Developing a Numerical Simulation Software for 3D Multibody Systems Based on a Unified Computational Modeling Technique

2009 ◽  
Author(s):  
Shahram Shokouhfar ◽  
Sayyid Mahdi Khorsandijou
Keyword(s):  
Numerical Simulation ◽  
Multibody Systems ◽  
Dynamic Models ◽  
Initial Conditions ◽  
Rigid Bodies ◽  
Simulation Software ◽  
Computational Technique ◽  
Main Task ◽  
Algebraic Equations ◽  
Time Step

This article represents the features and capabilities of a newly developed application namely MASS (Mechanisms Analysis and Simulation Software) and the formulation and techniques therein. MASS is a general C++ application program whose main task is to construct and solve the governing algebraic differential motion equations of 3D multibody systems automatically in matrix forms complying with the computational algorithms required for numerical simulation. Newton-Raphson and SVD methods have been used for kinematical assembling and producing consistent initial conditions. Adaptive time-step Runge-Kutta-Fehlberg numerical integration methods might be used for forward dynamics problems. The governing equations perfectly describe the kinematics and dynamics of multibody systems within which 3D kinematical joints and collisions between rigid bodies might be taken into consideration. The unified computational technique for mathematical modeling of kinematical joints is the most important concept on top of which MASS has been implemented. It has occurred due to the existence of thirteen basic kinematical constraint equations. Each kinematical joint might be defined by a set of algebraic equations being selected from the mentioned basic equations. The unified dynamic models for collisions and impulsive loads have been also achieved using the mentioned technique. Simulation results obtained from MASS have been compared with that of the corresponding software of Working Model ver. 6 and a discussion about the coincidences and differences has been exposed.

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.

A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Paulo Flores ◽  
Margarida Machado ◽  
Eurico Seabra ◽  
Miguel Tavares da Silva
Keyword(s):  
Parametric Study ◽  
Multibody Systems ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Forward Dynamics ◽  
Stabilization Method ◽  
Time Step ◽  
Constrained Multibody Systems ◽  
Laplace Transform Technique ◽  
Baumgarte Stabilization

This paper presents and discusses the results obtained from a parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. The main purpose of this work is to analyze the influence of the variables that affect the violation of constraints, chiefly the values of the Baumgarte parameters, the integration method, the time step, and the quality of the initial conditions for the positions. In the sequel of this process, the formulation of the rigid multibody systems is reviewed. The generalized Cartesian coordinates are selected as the variables to describe the bodies’ degrees of freedom. The formulation of the equations of motion uses the Newton–Euler approach, augmented with the constraint equations that lead to a set of differential algebraic equations. Furthermore, the main issues related to the stabilization of the violation of constraints based on the Baumgarte approach are revised. Special attention is also given to some techniques that help in the selection process of the values of the Baumgarte parameters, namely, those based on the Taylor’s series and the Laplace transform technique. Finally, a slider-crank mechanism with eccentricity is considered as an example of application in order to illustrate how the violation of constraints can be affected by different factors.

scholarly journals 2D TESTING OF A FINITE DIFFERENCE SCHEME FOR MODELLING OF A VISCOUS DIFFUSION PROCESS IN COMPRESSIBLE GAS

2020 ◽  
Vol 22 (5) ◽  
pp. 128-131
Author(s):  
V.V. Nikonov ◽  
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Initial Conditions ◽  
Stokes Problem ◽  
Velocity Fields ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Time Step ◽  
Acceptable Accuracy ◽  
Compressible Gas

Viscous subproblem of direct numerical simulation of compressible gas is solved. This subproblem is tested on the two-dimensional problem of impulse start of a flat plate (Stokes’ problem). Three calculations were made with the different initial conditions and velocity fields were obtained. The numerical results are compared with the solution of Stokes’ problem. Analyzing the results, we can conclude that in order to achieve acceptable accuracy, it suffices to choose a time step according to the rule that the author formulated in his earlier works.

Modular Modeling Using Lagrangian DAEs

2000 ◽  
Author(s):  
Robert Piché ◽  
Mikko Palmroth
Keyword(s):  
Software Design ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Simulation Software ◽  
Algebraic Equations ◽  
Feedback Control System ◽  
Physical Systems ◽  
Modular Modeling ◽  
Index Reduction ◽  
Analytical System

Abstract Layton’s Analytical System Dynamics theory for modeling multidisciplinary physical systems with Lagrangian differential algebraic equations (DAEs) is extended by introducing a technique for using hierarchical reusable modules. Connections between submodels are represented in a systematic manner using kinematic constraints and Lagrange multipliers. Simulation software design issues are discussed: data structures, consistent initial conditions, index reduction, and DAE solvers. An example of an electromechanical feedback control system is presented in detail.

Applicability of Attractor Control Techniques for a Particle Conveyed by a Propagating Wave

2004 ◽  
Vol 10 (7) ◽  
pp. 1057-1070 ◽  
Author(s):  
M. Ragulskis ◽  
K. Koizumi
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Time Integration ◽  
Algebraic Equations ◽  
Reverse Time ◽  
Time Step ◽  
Control Techniques ◽  
Potential Applicability ◽  
Nonlinear Features ◽  
Time Marching

The governing equations of motion describing the dynamics of a conveyed particle by a propagating surface wave are derived. Although the problem may look rather primitive, it holds considerable complications first of all due to the fact that the shape of the surface cannot be described explicitly Special forward and reverse time marching numerical techniques, incorporating the solution of nonlinear algebraic equations in every time step, are developed for time integration of derived differential equations. It is shown that the described system possesses numerous nonlinear features such as sensitivity to initial conditions. cocxistint, attractors. This fact builds the foundation for the potential applicability of attractor control techniques based on small external impulses.

