scholarly journals A Symbolic Approach to the Multibody Modeling of Road Vehicles

2017 ◽  
Vol 09 (05) ◽  
pp. 1750068 ◽  
Author(s):  
Roberto Lot ◽  
Matteo Massaro
Keyword(s):  
Equations Of Motion ◽  
Automatic Generation ◽  
General Purpose ◽  
Rigid Bodies ◽  
Simulation Code ◽  
Symbolic Form ◽  
Multibody Modeling ◽  
Mixed Coordinates ◽  
Computer Algebra Software ◽  
Symbolic Approach

This paper introduces MBSymba, an object-oriented language for the modeling of multibody systems and the automatic generation of equations of motion in symbolic form. MBSymba has built upon the general-purpose computer algebra software Maple and it is freely available for teaching and research purposes. With MBSymba, objects such as points, vectors, rigid bodies, forces and torques, and the relationships among them may be defined and manipulated both at high and low levels. Absolute, relative or mixed coordinates may be used, as well as combination of infinitesimal and noninfinitesimal variables. Once the system has been modeled, Lagrange’s and/or Newton’s equations can be derived in a quasi-automatic way, either in an inertial or noninertial reference frame. Equations can be automatically converted into Matlab, C/C++ or Fortan code to produce stand alone, numerically optimized simulation code. MBSymba is particularly suited for the modeling of ground, water or air vehicles; therefore, the mathematical model of a passenger car with trailer is illustrated as a case study. Time domain simulations, steady state analysis and stability results are also presented.

A General Purpose Formulation for Nonsmooth Dynamics With Finite Rotations: Application to the Woodpecker Toy

2020 ◽  
Vol 16 (3) ◽  
Author(s):  
Alejandro Cosimo ◽  
Federico J. Cavalieri ◽  
Javier Galvez ◽  
Alberto Cardona ◽  
Olivier Brüls
Keyword(s):  
Finite Element ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Horizontal Displacement ◽  
General Purpose ◽  
Nonsmooth Dynamics ◽  
Unilateral Constraints ◽  
Simulation Code ◽  
Frictional Contacts ◽  
Large Rotations

Abstract The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. The nonsmooth generalized-α (NSGA) scheme is adopted, which imposes bilateral and unilateral constraints both at position and velocity levels avoiding drift phenomena. This scheme can be implemented in a general purpose simulation code with limited modifications of pre-existing elements. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the NSGA scheme within the context of a general finite element framework. This example has already been studied by many authors who generally adopted a model with a minimal set of coordinates and small rotations. It is shown that good results are obtained using a general purpose finite element code for multibody dynamics, in which the equations of motion are assembled automatically and large rotations are easily taken into account. In addition, comparing results between different models of the woodpecker toy, the importance of modeling large rotations and the horizontal displacement of the woodpecker's sleeve is emphasized.

The Theory and Application of a Classical Eulerian Multibody Code

2005 ◽  
Vol 33 (2) ◽  
pp. 149-176 ◽  
Author(s):  
D. I. M. Forehand ◽  
M. P. Cartmell ◽  
R. Khanin
Keyword(s):  
Analytical Solutions ◽  
Equations Of Motion ◽  
Automatic Generation ◽  
Subject Area ◽  
Physical Problem ◽  
Symbolic Form ◽  
Worked Example ◽  
Approximate Analytical Solutions ◽  
Difficult Subject ◽  
Selection Of

The topic of multibody analysis deals with the automatic generation and subsequent solution of the equations of motion for a system of interconnected bodies. Many academic and industrial computer programs have been developed to carry out this task. However, although some of these programs can obtain the equations of motion in fully symbolic form, it is believed that all the existing programs for multibody analysis solve these equations numerically. The idea behind the research which underpins this paper is to select and implement a symbolic version of an existing multibody algorithm and then to integrate it with a recently developed solver which can obtain approximate analytical solutions to the equations of motion. The present paper deals with the selection of this multibody method. The theory behind the chosen method (the Roberson and Schwertassek algorithm) is described in some detail but also in a much more concise form than can be found in the literature. In addition, a fully worked example of the application of the multibody algorithm to a practical physical problem is given. Such examples are rare in the literature, and so it is intended that this paper can serve as a basis for enhanced didactic practice in this traditionally difficult subject area.

A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations

1986 ◽  
Vol 108 (2) ◽  
pp. 176-182 ◽  
Author(s):  
S. S. Kim ◽  
M. J. Vanderploeg
Keyword(s):  
Equations Of Motion ◽  
General Purpose ◽  
Rigid Bodies ◽  
Transformation Matrix ◽  
Cartesian Coordinates ◽  
Velocity Transformation ◽  
Joint Coordinates ◽  
Relative Coordinates ◽  
General Purpose Computer ◽  
New Formulation

This paper presents a new formulation for the equations of motion of interconnected rigid bodies. This formulation initially uses Cartesian coordinates to define the position of the system, the kinematic joints between bodies, and forcing functions on and between bodies. This makes initial system definition straightforward. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates relative coordinates to Cartesian coordinates. It is derived using kinematic relationships for each joint type and graph theory for identifying the system topology. By using relative coordinates, the equations of motion are efficiently integrated. Use of both Cartesian and relative coordinates produces an efficient set of equations without loss of generality. The algorithm just described is implemented in a general purpose computer program. Examples are used to demonstrate the generality and efficiency of the algorithms.

