Advances in Discrete Time Transfer Matrix Method of Multibody System

In large, rigid multibody dynamics problems with friction and contact, encountered for instance in granular flows, one can witness distinctly different system-level dynamics. This contribution concentrates on the case of fluid-like behavior of large multibody dynamics systems such as granular materials, when the system experiences large strains. The results reported herein draw on computer simulation; on the one hand, we solve the Newton-Euler equations of motion, which govern the evolution of multibody dynamics system featuring frictional contact. On the other hand, we solve the Navier-Stokes equations which describe the time evolution of fluids. To demonstrate the similarities and differences between the multibody and fluid dynamics we consider three problems modeled and solved using different methods; (i) a compressibility test; (ii) the classical dam break problem, and (iii) the dam break simulation with an obstacle. These experiments provide insights into conditions under which on can expect similar characteristics from multibody and fluid dynamics systems governed by manifestly different equations of motion and solved by vastly different numerical solution methods. The models and simulation platform used are publicly available and part of an open source code called Chrono. Both the multibody and fluid dynamics simulations are carried out using GPU computing.

Data standardization is still an open research field in multibody system (MBS) dynamics, and the lack of a standard neutral data format to encode information about MBS models (topology, geometry, rigid and flexible body data, applied forces, type of analysis, …) hinders the exchange and share of models between users of MBS software. Therefore, the MBS research community should start to address the interoperability needs in this field as soon as possible. This article presents some foundations for that task: the requirements for a neutral data format are presented, the current interoperability state in MBS dynamics is evaluated, and two data modeling technologies (STEP and XML) are compared in order to develop a robust yet easy-to-use neutral data format for multibody systems. An XML-based prototype implementation of such a format is proposed, demonstrating the excellent aptitudes of XML for this task. Finally, guidelines for future standardization of multibody system data are given. In conclusion, both STEP and XML should be combined in the future to solve the interoperability problems in multibody system dynamics in an effective way.

This paper presents a new and computationally efficient method for the modelling of flexible robot manipulators. The proposed method avoids the global dynamics by decomposing it to the component dynamics. The component dynamics is established, and is linearized based on the acceleration-based state vector. The transfer matrices for different type of components are created, and the systematic dynamics of a flexible robot manipulator is then established by transferring the state vector from the base to the end-effector without increasing the order of the system matrices. The numerical simulations of a flexible manipulator are conducted for verifying the proposed methodologies.

Multibody systems in planar motion are modelled as two or more rigid components that are connected and can move relative to each other. The dynamics of such multibody systems in planar motion in a central gravitational force field is analysed. The equations of motion of the system include the equations for the orbital motion of the bodies, the orientation (attitude) of the assembly, and the relative orientation (shape) of the bodies with respect to each other. Dynamic coupling between these degrees of freedom gives rise to complex dynamical systems that are usually not integrable. Relative equilibria, corresponding to circular orbits of the multibody system, are obtained. The free dynamics has a symmetry due to a cyclic coordinate. Routh reduction is carried out to eliminate this coordinate and obtain the reduced dynamics. The stability of the relative equilibria is analysed using the Routh stability criterion when it is applicable; an expansion of the Hamiltonian in normal form is used otherwise. We apply the general results to a multibody system consisting of two hinged planar bodies, each modelled as a rigid massless link with a point mass at one end with their other ends connected by a hinge joint. We obtain the relative equilibria of this model, and carry out a stability analysis for the relative equilibria. Numerical simulations using a symplectic integrator are carried out for perturbations to these relative equilibria, to confirm their stability properties.

It is an exceptional success when multibody dynamics researchers Multibody System Dynamics journal one of the most highly ranked journals in the last 10 years. In the inaugural issue, Professor Schiehlen wrote an interesting article explaining the roots and perspectives of multibody system dynamics. Professor Shabana also wrote an interesting article to review developments in flexible multibody dynamics. The application possibilities of multibody system dynamics have grown wider and deeper, with many application examples being introduced with multibody techniques in the past 10 years. In this paper, the development of multibody dynamics is briefly reviewed and several applications of multibody dynamics are described according to the author’s research results. Simulation examples are compared to physical experiments, which show reasonableness and accuracy of the multibody formulation applied to real problems. Computer simulations using the absolute nodal coordinate formulation (ANCF) were also compared to physical experiments; therefore, the validity of ANCF for large-displacement and large-deformation problems was shown. Physical experiments for large deformation problems include beam, plate, chain, and strip. Other research topics currently being carried out in the author’s laboratory are also briefly explained.

