This paper presents a finite element approach of multibody systems using the special Euclidean group framework. The development leads to a compact and unified mixed coordinate formulation of the rigid bodies and the kinematic joints. Flexibility in the kinematic joints is also easily introduced. The method relies on local description of motions, so that it provides a singularity-free formulation and exhibits important advantages regarding numerical implementation. A practical case is presented to illustrate the method.
Issue Section:
Research Papers
References
1.
Géradin
, M.
and Cardona
, A.
, 2001
, Flexible Multibody Dynamics: A Finite Element Approach
, John Wiley and Sons
, Chichester
, UK.2.
Bauchau
, O. A.
, 2011
, Flexible Multibody Dynamics
(Solid Mechanics and Its Applications), Vol. 176
, Springer
, New York
.3.
Wasfy
, T.
and Noor
, A.
, 2003
, “Computational Strategies for Flexible Multibody Systems
,” Appl. Mech. Rev.
, 56
(6
), pp. 553
–613
.10.1115/1.15903544.
Brüls
, O.
, Arnold
, M.
, and Cardona
, A.
, 2011
, “Two Lie Group Formulations for Dynamic Multibody Systems With Large Rotations
,” Proceedings of the IDETC/MSNDC Conference
, Washington, DC, August 28–31, 2011, ASME
, Paper No. DETC2011-48132, pp. 85–94.10.1115/DETC2011-481325.
Brüls
, O.
, Cardona
, A.
, and Arnold
, M.
, 2012
, “Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
,” Mech. Mach. Theory
, 48
, pp. 121
–137
.10.1016/j.mechmachtheory.2011.07.0176.
Brüls
, O.
and Cardona
, A.
, 2010
, “On the Use of Lie Group Time Integrators in Multibody Dynamics
,” ASME J. Comput. Nonlinear Dyn.
, 5
(3
), p. 031002
.10.1115/1.40013707.
Murray
, R. M.
, Li
, Z.
, and Sastry
, S. S.
, 1994
, A Mathematical Introduction to Robotic Manipulation
, CRC
, Boca Raton
, FL.8.
Selig
, J. M.
, 2005
, Geometric Fundamentals of Robotics
(Monographs in Computer Science), Springer
, New York
.9.
Borri
, M.
, Trainelli
, L.
, and Bottasso
, C.
, 2000
, “On Representations and Parameterizations of Motion
,” Multibody Syst. Dyn.
, 4
(2–3
), pp. 129
–193
.10.
Borri
, M.
, Bottasso
, C.
, and Trainelli
, L.
, 2001
, “Integration of Elastic Multibody Systems by Invariant Conserving/Dissipating Algorithms—Part I: Formulation
,” Comput. Methods Appl. Mech. Eng.
, 190
(29/30
), pp. 3669
–3699
.10.1016/S0045-7825(00)00286-311.
Sonneville
, V.
and Brüls
, O.
, 2012
, “Formulation of Kinematic Joints and Rigidity Constraints in Multibody Dynamics Using a Lie Group Approach
,” Proceedings of the 2nd Joint International Conference on Multibody System Dynamics (IMSD)
, Stuttgart, Germany, May, 2012. Available at: http://hdl.handle.net/2268/120012.12.
Park
, J.
and Chung
, W.
, 2005
, “Geometric Integration on Euclidean Group With Application to Articulated Multibody Systems
,” IEEE Trans. Rob.
, 21
(5
), pp. 850
–863
.10.1109/TRO.2005.85225313.
Haug
, E. J.
, 1989
, Computer Aided Kinematics and Dynamics of Mechanical Systems, Vol. 1: Basic Methods, Allyn and Bacon, Needham Heights, MA.14.
Sonneville
, V.
, Cardona
, A.
, and Brüls
, O.
, 2014
, “Geometrically Exact Beam Finite Element Formulated on the Special Euclidean Group SE(3)
,” Comput. Methods Appl. Mech. Eng.
, 268
, pp. 451
–474
.10.1016/j.cma.2013.10.008Copyright © 2014 by ASME
You do not currently have access to this content.
