Javier García de Jalón

• Universidad Politécnica de Madrid

A number of strategies can be followed for the real-time simulation of multibody systems. The main contributing factor to computational efficiency is usually the algorithm itself (the number of equations and their structure, the number of coordinates, the time integration scheme, etc.). Additional (but equally important) aspects have to do with imp...

Ten years ago, an original semi-recursive formulation for the dynamic simulation of large-scale multibody systems was presented by García de Jalón et al. (Advances in Computational Multibody Systems, pp. 1–23, 2005). By taking advantage of the cut-joint and rod-removal techniques through a double-step velocity transformation, this formulation prove...

A great variety of formulations exist for the numerical simulation of rigid-body systems, particularly of medium-large systems such as vehicles. Topological formulations, which are considered to be the most efficient ones, are often cumbersome and not necessarily easy to implement. As a consequence, there is a lack of comparative evidence to suppor...

La seguridad activa de los vehículos se ve afectada por las variaciones de las condiciones de operación y por la degradación de los diferentes sistemas (suspensión, dirección, neumáticos, etc.). Una de la variables de operación que más afecta a la seguridad es la carga y su distribución el en vehículo. En el caso de los vehículos para el transporte...

Analysis of the fatigue life of a semitrailer structure necessitates identification of the loads and dynamic solicitations in the structure. These forces can be introduced in computer simulation software (multibody + finite element) for analysing the response of different design solutions to them. These numerical models must be validated and some p...

This paper presents a method for solving the dynamic equations of multibody systems containing both rigid and flexible bodies. The proposed method uses independent coordinates and projects the dynamic equations on the constraint tangent manifold by means of a velocity transformation matrix. It can be used with a wide variety of integration formulae...

Some topological formulations in terms of semi-recursive fashion have been proposed recently to improve computational efficiency in complex multibody systems (MBS). An improved semi-recursive method has been developed by García de Jalón [1-2], Kim has introduced a subsystem synthesis method [3-4], and Bae has implemented an implicit generalized sem...

This article deals with the dynamic response optimization of mechanical systems, based on the computation of independent state sensitivities. Specifically, the dynamic behavior of a coach is analyzed in detail so as to improve its response in terms of handling and ride comfort behaviors. To that end, the coach is modeled as an 18-DOF multibody syst...

A method for producing low cost dynamometric wheels is presented in this paper. For carrying out this method, the metallic part of a commercial wheel is instrumented with strain gauges, which must be grouped in at least three circumferences and in equidistant radial lines. The strain signals of the same circumference are linearly combined to obtain...

It is common in mechanical simulation to not know the value of key system parameters. When the simulation is very sensitive to those design parameters and practical or budget limitations prevent the user from measuring the real values, parameter identification methods become essential. Kalman filter methods and optimization methods are the most wid...

The usefulness of sensitivity analyses in mechanical engineering is very well-known. Interesting examples of sensitivity analysis applications include the computation of gradients in gradient-based optimization methods and the determination of the parameter relevance on a specific response or objective. In the field of multibody dynamics, analytica...

This article presents three multibody formulations with improved efficiency in order to achieve real-time simulations for the forward dynamic of two real-life road vehicles. The bigger is a semi-trailer truck with 40 degrees of freedom (DOF). Two topological and semi-recursive formulations are used as well as a global formulation based on the use o...

Within the multibody systems literature, few attempts have been made to use automatic differentiation for solving forward multibody dynamics and evaluating its computational efficiency. The most relevant implementations are found in the sensitivity analysis field, but they rarely address automatic differentiation issues in depth. This paper present...

Efficient dynamic simulation code is essential in many situations (including hardware-in-the-loop and model-predictive control applications), and highly beneficial in others (such as design optimization, sensitivity analysis, parameter identification, and controller tuning tasks). When the number of modeling coordinates n exceeds the degrees-of-fre...

This article shows an efficient implementation of a dynamic semi-recursive formulation for large and complex multibody system simulations, with interesting applications in the automotive field and especially with industrial vehicles. These systems tend to have a huge amount of kinematic constraints, becoming usual the presence of redundant but comp...

This paper addresses some important issues for multibody dynamics; issues that are basic and really not too difficult to solve, but rarely considered in the literature. The aim of this paper is to contribute to the resolution and clarification of these topics in multibody dynamics. There are many formulations for determining the equations of motion...

In this paper, a novel method for producing dynamometric wheels that measure the forces and moments acting at the tyre/road contact patch is presented. Those forces and moments are obtained from the strain signals measured at different points of the original wheel of the vehicle with strain gauges. These signals do not only depend on the forces and...

This article deals with the dynamic response optimization of mechanical systems. Specifically, the dynamic behavior of a coach is analyzed in detail, so as to improve its response in terms of handling and comfort characteristics. To that end, the coach is modeled as a 15-DOF multibody system by means of an efficient double-step semi-recursive formu...

