Energy-Momentum Integrators for Elastic Cosserat Points, Rigid Bodies, and Multibody Systems

2016 ◽  
pp. 31-89 ◽  
Author(s):  
Peter Betsch
Keyword(s):  
Multibody Systems ◽  
Rigid Bodies

Numerical Simulation of Multibody Systems With Time Dependant Structure

1993 ◽  
Author(s):  
Pierre Joli ◽  
Madeleine Pascal ◽  
René Gibert
Keyword(s):  
Numerical Simulation ◽  
Multibody Systems ◽  
Computational Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Integration Step ◽  
General Systems ◽  
Articulated Systems ◽  
Jump Velocity ◽  
Assembly Tasks

Abstract Current dynamic simulation programs are able to calculate the continuous motions of articulated systems or more general systems of rigid bodies in the absence of contact between members of the system or between the system and its environment. Some are able to simulate the effects of isolated contacts and impacts but none are able to simulate the motion with unrestricted multiple concurrent contacts. However, in special robotic programs such as robots performing assembly tasks or walking, it would be very interesting to simulate appropriate commands before implementing them on the robots. This paper develops intrinsic problems of collision to produce an efficient computational algorithm. This algorithm handles the detection of collision in three dimensions, the reduction of the integration step in order to avoid interpenetration between the bodies before impact, the jump velocity caused by a new collision and indicator magnitudes which determine the addition or deletion of constraints.

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.

A Software Tool for WWW-Based Learning of Multibody Kinematics

2000 ◽  
Author(s):  
Carlo Galletti ◽  
Elena Giannotti
Keyword(s):  
Kinematic Analysis ◽  
Multibody Systems ◽  
Multibody System ◽  
Object Oriented ◽  
Software Tool ◽  
Rigid Bodies ◽  
Closed Form Solutions ◽  
Object Oriented Approach ◽  
Maple Code ◽  
Oriented Approach

Abstract In this work we present a new software tool for helping students perform basic kinematic analysis using Internet. It allows students to model and analyze planar multibody systems with rigid bodies. Master objects that contain data and algorithms for modeling and analyzing rigid bodies and lower kinematic pairs have been developed following an object-oriented approach. The layouts of the objects are discussed and the way of instancing them for defining a model of a multibody system is described. The student can analyze interactively the model created in this way, using the software tool itself, or he can export it to the MAPLE code. From MAPLE the student can obtain, in an automatic way, numerical or closed-form solutions of the kinematic equations.

Generalized Vector-Network Formulation for the Dynamic Simulation of Multibody Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 322-329 ◽  
Author(s):  
M. J. Richard ◽  
R. Anderson ◽  
G. C. Andrews
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
New Approach ◽  
System Description ◽  
Nonlinear Equations Of Motion ◽  
Systematic Formulation ◽  
Multi Body ◽  
Entire Procedure

This paper describes the vector-network approach which is a comprehensive mathematical model for the systematic formulation of the nonlinear equations of motion of dynamic three-dimensional constrained multi-body systems. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics have been combined. The main concepts of the method have been explained in previous publications but the work described herein is an appreciable extension of this relatively new approach. The method casts simultaneously the three-dimensional inertia equations associated with each rigid body and the geometrical expressions corresponding to the kinematic restrictions into a symmetrical format yielding the differential equations governing the motion of the system. The algorithm is eminently well suited for the computer-aided simulation of arbitrary interconnected rigid bodies; it serves as the basis for a “self-formulating” computer program which can simulate the response of a dynamic system, given only the system description.

Singularly Perturbed Bond Graph Models for Simulation of Multibody Systems

1995 ◽  
Vol 117 (3) ◽  
pp. 401-410 ◽  
Author(s):  
A. A. Zeid ◽  
J. L. Overholt
Keyword(s):  
Time Scale ◽  
Multibody Systems ◽  
Graph Model ◽  
Bond Graph ◽  
Rigid Bodies ◽  
Singularly Perturbed ◽  
Bond Graphs ◽  
Graph Models ◽  
Multibody Modeling ◽  
Nonlinear Properties

This paper develops a bond graph-based formalism for modeling multibody systems in a singularly perturbed formulation. As opposed to classical multibody modeling methods, the singularly perturbed formulation is explicit, which makes it suitable for modular simulation. Kinematic joints that couple rigid bodies are described by a set of differential equations with an order of magnitude smaller time scale than that of the system. Singularly perturbed models of joints can be used to investigate nonlinear properties of joints, such as clearance and friction. The main restriction of this approach is that the simulation may need to be computed using 64 bits precision because of the two-time scale nature of the solution. The formalism is based on developing bond graph models of an elementary set of graphical velocity-based constraint functions. This set can be used to construct bond graphs of any type of mechanical joint. Here, this set is used to develop bond graphs of several joints used in multibody systems and spatial mechanisms. Complex models of multibody systems may now be built by graphically concatenating bond graphs of rigid bodies and bond graphs of joints. The dynamic equations of the system are automatically generated from the resulting bond graph model. The dynamic equation derived from the bond graph are in explicit state space form, ready for numerical integration, and exclude the computationally intensive terms that arise from acceleration analysis.

Optimal Damping of Vibrations in Multibody Systems Through Equivalent Friction Control Laws

1995 ◽  
Author(s):  
Nikolay V. Dakev ◽  
Andrew J. Chipperfield ◽  
Peter J. Fleming
Keyword(s):  
Vibration Control ◽  
Multibody Systems ◽  
Rigid Bodies ◽  
Control Problems ◽  
Reference Trajectory ◽  
Unified Framework ◽  
Control Laws ◽  
Friction Laws ◽  
Search Mechanism ◽  
Modelling And Optimization

Abstract In the paper modelling and optimization of friction laws and energy exchange processes in multibody systems are considered. The multibody systems are regarded as chains of absolutely rigid bodies with compliance and friction concentrated at the connections. It is proposed to control the vibration level of such systems by introducing equivalent frictional forces. Such an approach enables modelling and optimization of passive and semi-active damping methods together with active control of vibrations in multibody systems within a unified framework. In particular, the equivalent friction laws can be regarded as controls minimizing deviations of the multibody system motion from the reference trajectory and used for total compensation of links cross interactions and stabilization of fast modes. The corresponding optimal vibration control problem is formulated and reduced to a constrained optimization one in order to determine the optimal friction laws dissipating the oscillation energy. For linear vibration control problems numerical methods based on solving matrix Lyapunov and Riccati equations are discussed. Additionally, an approach employing a global search mechanism, the genetic algorithm, and parallel processing techniques, to alleviate the problem of computational burden, is proposed to solve general control problems for optimal vibration damping. Two examples are presented in order to illustrate the proposed approach.

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