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The Scientific World Journal
Volume 2014, Article ID 409402, 14 pages
http://dx.doi.org/10.1155/2014/409402
Research Article

Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

Mechanical Engineering Department, Taibah University, Almadinah Almonawwarah 42353, Saudi Arabia

Received 15 March 2014; Accepted 28 March 2014; Published 19 June 2014

Academic Editor: Belal F. Yousif

Copyright © 2014 Mohamed A. Omar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Giampiero and P. Manfred, Simulation Algorithms in Vehicle System Dynamics, CRC Press, 2004.
  2. M. A. Omar, “An applied approach for large-scale multibody dynamics simulation and machine-terrain interaction,” SAE International Journal of Passenger Cars—Electronic and Electrical Systems, vol. 1, no. 1, pp. 820–828, 2009. View at Google Scholar · View at Scopus
  3. J. Y. Wong, “Dynamics of tracked vehicles,” Vehicle System Dynamics, vol. 28, no. 2-3, pp. 197–219, 1997. View at Google Scholar · View at Scopus
  4. H. C. Lee, J. H. Choi, and A. A. Shabana, “Spatial dynamics of multibody tracked vehicles part II: contact forces and simulation results,” Vehicle System Dynamics, vol. 29, no. 2, pp. 113–137, 1998. View at Google Scholar · View at Scopus
  5. Z.-D. Ma and N. C. Perkins, “A track-wheel-terrain interaction model for dynamic simulation of tracked vehicles,” Vehicle System Dynamics, vol. 37, no. 6, pp. 401–421, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. Z.-D. Ma and N. C. Perkins, “An efficient multibody dynamics model for internal combustion engine systems,” Multibody System Dynamics, vol. 10, no. 4, pp. 363–391, 2003. View at Publisher · View at Google Scholar · View at Scopus
  7. P. Roland, D. Daniel, S. Emilio, and Á. N. Miguel, “Validation of a multibody model for an X-by-wire vehicle prototype through field testing,” in Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics, J. C. Samin and P. Fisette, Eds., Brussels, Belgium, July 2011.
  8. A. A. Shabana, Dynamics of Multibody Systems, Cambridge University Press, Cambridge, UK, 3rd edition, 2005.
  9. P. E. Nikravesh, An Overview of Several Formulations for Multibody Dynamics, Product Engineering, 2005.
  10. R. Featherstone, Rigid Body Dynamics Algorithms, Springer, New York, NY, USA, 2008.
  11. R. Featherstone, “The acceleration vector of a rigid body,” International Journal of Robotics Research, vol. 20, no. 11, pp. 841–846, 2001. View at Google Scholar · View at Scopus
  12. R. Featherstone and D. Orin, “Robot dynamics: equations and algorithms,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '00), pp. 826–834, April 2000. View at Scopus
  13. R. Featherstone, “Efficient factorization of the joint-space inertia matrix for branched kinematic trees,” International Journal of Robotics Research, vol. 24, no. 6, pp. 487–500, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. R. A. Wehage and E. J. Haug, “Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems,” Journal of Mechanical Design, vol. 134, pp. 247–255, 1982. View at Google Scholar
  15. R. A. Wehage and M. J. Belczynski, “High resolution vehicle simulations using precomputer coefficients,” in Proceedings of the Winter Annual Meeting of the American Society of Mechanical Engineers, vol. 44, pp. 311–325, November 1992. View at Scopus
  16. G. Rodriguez, A. Jain, and K. Kreutz-Delgado, “Spatial operator algebra for multibody system dynamics,” Journal of the Astronautical Sciences, vol. 40, no. 1, pp. 27–50, 1992. View at Google Scholar · View at Scopus
  17. G. Rodriguez, A. Jain, and K. Kreutz-Delgado, “Spatial operator algebra for manipulator modeling and control,” International Journal of Robotics Research, vol. 10, no. 4, pp. 371–381, 1991. View at Google Scholar · View at Scopus