The utility of sensitivity analyses in mechanical engineering for various purposes is very well-known. In the field of multibody dynamics, sensitivity methods tend to be very complex and numerical differentiation is often used instead. In this work, a method based on the differentiation of a recursive Maggi's formulation is presented. Efficiency an...

According to a recent paper (Laulusa and Bauchau, 2008, “Review of Classical Approaches for Constraint Enforcement in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 3 (1), 011004), Maggi’s formulation is a simple and stable way to solve the dynamic equations of constrained multibody systems. Among the difficulties of Maggi’s formulation, Laulu...

According to a recent paper by Laulusa and Bauchau [1], Maggi’s formulation is a simple and stable way to solve the dynamic equations of constrained multibody systems. Among the difficulties of Maggi’s formulation, Laulusa and Bauchau quoted the need for an appropriate choice (and change, when necessary) of independent coordinates, as well as the h...

Among the many different approaches to teach engineering subjects, the project-based methodology turns out to be one of the most effective ones. In the field of undergraduate numerical methods, it can overcome some of its inherent difficulties. This paper considers a particular context: a general 90-hour numerical methods subject in an Industrial-M...

Automatic differentiation is a very powerful computational-mathematical technique that is capable of differentiating any type of computer function. Among its advantages over other ways of computing derivatives, the most important are accuracy, scalability, efficiency and short development time. This article is about the implementation of automatic...

Multibody dynamics discipline is so mature and has so many applications in the industry, that currently it is essential for mechanical engineering students to learn its basic theoretical foundations. However, universities cannot always integrate the matter as a standalone subject. This article presents an efficient methodology to teach kinematic an...

El trabajo presentado en este artículo está orientado a la obtención de simulaciones en tiempo real de sistemas multicuerpo de gran tamaño y complejidad, con particulares aplicaciones en el campo de la automoción. La complejidad de las operaciones numéricas necesarias crece significativamente en sistemas multicuerpo con cadenas cerradas y un ele...

INTRODUCCIÓN Desde el punto de vista de la topología, las dos grandes familias de sistemas multicuerpo son los mecanismos de cadena abierta y los mecanismos de cadena cerrada. Existe una gran variedad de métodos para el cálculo dinámico de ambas familias, que generalmente se clasifican en métodos globales y métodos topológicos. Los segundos son muc...

Multibody systems (MBS) are so mature and have so many applications in industry, that currently it is essential for Mechanical Engineering students to learn the basic theoretical elements. However, universities cannot always integrate the matter as a standalone subject, and there is not a consensus among academic authorities on which is the best wa...

This paper presents a new semi-recursive method for solving the dynamic equations of rigid body multibody systems with implicit integrators, closely related with the methods presented by Bae et al. (2001) and Rodriguez et al. (2004). This method considers the open chain relative coordinates as position variables, but only the independent relative v...

This article presents a simple and powerful simulation framework for the dynamic analysis of complex multibody vehicle models. The framework is based on an efficient semi-recursive multibody formulation which makes the most of the system's topology and achieves better computation times than those of commercial multibody tools. The implementation is...

This article presents a powerful implementation of an open source 3D graphics library into a mixed MATLAB/C++ MBS framework. Firstly, the authors make a summary of the framework. Its core is an efficient semi-recursive formulation which makes the most of the system topology and that is especially suitable for large and complex MBSs. It uses optimiz...

In this article, two formulations implemented in Matlab™ for the dynamic simulation of multibody systems are described. The developed framework allows a rapid development of pro-grams and a clean implementation of algorithms, offering many aids to make the data pre and post-process. However, Matlab is not efficient at all when working with small ma...

La Diferenciación Automática (DA) es una nueva técnica que permite obtener, de forma automática y exacta, las derivadas de funciones definidas mediante código de ordenador. En este trabajo la DA se ha aplicado al cálculo de las Jacobianas de las ecuaciones de restric-ción. Como ejemplos concretos se presentan los casos de un robot y de un turismo.

In the early eighties, the author and co-workers created and further developed the natural coordinates to describe the motion of 2-D and 3-D multibody systems. Natural coordinates do not need angles or angular parameters to define orientation, leading to constant inertia matrices and to the simplest form of the constraint equations. Natural coordin...

This paper deals with teaching kinematic and dynamic analysis of 3-D multibody systems in a context of courses with severe time constraints and the objective of attaining practical abilities. This high course efficiency is intended by the use of a simple theoretical approach (the natural or fully Cartesian coordinates) and a high level programming...

MechXML is an XML-based language aimed at describing multibody systems and their simulations (see a more detailed description in [1]). With the appropriate easy-to-build parsers, a data file written in this language can be executed with little or no modification at all in many commercial and research-oriented programs. The purpose of this paper is...

