts.Google Scholar
  9. Rimrott, F. P. J., 1989, Introductory Attitude Dynamics, Springer-Verlag, New York.MATHGoogle Scholar
  10. Rosenberg, R., M. 1977, Analytical Dynamics of Discrete Systems, Plenum Publishing Co., New York.MATHGoogle Scholar
  11. Schaub, H., and Junkins, J. L., 2003, Analytical Mechanics of Space Systems, AIAA Educational Series, American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia.Google Scholar
  12. Spong, M. W., Hutchinson, S., and Vidyasagar, M., 2006, Robot Modeling and Control, John Wiley & Sons, New York.Google Scholar
  13. Suh, C. H., and Radcliff, C. W., 1978, Kinematics and Mechanisms Design, John Wiley & Sons, New York.Google Scholar
  14. Tsai, L. W., 1999, Robot Analysis, John Wiley & Sons, New York.Google Scholar
  15. Wittenburg, J., and Lilov, L., 2003, Decomposition of a finite rotation into three rotations about given axes, Multibody System Dynamics, 9, 353–375.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Reza N. Jazar
    • 1
  1. 1.Department of Mechanical EngineeringManhattan CollegeRiverdale

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