Hostname: page-component-54dcc4c588-2ptsp Total loading time: 0 Render date: 2025-09-11T11:49:08.098Z Has data issue: false hasContentIssue false
  • English
  • Français

A fresh insight into Kane's equations of motion

Published online by Cambridge University Press:  17 August 2015

H. Nejat Pishkenari ,
S. A. Yousefsani ,
A. L. Gaskarimahalle  and
S. B. G. Oskouei
H. Nejat Pishkenari*
Affiliation:
Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
S. A. Yousefsani
Affiliation:
Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
A. L. Gaskarimahalle
Affiliation:
Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
S. B. G. Oskouei
Affiliation:
Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
*
*Corresponding author. E-mail: nejat@sharif.edu
Get access Rights & Permissions [Opens in a new window]

Summary

With rapid development of methods for dynamic systems modeling, those with less computation effort are becoming increasingly attractive for different applications. This paper introduces a new form of Kane's equations expressed in the matrix notation. The proposed form can efficiently lead to equations of motion of multi-body dynamic systems particularly those exposed to large number of nonholonomic constraints. This approach can be used in a recursive manner resulting in governing equations with considerably less computational operations. In addition to classic equations of motion, an efficient matrix form of impulse Kane formulations is derived for systems exposed to impulsive forces.

Keywords

DynamicsKane methodGeneralized speedMulti-body systemNonholonomic constraintImpulse Kane formulation

Information

Type
Articles
Information
Robotica , Volume 35 , Issue 3 , March 2017 , pp. 498 - 510
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Kane, T. R., “Dynamics of nonholonomic systems,” J. Appl. Mech. 28, 574–578 (1961).CrossRefGoogle Scholar
2. Kane, T. R. and Levinson, D. A., “Formulation of equations of motion for spacecraft,” J. Guid. Control, 3 (2), 3–21 (1980).Google Scholar
3. Kane, T. R. and Levinson, D. A., Dynamics: Theory and Applications (McGraw-Hill Press, New York, 1985).Google Scholar
4. Gibbs, J. W., “On the fundamental formulas of dynamics,” Am. J. Math. 2, 49–64 (1879).CrossRefGoogle Scholar
5. Appell, P., “Sur les mouvements de roulment; equations du mouvement analougues a celles de Lagrange,” CR. Acad. Sci. Paris, 129, 317–320 (1899).Google Scholar
6. Baruh, H., Analytical Dynamics (International Editions, McGraw-Hill Press, Singapore, 1999).Google Scholar
7. Sharf, I., D'Eleuterio, G. M. T. and Hughes, P. C., “On the dynamics of Gibbs, Appell, and Kane,” Eur. J. Mech. A-Solids, 11 (2), 145–155 (1992).Google Scholar
8. Desloge, E. A., “A comparison of Kane's equations of motion and Gibbs-Appell equations of motion,” Am. J. Phys. 54 (5), 470–471 (1986).Google Scholar
9. Levinson, D. A., “Comment on relationship between Kane's equations and Gibbs-Appell equations,” J. Guid. Control Dyn. 10 (6), 595–596 (1987).CrossRefGoogle Scholar
10. Townsend, M. A., “Equivalence of Kane's, Gibbs-Appell's, and Lagrange's equations,” J. Guid. Control Dyn. 15 (5), 1289–1292 (1992).Google Scholar
11. Piedbeuf, J. C., “Kane's Equations or Jourdain's Principle?,” Circuits and Systems, 1993., Proceedings of the 36th Midwest Symposium on, Detroit, MI, USA (1993), vol. 2, pp. 1471–1474.Google Scholar
12. Pishkenari, H. N., Gaskarimahalle, A. L., Oskouei, S. B. G. and Meghdari, A. “An Applied Form of Kane's Equations of Motions,” ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, USA (2005), pp. 2103–2110.Google Scholar
13. Banerjee, A. K., “Comment on relationship between Kane's equations and Gibbs-Appell equations,” J. Guid. Control Dyn. 10 (6), 596–597 (1987).CrossRefGoogle Scholar
14. Gillespie, R. B., “Kane's equations for haptic display of multibody systems,” Haptics-e, Ann Arbor, MI, USA (2003), vol. 3, no. 2, pp. 1–20.Google Scholar
15. Mitiguy, P. C. and Kane, T. R., “Motion variables leading to efficient equations of motion,” Int. J. Rob. Res. 15 (5), 522–532 (1996).Google Scholar
16. Bajodah, A. H., Hodges, D. H. and Chen, Y. H., “Nonminimal Kane's equations of motion for multibody dynamical systems subject to nonlinear nonholonomic constraints,” Multibody Syst. Dyn. 14, 155–187 (2005).CrossRefGoogle Scholar
17. Bajodah, A. H., Hodges, D. H. and Chen, Y. H., “Nonminimal generalized Kane's impulse-momentum relations,” J. Guid. Control Dyn. 27 (6), 1088–1092 (2004).Google Scholar
18. Bajodah, A. H., Hodges, D. H. and Chen, Y. H., “New form of Kane's equations of motion for constrained systems,” J. Guid. Control Dyn. 26 (1), 79–88 (2003).CrossRefGoogle Scholar
19. Roithmayr, C. M., Bajodah, A. H., Hodges, D. H. and Chen, Y. H., “Corrigendum: New form of Kane's equations of motion for constrained systems,” J. Guid. Control Dyn. 30 (1), 286–288 (2007).Google Scholar
20. Roithmayr, C. M. and Hodges, D. H., “Forces associated with non-linear non-holonomic constraint equations,” Int. J. Nonlin. Mech. 45, 357–369 (2010).Google Scholar
21. Lesser, M., “A geometrical interpretation of Kane's equations,” Proc. R. Soc. A-Math Phys. 436 (1896), 69–87 (1992).Google Scholar
22. Hu, Q., Jia, Y. and Xu, S., “A new computer-oriented approach with efficient variables for multibody dynamics with motion constraints,” Acta Astronaut. 81, 380–389 (2012).Google Scholar
23. Tarn, T. J., Shoults, G. A. and Yang, S. P., “A dynamic model of an underwater vehicle with a robotic manipulator using Kane's method,” Auton. Robot. 3, 269–283 (1996).Google Scholar
24. Liu, W. F., Gong, Z. B. and Wang, Q. Q., “Investigation on Kane dynamic equations based on screw theory for open-chain manipulators,” Appl. Math. Mech. 26 (5), 627–635 (2005).Google Scholar
25. Tanner, H. G. and Kyriakopoulos, K. J., “Mobile manipulator modeling with Kane's approach,” Robotica, 19, 675–690 (2001).Google Scholar
26. Nukulwuthiopas, W., Maneewan, T. and Laowattana, S., “Dynamic Modeling of a One-wheel Robot by using Kane's Method,” Industrial Technology, 2002. IEEE ICIT'02, 2002 IEEE International Conference on (2002), vol. 1, pp. 524–529.Google Scholar
27. Meghdari, A., Karimi, R., Pishkenari, H. N., Gaskarimahalle, A. L. and Mahboobi, S. H., “An effective approach for dynamic analysis of rovers,” Robotica, 23, 771–780 (2005).Google Scholar
28. Tavakoli Nia, H., Pishkenari, H. N. and Meghdari, A., “A recursive approach for the analysis of snake robots using Kane's equations,” Robotica, 24 (2), 251–256 (2006).Google Scholar