Dynamics of Multibody Systems With Variable Kinematic Structure

1986 ◽  
Vol 108 (2) ◽  
pp. 167-175 ◽  
Author(s):  
Y. A. Khulief ◽  
A. A. Shabana
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Kinematic Structure ◽  
The Finite Element Method ◽  
Flexible Bodies ◽  
Generalized Coordinates ◽  
Structure Changes ◽  
Dynamics Of Multibody Systems ◽  
Analysis Scheme ◽  
Deformation Modes

The problem of predicting the dynamic behavior of a general multibody system subject to kinematic structure changes is addressed using a mixed set of Lagrangian coordinates. Changes in the kinematic structure may occur smoothly or accompanied by a change in the system momenta. The finite element method is employed to estimate the modal characteristics of flexible bodies. An automated pieced-interval computational scheme that accounts for the change in the dynamic characteristics due to the imposition of new sets of constraints on the boundaries of flexible components is developed. The resulting change in the deformation modes and the associated change in basis of the configuration space requires a new set of generalized coordinates for each subinterval of the analysis. A numerical example is used to demonstrate the analysis scheme developed in this paper.

Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 1—Dynamic Model

1990 ◽  
Vol 112 (2) ◽  
pp. 153-159 ◽  
Author(s):  
C. W. Chang ◽  
A. A. Shabana
Keyword(s):  
Configuration Space ◽  
Multibody Systems ◽  
Spatial Configuration ◽  
Deformable Body ◽  
Smooth Transition ◽  
Kinematic Structure ◽  
Analysis Scheme ◽  
Topology Changes ◽  
Deformation Modes ◽  
System Topology

In this paper a method for the spatial kinematic and dynamic analysis of deformable multibody systems that are subject to topology changes is presented. A pieced interval analysis scheme that accounts for the change in the spatial system topology due to the changes in the connectivity between bodies is developed. Deformable bodies in the system are discretized using the finite element method and accordingly a finite set of deformation modes is employed to characterize the system vibration. Even though there are infinitely many arrangements for deformable body axes, computational difficulties may be encountered due to the use of a limited number of deformation modes. Therefore, the deformable body references have to be carefully selected, and accordingly as the system topology changes, new bases for the configuration space have to be identified. In order to guarantee a smooth transition from one configuration space to another, a set of spatial interface conditions or compatibility conditions that are formulated using a set of nonlinear algebraic equations are developed and solved in this paper. The solution of these equations uniquely define the spatial configuration of the deformable multibody system after the change in the system kinematic structure.

Kinematics Analysis of Mechanisms Based on Dynamics Multibody Systems in Virtual Assembly Environment

2010 ◽  
Vol 102-104 ◽  
pp. 214-218
Author(s):  
Zhi Xian Zhang ◽  
Jian Hua Liu ◽  
Ru Xin Ning
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Virtual Assembly ◽  
Assembly System ◽  
Prototype System ◽  
Motion Simulation ◽  
Kinematics Analysis ◽  
Simulation Process ◽  
Dynamics Of Multibody Systems ◽  
Kinematics Parameters

In recent years, in view of the absence of kinematics analysis function of mechanisms in the virtual assembly system, the method of kinematics analysis of mechanisms based on dynamics of multibody systems in virtual assembly environment is presented. A mechanism is considered as a multibody system and the kinematics equations are established based on Descartes coordinate system. All the kinematics parameters, just like position, speed and acceleration, can be obtained through solving the kinematics equations. In addition, the realization method of mechanism motion simulation in virtual assembly system is also proposed which contains the hiberarchy, data structure, module classes and simulation process of the system. The method is implemented and validated based on the prototype system VAPP(Virtual Assembly Process Planning).

Globally Independent Coordinates for Real-Time Vehicle Simulation

1998 ◽  
Vol 122 (4) ◽  
pp. 575-582 ◽  
Author(s):  
Radu Serban ◽  
Edward J. Haug
Keyword(s):  
State Space ◽  
Real Time ◽  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Vehicle Simulation ◽  
Generalized Coordinates ◽  
Dynamics Of Multibody Systems ◽  
Improved Performance ◽  
Control Forces

Models of the dynamics of multibody systems generally result in a set of differential-algebraic equations (DAE). State-space methods for solving the DAE of motion are based on reduction of the DAE to ordinary differential equations (ODE), by means of local parameterizations of the constraint manifold that must be often modified during a simulation. In this paper it is shown that, for vehicle multibody systems, generalized coordinates that are dual to suspension and/or control forces in the model are independent for the entire range of motion of the system. Therefore, these additional coordinates, together with Cartesian coordinates describing the position and orientation of the chassis, form a set of globally independent coordinates. In addition to the immediate advantage of avoiding the computationally expensive redefinition of local parameterization in a state-space formulation, the existence of globally independent coordinates leads to efficient algorithms for recovery of dependent generalized coordinates. A topology based approach to identify efficient computational sequences is presented. Numerical examples with realistic vehicle handling models demonstrate the improved performance of the proposed approach, relative to the conventional Cartesian coordinate formulation, yielding real-time for vehicle simulation. [S1050-0472(00)00404-9]

Aspects of Symbolic Formulations in Flexible Multibody Systems

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Markus Burkhardt ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Fem Model ◽  
Local Shape ◽  
Flexible Bodies ◽  
Elastic Bodies ◽  
Flexible Multibody

The symbolic modeling of flexible multibody systems is a challenging task. This is especially the case for complex-shaped elastic bodies, which are described by a numerical model, e.g., an FEM model. The kinematic and dynamic properties of the flexible body are in this case numerical and the elastic deformations are described with a certain number of local shape functions, which results in a large amount of data that have to be handled. Both attributes do not suggest the usage of symbolic tools to model a flexible multibody system. Nevertheless, there are several symbolic multibody codes that can treat flexible multibody systems in a very efficient way. In this paper, we present some of the modifications of the symbolic research code Neweul-M2 which are needed to support flexible bodies. On the basis of these modifications, the mentioned restrictions due to the numerical flexible bodies can be eliminated. Furthermore, it is possible to re-establish the symbolic character of the created equations of motion even in the presence of these solely numerical flexible bodies.

