scholarly journals Special Coordinates Associated With Recursive Forward Dynamics Algorithm for Open Loop Rigid Multibody Systems

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
Ashitava Ghosal
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Equations Of Motion ◽  
Special Property ◽  
Open Loop ◽  
Forward Dynamics ◽  
Rigid Multibody Systems ◽  
Two Stages ◽  
Rigid Multibody ◽  
General Tree

The recursive forward dynamics algorithm (RFDA) for a tree structured rigid multibody system has two stages. In the first stage, while going down the tree, certain equations are associated with each node. These equations are decoupled from the equations related to the node’s descendants. We refer them as the equations of RFDA of the node and the current paper derives them in a new way. In the new derivation, associated with each node, we recursively obtain the coordinates, which describe the system consisting of the node and all its descendants. The special property of these coordinates is that a portion of the equations of motion with respect to these coordinates is actually the equations of RFDA associated with the node. We first show the derivation for a two noded system and then extend to a general tree structure. Two examples are used to illustrate the derivation. While the derivation conclusively shows that equations of RFDA are part of equations of motion, it most importantly gives the associated coordinates and the left out portion of the equations of motion. These are significant insights into the RFDA.

SYMBOLIC TREATMENT FOR THE EQUATIONS OF MOTION FOR RIGID MULTIBODY SYSTEMS

2010 ◽  
Vol 34 (1) ◽  
pp. 37-55 ◽  
Author(s):  
Bukoko C. Ikoki ◽  
Marc J. Richard ◽  
Mohamed Bouazara ◽  
Sélim Datoussaïd
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
The World ◽  
Rigid Multibody Systems ◽  
Symbolic Approach ◽  
Rigid Multibody

The library of symbolic C++ routines is broadly used throughout the world. In this article, we consider its application in the symbolic treatment of rigid multibody systems through a new software KINDA (KINematic & Dynamic Analysis). Besides the attraction which represents the symbolic approach and the effectiveness of this algorithm, the capacities of algebraical manipulations of symbolic routines are exploited to produce concise and legible differential equations of motion for reduced size mechanisms. These equations also constitute a powerful tool for the validation of symbolic generation algorithms other than by comparing results provided by numerical methods. The appeal in the software KINDA resides in the capability to generate the differential equations of motion from the choice of the multibody formalism adopted by the analyst.

General Formulation of an Efficient Recursive Algorithm Based on Canonical Momenta for Forward Dynamics of Closed-Loop Multibody Systems

2005 ◽  
Author(s):  
Joris Naudet ◽  
Dirk Lefeber
Keyword(s):  
Multibody Systems ◽  
Closed Loop ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Open Loop ◽  
Forward Dynamics ◽  
Virtual Power ◽  
Generalized Coordinates ◽  
First Order

In previous work, a method for establishing the equations of motion of open-loop multibody mechanisms was introduced. The proposed forward dynamics formulation resulted in a Hamiltonian set of 2n first order ODE’s in the generalized coordinates q and the canonical momenta p. These Hamiltonian equations were derived from a recursive Newton-Euler formulation. It was shown how an O(n) formulation could be obtained in the case of a serial structure with general joints. The amount of required arithmetical operations was considerably less than comparable acceleration based formulations. In this paper, a further step is taken: the method is extended to constrained multibody systems. Using the principle of virtual power, it is possible to obtain a recursive Hamiltonian formulation for closed-loop mechanisms as well, enabling the combination of the low amount of arithmetical operations and a better evolution of the constraints violation errors, when compared with acceleration based methods.

Vibration Calculation of Spatial Multibody Systems Based on Constraint-Topology Transformation

2011 ◽  
Vol 27 (4) ◽  
pp. 479-491 ◽  
Author(s):  
W. Jiang ◽  
X. D. Chen ◽  
X. Luo ◽  
Y. T. Hu ◽  
H. P. Hu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Open Loop ◽  
Rigid Bodies ◽  
Constraint Matrix ◽  
Rigid Multibody Systems ◽  
Nonlinear Equations Of Motion ◽  
Traditional Approaches ◽  
Loop Constraint

ABSTRACTMany kinds of mechanical systems can be modeled as spatial rigid multibody systems (SR-MBS), which consist of a set of rigid bodies interconnected by joints, springs and dampers. Vibration calculation of SR-MBS is conventionally conducted by approximately linearizing the nonlinear equations of motion and constraint, which is very complicated and inconvenient for sensitivity analysis. A new algorithm based on constraint-topology transformation is presented to derive the oscillatory differential equations in three steps, that is, vibration equations for free SR-MBS are derived using Lagrangian method at first; then, an open-loop constraint matrix is derived to obtain the vibration equations for open-loop SR-MBS via quadric transformation; finally, a cut-joint constraint matrix is derived to obtain the vibration equations for closed-loop SR-MBS via quadric transformation. Through mentioned above, the vibration calculation can be significantly simplified and the sensitivity analysis can be conducted conveniently. The correctness of the proposed method has been verified by numerical experiments in comparison with the traditional approaches.

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