scholarly journals n Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part Two: Multibody Systems

2012 ◽  
Vol 33 (2) ◽  
pp. 61-68 ◽  
Author(s):  
Pål Johan From
Keyword(s):  
Multibody Systems ◽  
Mechanical Systems ◽  
Dynamic Equations ◽  
Explicit Formulation ◽  
Form Part ◽  
Lagrangian Form ◽  
Free Dynamic

A Comparative Study on Some Different Formulations of the Dynamic Equations of Constrained Mechanical Systems

1987 ◽  
Vol 109 (4) ◽  
pp. 466-474 ◽  
Author(s):  
J. Unda ◽  
J. Garci´a de Jalo´n ◽  
F. Losantos ◽  
R. Enparantza
Keyword(s):  
Comparative Study ◽  
Relative Efficiency ◽  
Multibody Systems ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Dynamic Equations ◽  
Natural Coordinates ◽  
Constrained Mechanical Systems ◽  
Computer Codes

This paper presents a comparative theoretical and numerical study on the efficiency of several numerical methods for the dynamic analysis of constrained mechanical systems, also called in the literature multibody systems. This comparative study has been performed between methods based on the use of “reference point” coordinates and those based on the use of “natural” coordinates. This study embraces different possibilities to formulate the differential equations of motion. The relative efficiency of the resulting algorithms has been analyzed theoretically in terms of the number of multiplications needed to evaluate the mechanism accelerations. This efficiency has also been studied implementing the methods into computer codes and testing them with different examples. Conclusions on the relative efficiency of the methods are finally presented.

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

Cayley kinematics and the Cayley form of dynamic equations

2005 ◽  
Vol 461 (2055) ◽  
pp. 761-781 ◽  
Author(s):  
Andrew J. Sinclair ◽  
John E. Hurtado
Keyword(s):  
Euler Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Matrix Form ◽  
Dynamic Equations ◽  
Cayley Transform ◽  
Higher Dimensional ◽  
The Matrix ◽  
General Motion

The Cayley transform and the Cayley–transform kinematic relationships are an important and fascinating set of results that have relevance in N –dimensional orientations and rotations. In this paper these results are used in two significant ways. First, they are used in a new derivation of the matrix form of the generalized Euler equations of motion for N –dimensional rigid bodies. Second, they are used to intimately relate the motion of general mechanical systems to the motion of higher–dimensional rigid bodies. This approach can be used to describe an enormous variety of systems, one example being the representation of general motion of an N –dimensional body as pure rotations of an ( N + 1)–dimensional body.

Dynamic Equilibrium Configurations of Multibody Systems

2014 ◽  
Vol 619 ◽  
pp. 8-12
Author(s):  
Ju Seok Kang
Keyword(s):  
Iteration Method ◽  
Multibody Systems ◽  
Equilibrium Configuration ◽  
Dynamic Equilibrium ◽  
Mechanical Systems ◽  
Railway Vehicle ◽  
Algebraic Form ◽  
Constrained Mechanical Systems ◽  
Speed Governor ◽  
Equilibrium Configurations

It is difficult to calculate dynamic equilibrium configuration in the mechanical systems, especially with the constraint conditions. In this paper, a method to calculate the dynamic equilibrium positions in the constrained mechanical systems is proposed. The accelerations of independent coordinates are derived in the algebraic form so that the numerical solution is easily obtained by the iteration method. The proposed method has been applied to calculate the dynamic equilibrium configuration for speed governor and the wheelset of railway vehicle.

Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
József Kövecses
Keyword(s):  
Configuration Space ◽  
Dynamic Equilibrium ◽  
Mechanical Systems ◽  
Constrained Systems ◽  
Dynamic Equations ◽  
Analytical Mechanics ◽  
Constrained Motion ◽  
Equilibrium Equations ◽  
Free Body Diagram ◽  
Free Body

In this paper, we generalize the idea of the free-body diagram for analytical mechanics for representations of mechanical systems in configuration space. The configuration space is characterized locally by an Euclidean tangent space. A key element in this work relies on the relaxation of constraint conditions. A new set of steps is proposed to treat constrained systems. According to this, the analysis should be broken down to two levels: (1) the specification of a transformation via the relaxation of the constraints; this defines a subspace, the space of constrained motion; and (2) specification of conditions on the motion in the space of constrained motion. The formulation and analysis associated with the first step can be seen as the generalization of the idea of the free-body diagram. This formulation is worked out in detail in this paper. The complement of the space of constrained motion is the space of admissible motion. The parametrization of this second subspace is generally the task of the analyst. If the two subspaces are orthogonal then useful decoupling can be achieved in the dynamics formulation. Conditions are developed for this orthogonality. Based on this, the dynamic equations are developed for constrained and admissible motions. These are the dynamic equilibrium equations associated with the generalized free-body diagram. They are valid for a broad range of constrained systems, which can include, for example, bilaterally constrained systems, redundantly constrained systems, unilaterally constrained systems, and nonideal constraint realization.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Discrete Adjoint Method for the Sensitivity Analysis of Flexible Multibody Systems

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Alfonso Callejo ◽  
Valentin Sonneville ◽  
Olivier A. Bauchau
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Adjoint Method ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Flexible Multibody Systems ◽  
Design Parameters ◽  
Integration Scheme ◽  
Discrete Version ◽  
Flexible Multibody

The gradient-based design optimization of mechanical systems requires robust and efficient sensitivity analysis tools. The adjoint method is regarded as the most efficient semi-analytical method to evaluate sensitivity derivatives for problems involving numerous design parameters and relatively few objective functions. This paper presents a discrete version of the adjoint method based on the generalized-alpha time integration scheme, which is applied to the dynamic simulation of flexible multibody systems. Rather than using an ad hoc backward integration solver, the proposed approach leads to a straightforward algebraic procedure that provides design sensitivities evaluated to machine accuracy. The approach is based on an intrinsic representation of motion that does not require a global parameterization of rotation. Design parameters associated with rigid bodies, kinematic joints, and beam sectional properties are considered. Rigid and flexible mechanical systems are investigated to validate the proposed approach and demonstrate its accuracy, efficiency, and robustness.

Sign in / Sign up

Export Citation Format

Share Document