A Recursive Algorithm for Solving the Generalized Velocities From the Momenta of Flexible Multibody Systems

2008 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Numerical Solution ◽  
Multibody Systems ◽  
Multibody System ◽  
Recursive Algorithm ◽  
Mass Matrix ◽  
Direct Methods ◽  
Flexible Multibody Systems ◽  
Hamiltonian Form ◽  
Generalized Coordinates ◽  
Flexible Multibody

The computation of the generalized velocities from the generalized momenta of a multibody system is a part of the numerical solution of the dynamics equations when they are given in the Hamiltonian form. The states of these equations are the generalized coordinates and momenta, (q, p). The generalized velocity, q˙, is defined by q˙ = J−1p, where J is the system mass matrix. The effort in solving q˙ by direct methods is order(N3) where N is the number of bodies in the system. This paper presents an order(N) recursive algorithm to compute q˙ for flexible multibody systems.

Simulation Based Optimal Tolerancing for Multibody Systems

2007 ◽  
Author(s):  
Henry Arenbeck ◽  
Samy Missoum ◽  
Anirban Basudhar ◽  
Parviz E. Nikravesh
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Failure Detection ◽  
Optimization Method ◽  
Computational Effort ◽  
Efficient Estimation ◽  
Design Parameters ◽  
Support Vector ◽  
Manufacturing Cost ◽  
Analysis Scheme

This paper introduces a new methodology for probabilistic optimal design of multibody systems. Specifically, the effects of dimensional uncertainties on the behavior of a system are considered. The proposed reliability-based optimization method addresses difficulties such as high computational effort and non-smoothness of the system’s responses, for example, as a result of contact events. The approach is based on decomposition of the design space into regions, corresponding to either acceptable or non-acceptable system performance. The boundaries of these regions are defined using Support Vector Machines (SVMs), which are explicit in terms of the design parameters. A SVM can be trained based on a limited number of samples, obtained from a design of experiments, and allows a very efficient estimation of probability of failure, even when Monte Carlo Simulation (MCS) is used. A modularly structured tolerance analysis scheme for automatic estimation of system production cost and probability of system failure is presented. In this scheme, detection of failure is based on multibody system simulation, yielding high computational demand. A SVM-based replication of the failure detection process is derived, which ultimately allows for automatic optimization of tolerance assignments. A simple multibody system, whose performance usually shows high tolerance sensitivity, is chosen as an exemplary system for illustration of the proposed approach. The system is optimally designed for minimum manufacturing cost while satisfying a target performance level with a given probability.

Globally Independent Coordinates for Real-Time Vehicle System Simulation

1998 ◽  
Author(s):  
Radu Serban ◽  
Edward J. Haug
Keyword(s):  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Generalized Coordinates ◽  
Constraint Manifold ◽  
Vehicle System ◽  
Dynamics Of Multibody Systems ◽  
Improved Performance ◽  
Cartesian Coordinate ◽  
Control Forces

Abstract Models of the dynamics of multibody systems generally result in a set of differential–algebraic equations (DAE). State–space methods for solving the DAE of motion are based on reduction of the DAE to ordinary differential equations (ODE), by means of local parameterizations of the constraint manifold that must be often modified during a simulation. In this paper it is shown that, for vehicle multibody systems, generalized coordinates that are dual to suspension and/or control forces in the model are independent for the entire range of motion of the system. In addition to the immediate advantage of avoiding the computationally expensive redefinition of local parameterization, the existence of globally independent coordinates leads to efficient algorithms for recovery of dependent generalized coordinates. A topology based approach to identify efficient computational sequences is presented. Numerical examples demonstrate the improved performance of the proposed approach, relative to the conventional Cartesian coordinate formulation.

scholarly journals Recursive Dynamic Algorithm of Open-Chain Multibody System

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ming Lu ◽  
Wenbin Gu ◽  
Jianqing Liu ◽  
Zhenxiong Wang ◽  
Zhisheng Jing ◽  
...  
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Structural Characteristics ◽  
Open Chain ◽  
Widespread Application ◽  
Dynamic Algorithm ◽  
Generalized Coordinates ◽  
The Relationship ◽  
Kane Method ◽  
Partial Velocity

Open-chain multibody systems have been extensively studied because of their widespread application. Based on the structural characteristics of such a system, the relationship between its hinged bodies was transformed into recursive constraint relationships among the position, velocity, and acceleration of the bodies. The recursive relationships were used along with the Huston-Kane method to select the appropriate generalized coordinates and determine the partial velocity of each body and to develop an algorithm of the entire system. The algorithm was experimentally validated; it has concise steps and low susceptibility to error. Further, the algorithm can readily solve and analyze open-chain multibody systems.

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