The principle of virtual work is used to derive the Euler-Lagrange equations of motion in order to describe the dynamics of multibody android systems. The constrained variational equations are in fact differential-algebraic equations of high index and are cast as ordinary differential equations through differentiation of the constraint equations. The integration routine LSODAR and the fourth-order Runge-Kutta method are used to compute the generalized coordinates, their time derivatives and the body forces of two android models. The graphs of the constraint forces reveal the whiplash effect on the neck and that the stiffness of both multibody systems is due to large magnitude impulsive forces experienced by many bodies simultaneously.

An accurate and computationally efficient framework was developed for dynamic soft robotic systems modelled as rigid-flexible multi-body systems. A recursive parameterization-free formulation for the dynamics of multi-body systems composed of bodies serially connected with single degree of freedom actuated joints from a fixed base is expressed on the SE(3). The Newton-Euler equation of motion for a rigid body and a set of Partial Differential Equations (PDEs) for a dynamic Cosserat rod are coupled to recursively formulate the dynamics of multi-body systems. A shooting-method-based Boundary Condition (BC) solver is developed to determine the BCs and implement a finite difference solution. Geometric integrators are implemented with the geometrically exact model of the multi-body system for an accurate solutions. The recursive formulation of dynamics and application of finite difference yields a computationally efficient solution with potential for real-time application.

This text is a classical and complete book on rigid multibody dynamics. Some of the topics covered include: various angular orientation descriptions, including Euler angles, Bryan angles, and Euler-Rodrigues parameters; quaternion algebra; virtual power; graph theory; and vibration analysis of chains of bodies. The textbook is an excellent reference, containing valuable material for graduate students and researchers. The chapters have an average of six example and problem sets, for which solutions are provided. Aside from the lack of problems, the book can easily be used as a text for a graduate course on the dynamics of rigid multibody systems.

<abstract> <p>Constraint violation correction is an important research topic in solving multibody system dynamics. For a multibody system dynamics method which derives acceleration equations in a recursive manner and avoids overall dynamics equations, a fast and accurate solution to the violation problem is paramount. The direct correction method is favored due to its simplicity, high accuracy and low computational cost. This method directly supplements the constraint equations and performs corrections, making it an effective solution for addressing violation problems. However, calculating the significant Jacobian matrices for this method using dynamics equations can be challenging, especially for complex multibody systems. This paper presents a programmatic framework for deriving Jacobian matrices of planar rigid-flexible-multibody systems in a simple semi-analytic form along two paths separated by a secondary joint. The approach is verified by comparing constraint violation errors with and without the constraint violation correction in numerical examples. Moreover, the proposed method's computational speed is compared with that of the direct differential solution, verifying its efficiency. The straightforward, highly programmable and universal approach provides a new idea for programming large-scale dynamics software and extends the application of dynamics methods focused on deriving acceleration equations.</p> </abstract>

In this paper, a multi-body system dynamics problem is considered as a complex system modeling and computation problem. A parallel programming model and its execution environment are designed to reduce model complexity and to improve computational speed. In this architecture, the problem is divided into two levels: 1. Find a parallel mathematical algorithm to describe the behavior of this multi-body system. 2. Build a unified programming language that could leverage many different pieces of computational resources, such as symbolic computing, and numerical libraries. To tackle the first level, Space-Time Finite Element Method (FEM) is applied. The Space-Time FEM formats of Newton-Euler formula is given, as well as its constraint formula. This algorithm has avoided the loop operation during the time field solving. To tackle the second level, a network-based functional programming language - Object Computing Network (OCN) is designed. OCN is inspired by Object-Process Methodology (OPM). In OCN, every computation behavior is treated as a function, which is constructed by a three element set: {Var, Rule. Condition}. Three basic patterns - Branching, Synchronizing, Merging are given in OCN to prove the flexibility of OCN. An communication interface is designed in OCN to connect different programming languages together. Two multi-body system dynamics computing models - Semi-discretization method and Space-Time discretization method - are constructed with OCN, and a significant contrast in task parallelization is shown by different OCN models.