scholarly journals Application of software tools for symbolic description and modeling of mechanical systems

2020 ◽  
Author(s):  
A. Banshchikov ◽  
A. Vetrov
Keyword(s):  
Mechanical System ◽  
Software Package ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Mechanical Systems ◽  
Software Tools ◽  
Rigid Bodies ◽  
Symbolic Form ◽  
The Stability ◽  
Lagrange Formalism

The paper presents two software tools (graphical editor and software package). The editor is designed for the formation of a symbolic description of a mechanical system using the Lagrange formalism. A system of the absolutely rigid bodies connected by joints is considered as a mechanical system. The editor is a user interface by which one sets the structure of the interconnection of bodies (system configuration) as well as the geometric and kinematic characteristics for each body of the system. The created structure and the entered data are automatically presented in the form of a text file, which is used as an input file for the software package for modeling mechanical systems in a symbolic form with a computer. The use of these software tools is shown in detail in the example of the analysis of the dynamics of a satellite with a gravitational stabilizer in a circular orbit. For this system, the kinetic energy and force function of an approximate Newtonian gravitational field were obtained, nonlinear and linearized equations of motion were constructed, and the question of the stability of the relative equilibrium position was considered.

A General Purpose Formulation for Nonsmooth Dynamics Including Large Rotations: Application to the Woodpecker Toy

2019 ◽  
Author(s):  
Javier Galvez ◽  
Alejandro Cosimo ◽  
Federico J. Cavalieri ◽  
Alberto Cardona ◽  
Olivier Brüls
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
General Purpose ◽  
Rigid Bodies ◽  
Nonsmooth Dynamics ◽  
Minimal Set ◽  
Frictional Contacts ◽  
Bilateral Constraints ◽  
Large Rotations ◽  
Element Approach

Abstract The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. Since rigid bodies and joints involve bilateral constraints, it is important to avoid any drift phenomenon. Therefore, the nonsmooth generalized-α method is used, which imposes the constraints both at position and at velocity levels. Its low intrusiveness allows one to reuse an existing library of elements without major modifications. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the nonsmooth generalized-α within the context of a general finite element framework. This example has already been studied by many authors who generally adopt a model with a minimal set of coordinates and small rotations. We show that using a finite element approach, the equations of motion can be assembled automatically, and large rotations can be easily considered.

General Dynamic Model of Flexible Multi-Body Systems With Its Application in Gun Systems

2003 ◽  
Author(s):  
GuoLai Yang ◽  
Yunsheng Chen
Keyword(s):  
Dynamic Model ◽  
Dynamic Simulation ◽  
Equations Of Motion ◽  
Automatic Generation ◽  
General Purpose ◽  
Automatic Identification ◽  
Automatic Modeling ◽  
Kane’S Equation ◽  
Multi Body ◽  
General Dynamic

General purpose software for kinematic and dynamic simulation of flexible multi-body systems is serviced widely to practical engineering fields. In this paper general dynamic model of flexible multi-body systems with its application in gun systems is set up vie Kane’s equation. The “0-1” method is presented for calculating partial velocities, partial angular velocities and coefficients matrix of the differential equations of motion. Techniques of automatic modeling for dynamic analysis of flexible multi-body systems of gun systems are introduced in this paper, which include automatic identification of systems configuration, automatic determination of degrees of freedom, automatic derivation of kinematic formulas, automatic application of load, automatic generation and solution of motion equations and so on. Because of automatic modeling, overelaborate procedures are avoided, and model on general purpose is realized, which can be conveniently used in dynamic simulation for launching process of gun systems and validly applied to design of them. Finally, a numerical example is given to demonstrate the feasibility of general algorithms proposed.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

scholarly journals A Symbolic Approach to Explaining Bayesian Network Classifiers

2018 ◽  
Author(s):  
Andy Shih ◽  
Arthur Choi ◽  
Adnan Darwiche
Keyword(s):  
Bayesian Network ◽  
Case Studies ◽  
Decision Diagrams ◽  
Minimal Set ◽  
Symbolic Form ◽  
Bayesian Network Classifiers ◽  
Current State ◽  
Current Classification ◽  
Decision Functions ◽  
Symbolic Approach

We propose an approach for explaining Bayesian network classifiers, which is based on compiling such classifiers into decision functions that have a tractable and symbolic form. We introduce two types of explanations for why a classifier may have classified an instance positively or negatively and suggest algorithms for computing these explanations. The first type of explanation identifies a minimal set of the currently active features that is responsible for the current classification, while the second type of explanation identifies a minimal set of features whose current state (active or not) is sufficient for the classification. We consider in particular the compilation of Naive and Latent-Tree Bayesian network classifiers into Ordered Decision Diagrams (ODDs), providing a context for evaluating our proposal using case studies and experiments based on classifiers from the literature.

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