  18. E. Eich-Soellner and C. Führer, Numerical Methods in Multibody Dynamics, Teubner, Stuttgart, Germany, 1998.
  19. C. Yang, D. Cao, Z. Zhao, Z. Zhang, and G. Ren, “A direct eigenanalysis of multibody system in equilibrium,” Journal of Applied Mathematics, vol. 2012, Article ID 638546, 12 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. J. García de Jalón and E. Bayo, Kinematic and Dynamic Simulation of Multibody Systems, the Real-Time Challenge, Springer, New-York, NY, USA, 1994.
  21. R. Avilés, G. Ajuria, V. Gómez-Garay, and S. Navalpotro, “Comparison among nonlinear optimization methods for the static equilibrium analysis of multibody systems with rigid and elastic elements,” Mechanism and Machine Theory, vol. 35, no. 8, pp. 1151–1168, 2000. View at Publisher · View at Google Scholar · View at Scopus
  22. Z. S. Wang, Y. Y. Tao, and Q. Y. Wen, “A vector bond graph method of kineto-static analysis for spatial multibody systems,” Applied Mechanics and Materials, vol. 321–324, pp. 1725–1729, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. M. A. Omar, “Modeling flexible bodies in multibody systems in joint-coordinates formulation using spatial algebra,” Advances in Mechanical Engineering, vol. 2014, Article ID 468986, 18 pages, 2014. View at Publisher · View at Google Scholar
  24. R. W. Wehage, “Automated procedures for robust and efficient solution of over-constrained multibody dynamics,” in Proceeding of ASME International Mechanical Engineering Congress and Exposition (IMECE '12), vol. 85259, Huston, Tex, USA, November 2012.
  25. P. E. Nikravesh, “Construction of the equations of motion for multibody dynamics using point and joint coordinates,” in Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, vol. 268 of NATO ASI Series E: Applied Sciences, pp. 31–60, Kluwer Academic Publishers, 1994. View at Google Scholar
  26. A. Jain, “Multibody graph transformations and analysis—part I: tree topology systems,” Nonlinear Dynamics, vol. 67, no. 4, pp. 2779–2797, 2012. View at Publisher · View at Google Scholar · View at Scopus
  27. M. A. Omar, Finite Element Modeling of Leaf Springs in Multibody Systems, VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG, Saarbrücken, Germany, 2010.
  28. M. A. Omar, A. A. Shabana, A. Mikkola, W.-Y. I. Loh, and R. Basch, “Multibody system modeling of leaf springs,” Journal of Vibration and Control, vol. 10, no. 11, pp. 1601–1638, 2004. View at Publisher · View at Google Scholar · View at Scopus
  29. K. J. Bathe, Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ, USA, 1996.
  30. T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover, New York, NY, USA, 2000.
  31. R. R. Craig and M. C. Bampton, “Coupling of substructures for dynamic analyses,” AIAA Journal, vol. 6, no. 7, pp. 1313–1319, 1968. View at Google Scholar
  32. R. R. Craig and C. J. Chang, “On the use of attachment modes in substructure coupling for dynamic analysis,” in Proceedings of the 18th Conference on Structures, Structural Dynamics and Materials, San Diego, Calif, USA, 1977.
  33. A. A. Shabana, Computational Dynamics, John Wiley & Sons, 3rd edition, 2010.
  34. U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1998.
  35. K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical Solutions of Initial-Value Problems in Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, New York, NY, USA, 1996.
  36. J. García de Jalón and E. Bayo, Kinematic and Dynamic Simulation of Multibody Systems, the Real-Time Challenge, Springer, NewYork, NY, USA, 1994.
  37. J. Baumgarte, “Stabilization of constraints and integrals of motion in dynamical systems,” Computer Methods in Applied Mechanics and Engineering, vol. 1, no. 1, pp. 1–16, 1972. View at Google Scholar · View at Scopus