This paper presents a finite element approach of multibody systems using the special Euclidean group SE(3) 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.

References

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
.10.1115/1.1590354
4.
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/DETC2011-48132
5.
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.2011.07.017
6.
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
.10.1115/1.4001370
7.
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)00286-3
11.
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.2005.852253
13.
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.2013.10.008
You do not currently have access to this content.