Kinematic model of a multi-beam structure undergoing large elastic displacements and rotations.: Part one: Model of an isolated beam

Mechanism and Machine Theory

Volumn 34, Issue 2, 1999, Pages 205-222

  Boyer, Frederic ^a   Khalil, Wisama ^b  

^a ECOLE DES MINES DE NANTES   (France)

^b ECOLE CENTRALE DE NANTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMS AND GIRDERS; COMPUTER SIMULATION; DEFORMATION; ELASTICITY; KINEMATICS; STRUCTURAL ANALYSIS;

MULTIBODY SYSTEMS;

FLEXIBLE STRUCTURES;

EID: 0033078013     PISSN: 0094114X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0094-114X(98)00022-6     Document Type: Article

References (33)

1. Damaren C., Sharf I. Simulation of flexible-link manipulators with inertial and geometric nonlinearities. J. Dynamic Systems, Measurement Control. 117:1995;74-87.
2. R.A. Wehage, A.A. Shabana, Application of generalized Newton-Euler equations and recursive projections methods to dynamics of deformable multibody systems, In: Proc. ASME Design, Technical Conferences-15th, Vol. 19, 3, Design Automation Conference, Montreal, 1989, pp. 17-25.
3. I. Sharf, G.M.T. Deleuterio, Computer simulation of elastic chains using recursive formulation, In: IEEE International Conf. on Robotics and Automation, 1988, pp. 1539-1545.
4. Kim S.S., Haug E.J. A recursive formulation for flexible multibody dynamics, Part 1: open loop systems. J. Comput. Meth. Appl. Mech. Engng. Vol. 71:1988;293-314.
5. M.A. Serna, E. Bayo, A modified Lagrangian formulation for elastic robots, In: Proc. 2nd Int. Symposium on Robotics and Manufacturing: Research, Education and Applications, New Mexico, 1987, pp. 513-520.
6. Kane T.R., Ryan R.R., Banerjee A.K. Dynamics of a cantilever beam attached to a moving base. J. Guidance Control Dynamics. 10:(2):1987;139-151.
7. Padilla C.E., Von Flotow A.H. Nonlinear strain displacement relations and flexible multibody dynamics. J. Guidance, Control Dynamics. 15:(1):1992;128-136.
8. Vu-Quoc L., Simo J.C. Dynamics of earth-orbiting flexible satellites with multibody components. J. Guidance. 16:(6):1987;549-558.
9. Cardona A., Géradin M. A beam finite-element nonlinear theory with finite rotations. International J. Numer. Meth. Engng. 26:1988;2406-2438.
10. Kane T.R., Levinson D.A. Formulation of equations of motion for complex spacecraft. J. Guidance, Control Dynamics. 3:1980;99-112.
11. Meirovitch L. Hybrid state equations of motion for flexible bodies in terms of quasi-coordinates. J. Guidance, Control Dynamics. 14:(5):1991;1008-1013.
12. Sincarsin G.B., Hughes P.C. Dynamics of elastic multibody chains: Part A - Body motion equations. J. Dynamic Stability Systems. 4:(34):1990;209-226.
13. Shabana A.A. Dynamics of flexible bodies using generalized Newton-Euler equations. J. Dynamic Systems, Measurement Control. 112:1990;496-503.
14. Boyer F., Coiffet P. Generalization of Newton-Euler model for flexible manipulators. J. Robotic Systems. 13:(1):1996;11-24.
15. I. Sharf, Damaren C, Simulation of flexible-link manipulators: basis functions and nonlinear terms in the motions equations, in: in: Proc. 1992 IEEE Conference on Robotics and Automation, Nice, France, 1992, pp. 1956-1962.
16. M. Geradin, D. Rixen, Théorie des vibrations, application á la dynamique des structures. ed. Masson, Paris, 1993.
17. Shabana A.A. Constrained motion of deformable bodies. International Journal for Numer. Meth. Engng. 32:1991;1813-1831.
18. S.P. Timoshenko, Strength of materials, 3rd ed., Vol. 2, Van Nostrand, Princeton, NJ, 1955.
19. L.E. Malvern, Introduction to the mechanics of a continuous medium. Prentice-Hall, NY, 1969.
20. Vigneron F.R. Comment on Mathematical modeling of spinning elastic bodies for modal analysis. AIAA J. 13:1975;126-127.
21. Kaza K.R., Kwaternik R.G. Nonlinear flap-lag-axial equations of a rotating beam. Acta Astronautica. 7:1977;1349-1360.
22. Sharf I. Geometric stiffening in multibody dynamics formulations. J. Guidance, Control Dynamics. 18:(4):1995.
23. Simo J.C., Vu-Quoc L. A three dimensional finite-strain rod model, Part 2: computational aspects. J. Comput. Meth. Appl. Mech. Engng. 58:1986;79-116.
24. F. Germain, Contribution á la simulation du comportement mécanique des matériaux en grandes transformations, en statique et dynamique, Etude d'une nouvelle formulation poutre, Université de Bretagne Sud, 1996.
25. Book W.J. Recursive Lagrangian Dynamics of flexible manipulators arms. Int. Journal of Robotic Research. 3:1984;87-101.
26. Lin L.C., Yuan K. A Lagrange-Euler assumed modes approach to modeling flexible manipulators. Journal of the Chinese Institute of Engineers. 11:(4):1988;335-347.
27. R.P. Singh, R.J. Vander Voort, P.W. Likins, Dynamics of flexible bodies in tree topology: a computer oriented approach, In: Proc. AIAA Dyn. Specialist Conf., Palm Springs, California, 1984, pp. 327-337.
28. Naganathan G., Soni A.H. Nonlinear modeling of kinematics and flexibility effects in manipulators design. ASME J. Mech. Transmissions, Automation Design. 110:1988;243-254.
29. Piedbeuf J.C. The Jacobian matrix for a flexible manipulators. J. Robotic Systems. 12:(11):1995;709-726.
30. Hodges D.H. Nonlinear beam kinematics for small strains and finite rotations. Vertica. 11:(3):1987;573-589.
31. J.E. Lagnese, G. Leugering, E.J.P.G. Schmidt, Modeling, Analysis and Control of Dynamic Elastic Multi-link Structures. Birkhaüser, Boston, 1994.
32. J. Angeles, Rational Kinematics, in: Springer Tracts in Natural Philosophy, Vol. 34, Springer-Verlag, NY, 1988.
33. R.C.P. Paul, Robot manipulators: mathematics, programming and control. MIT Press, Cambridge, MA, 1981.