Dynamic Simulation of Dielectric Elastomer Actuated Multibody Systems

2016 ◽  
Author(s):  
T. Schlögl ◽  
S. Leyendecker
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Multibody System ◽  
Humanoid Robots ◽  
Differential Algebraic Equations ◽  
Rigid Bodies ◽  
Integration Scheme ◽  
Artificial Muscles ◽  
Algebraic Equations ◽  
Energy Behavior

A three-dimensional electro-mechanically coupled finite element model for dielectric elastomers is used to actuate multibody systems. This setting allows exploring the complex behavior of humanoid robots that are driven by artificial muscles instead of electrical drives. The coupling between the finite element muscle model and the rigid bodies is formulated at configuration level, where Lagrange multipliers account for constraint forces, leading to differential algebraic equations of index-3. A well-chosen set of redundant configuration variables for the multibody system avoids any rotational degrees of freedom and leads to linear coupling constraints. As a result, the coupling between the artificial muscles and the multibody system can be formulated in a very modular way that allows for easy future extension. The applied structure preserving time integration scheme provides excellent long time energy behavior. In addition, the index-3 system is solved directly with numerical accuracy, avoiding index reduction approximations.

A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems

2009 ◽  
Author(s):  
Paulo Flores ◽  
Margarida Machado ◽  
Eurico Seabra ◽  
Miguel Tavares da Silva
Keyword(s):  
Parametric Study ◽  
Multibody Systems ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Forward Dynamics ◽  
Stabilization Method ◽  
Time Step ◽  
Constrained Multibody Systems ◽  
Laplace Transform Technique ◽  
Baumgarte Stabilization

This paper presents and discusses the results obtained from a parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. The main purpose of this work is to analyze the influence of the variables that affect the violation of constraints, chiefly the values of the Baumgarte parameters, the integration method, the time step and the quality of the initial conditions for the positions. In the sequel of this process the formulation of the rigid multibody systems is reviewed. The generalized Cartesian coordinates are selected as the variables to describe the bodies’ degrees of freedom. The formulation of the equations of motion uses the Newton-Euler approach that is augmented with the constraint equations that lead to a set of differential algebraic equations. Furthermore, the main issues related to the stabilization of the violation of constraints based on the Baumgarte approach are revised. Special attention is also given to some techniques that help in the selection process of the values of the Baumgarte parameters, namely those based on the Taylor’s series and Laplace transform technique. Finally, a slider crank mechanism with eccentricity is considered as an example of application in order to illustrated how the violation of constraints can be affected by different factors such as the Baumgarte parameters, integrator, time step and initial guesses.

Dynamics of Multibody Systems With Known Configuration Changes

1991 ◽  
Vol 58 (1) ◽  
pp. 215-221 ◽  
Author(s):  
J. J. McPhee ◽  
R. N. Dubey
Keyword(s):  
Numerical Simulation ◽  
Computer Program ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Rotation Vector ◽  
Dynamic Effects ◽  
Physical Systems ◽  
Dynamics Of Multibody Systems ◽  
Configuration Changes

The equations of motion are derived for a system with inertial properties that are varying in time as a result of known relative motions between the rigid bodies comprising the system. This vector-dyadic formulation has been encoded into a computer program, making use of the conformal rotation vector for the representation of rotations. The numerical simulation of two different physical systems is presented in order to illustrate the dynamic effects of the changing inertial properties, and the usefulness of the encoded formulation for modeling these effects.

Explicit Time Integration of Multibody Systems Modelled With Three Rotation Parameters

2020 ◽  
Author(s):  
Stefan Holzinger ◽  
Johannes Gerstmayr
Keyword(s):  
Lie Group ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Vector ◽  
Body Motion ◽  
Euler Parameters ◽  
Time Step ◽  
Rotation Parameters

Abstract Rigid bodies are an essential part of multibody systems. As there are six degrees of freedom in rigid bodies, it is natural but also precarious to use three parameters for the displacement and three parameters for the rotation parameters — since there is no singularity-free description of spatial rotations based on three rotation parameters. Standard formulations based on three rotation parameters avoid singularities, e.g. by applying reparameterization strategies during the time integration of the rotational kinematic equations. Alternatively, Euler parameters are commonly used to avoid singularities. State of the art approaches use Lie group methods, specifically integrators, to model rigid body motion without the need for the above mentioned solutions. However, the methods so far have been based on additional information, e.g., the rotation matrix, which has to been computed in each step. The latter procedure is thus difficult to be implemented in existing codes that are based on three rotation parameters. In this paper, we use the rotation vector to model large rotations. Whereby Lie group integration methods are used to compute consistent updates for the rotation vector in every time step. The resulting rotation vector update is finite, while the derivative of the rotation vector in the singularity becomes unbounded. The advantages of this method are shown in an example of a gyro. Additionally, the method is applied to a multibody system and the effects of crossing singularities are presented.

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