The methods of multibody system dynamics provide most of the numerical tools required to construct models of vehicles and to describe biomechanical models of occupants with accuracy. Some of the most recent developments in this area of applied mechanics extended the basic capabilities of the multibody formulations to include the description of the system components deformation. For a given model of a vehicle each moving part is represented as a rigid body or as a flexible body experiencing linear elastic or fully nonlinear deformations. The relative motion of the system components is described by imposing kinematic constraints between them. the interactions among the system components, with other objects and multibody systems or even the coupling with the equations of other disciplines to describe aerodynamics effects or contact-impact conditions are efficiently modeled in this numerical environment. These characteristics suggest that the multibody methodologies provide appropriate ingredients to develop not only the simple conceptual models used in the early phases of the design process but also the more elaborate models of complex systems required for analysis. In this work, the position and orientation of each body of the system is described by a set of Cartesian coordinates or by natural coordinates, which consist in a set of points and vectors representing each body. For flexible bodies. the linear or nonlinear deformations are described with reference to a body fixed coordinate system using an updated Lagrangean formulation and the finite element method. In this form the equations of motion of the flexible bodies exhibit the coupling between the gross rigid body motion and the component flexibility. The relative motion between each of the multibody, components is assured by imposing kinematic constraints in the form of algebraic equations that relate the coordinates used to describe the system. The contact and impact between the system components and other bodies, internal or external to the system. is described using a continuous contact force model. Alternatively, unilateral constraints representing motion restrictions for a particular body in contact, are used. For situations where the deformed region of the component in contact is much smaller than the region of the same body that behaves in a rigid manner a kinetostatic formulation is used. Here, the inertial coupling between the body deformations and its gross motion is neglected. Finally, the formulations reviewed are applied to the description of a biomechanical model and several vehicle models that are simulated in different scenarios, including vehicle rollovers with and without occupants and pedestrian impact. Based on these applications the advantages of using a unified formulation to describe all systems are discussed.

Professor Dr. Kurt Magnus (1912–2003) would celebrate his 100th birthday on September 8, 2012. That is a reason to remember this internationally renowned scientist in the field of mechanics, particularly gyrodynamics and multibody system dynamics. By him, the science of gyrodynamics had once again a golden age in Germany. He established branches of mechanics, which we call today “multibody system dynamics” and “mechatronics.” Also, he was very well known as the editor-in-chief of the Ingenieur-Archiv (Archive of Applied Mechanics) from 1963 to 1980. In this contribution, his scientific career will be described and his outstanding research work will be acknowledged. From 1966 to 1980, Kurt Magnus was Full Professor of Mechanics at the Munich University of Technology. During this period, the research field of multibody system dynamics became more and more interesting. Therefore, he initiated and chaired the first IUTAM Symposium on Dynamics of Multibody Systems at Munich, August 29–September 3, 1977. Excellent lectures and intensive discussions showed the state-of-the-art and the further potential for research and application. This contribution will remember these early steps of multibody system dynamics.

In industrial design processes, the system dynamics of complex engineering structures is modelled by a network approach that results in differentialalgebraic model equations. For this problem class, well-established modular simulation techniques like multi-rate or multi-method approaches, co-simulation or waveform relaxation may suffer from exponential instability. With a novel framework for the stability and convergence analysis of modular time integration methods for differential-algebraic systems the sources of numerical instability could be identified and eliminated. Stabilized modular methods have been developed for such diverse fields of application like multibody system dynamics and circuit simulation. This mathematical research has strongly influenced the design of an industrial interface standard for co-simulation in system dynamics.

The First Joint International Conference on Multibody System Dynamics (IMSD2010), held in May 2010 at the Lappeenranta University of Technology (LUT) in Finland, enabled the international multibody community to meet and exchange information and ideas on the theory and applications of multibody systems. It was sponsored by the ASME (American Society of Mechanical Engineers), IFToMM (International Federation for the Promotion of Mechanism and Machine Science), IUTAM (International Union of Theoretical and Applied Mechanics), KSME (Korean Society of Mechanical Engineers), and JSME (Japan Society of Mechanical Engineers). The conference, attended by 242 participants, featured more than 180 presentations, delivered by representatives of 29 countries. In view of the exceptional works presented and the discussions that followed, which included many of the foremost international researchers in Multibody Dynamics, a selected number of authors were invited to submit manuscripts to the Multibody Systems Dynamics journal where they have undergone a strict peer-review process. This issue of the Multibody Systems Dynamics journal presents six of these papers representing the range of topics addressed by Multibody Dynamics; vehicle dynamics, control and mechatronics, algorithms, integration codes, and software. These manuscripts suggest a trend towards theoretically and computationally challenging applications. We are confident that journal readers will find the contents of this issue informative and valuable in their activities related to multibody systems. We would like to take this opportunity to thank the sponsors, organizers, and all participants of the IMSD2010 conference. The success of this First Joint International Conference on Multibody System Dynamics would not have been possible without

The prelims comprise: Half-Title Page Title Page Copyright Page Table of Contents Introduction About the Author Foreword One for the Chinese Edition Foreword Two for the Chinese Edition Foreword Three for the Chinese Edition Foreword Four for the Chinese Edition Professor Rui's Method—Discrete Time Transfer Matrix Method for Multibody System Dynamics Preface