In this paper a family of methods for multi-body dynamic simulation is introduced. Equations of motion are obtained using a set of Cartesian coordinates and projected onto a set of independent relative coordinates using the concept of velocity transformation. Open-chain systems are solved directly following either a fully recursive or a semi-recurs...

In this paper a prototype of a computer program for multi-bodysimulation based on the use of CORBA, Java and XML is presented. Thisprototype makes use of a recursive dynamic formalism which outperformsmany implementations based on global formulations. The prototypepresented has been implemented using distributed Object OrientedProgramming technique...

This paper presents a new method for the factorization of the sparse system of linear equations arising from the kinematic simulation of multibody systems using natural coordinates. A special reordering of the jacobian matrix of the mechanism constraint equations will be described. This reordering depends only on the topology of the mechanism. In o...

This paper presents a new method for the factorization of the sparse system of linear equations arising from the kinematic simulation of multibody systems using natural coordinates. A special reordering of the jacobian matrix of the mechanism constraint equations will be described. This reordering depends only on the topology of the mechanism. In o...

A new reduced formulation for modeling elastic structures or structural components with geometric nonlinearities is presented. This formulation is obtained as a generalization of the concept of foreshortening, which has been successfully used by other authors to model beams. Some examples are provided that illustrate the generality and validity of...

In this paper, a new method for the dynamic simulation of mechanisms with flexible bodies is presented. The principal object of this work is to define the flexible bodies based on the modelization technique developed for rigid bodies using ‘natural co-ordinates’. In the rigid case, each body is defined by means of the Cartesian co-ordinates of some...

In this work, general purpose methodologies and formulations are developed for the optimization of the dynamic behaviour of 3D multibody systems. In order to achieve these goals, the latest advances in three fields are used: Dynamic formulations, object oriented programming languages and symbolic computation techniques. On the first field, constrai...

This paper presents an efficient algorithm based on velocity transformations for real-time dynamic simulation of multibody systems. Closed-loop systems are turned into open-loop systems by cutting joints. The closure conditions of the cut joints are imposed by explicit constraint equations. An algorithm for real-time simulation is presented that is...

Multibody systems are quite often a complex combination or assembly of mechanical elements with very different mechanical behavior: rigid or flexible, linear or non-linear, etc. Sometimes it can be very difficult to carry out an efficient dynamic simulation with a single software package. In practical applications, some bodies are so small and rigi...

This chapter deals with two important multibody problems related to forces: the determination of the static equilibrium position and the solution of the inverse dynamics. In both cases, it is assumed that the motion, that is, velocities and accelerations, is known, and, in the former case also, that the motion does not exist. At least, there is not...

The kinematic constraint equations corresponding to the natural coordinates were explained in detail in Chapter 2, both for planar and three-dimensional multibody systems. They were then compared to other types of coordinates. Attention was also given to the main sources of constraint equations with natural coordinates: rigid body constraints, join...

This chapter deals with several techniques to solve some problems of particular interest in multibody simulation that have not been considered in other chapters. These techniques are neither very sophisticated nor trivial. However, they may be very useful at the time of solving practical or real problems.

The formulation of the inertia and external forces appearing at any of the elements of a multibody system, in terms of the dependent coordinates that describe their position, velocity, and acceleration, is of fundamental importance for the solution of the dynamic analysis.

The kinematics and dynamics of multibody systems is an important part of what is referred to as CAD (Computer Aided Design) and MCAE (Mechanical Computer Aided Engineering). Figures 1.1 to 1.6 illustrate some practical examples of computer generated models for the simulation of real multibody systems. The mechanical systems included under the defin...

Several ways of formulating the differential equations of motion of a multibody system have been presented in Chapter 5. These equations are fully nonlinear in either the independent or dependent coordinates. The solution of these non linear equations is required in order to simulate the dynamic behavior of multibody systems that undergo large disp...

This chapter deals with the direct dynamic problem which consists of determining the motion of a multibody system that results from the application of the external forces and/or the kinematically controlled or driven degrees of freedom. The direct dynamic analysis is also commonly referred to as the dynamic simulation. Its importance is steadily in...

The general purpose dynamic formulations described in Chapter 5 are simple and efficient, but they are not suitable for real time dynamic simulation. Real time performance requires faster formulations. These can be developed by taking into account the system’s kinematic configuration or topology. In the last two decades, a big effort has been dedic...

In either the kinematic or dynamic analysis of multibody systems described in Chapter 1, the first issue to consider is that of modeling the system, which involves the selection of a set of parameters or coordinates that will allow one to define unequivocally at all times the position, velocity and acceleration of the multibody system. There are se...

Applications of artificial manipulation and robotics are steadily increasing in areas such as: microelectronics, agile space aircraft, vacuum mechatronics, satellite-mounted robots, biomedical sciences, teleoperation, assembly lines, manufacturing, and so forth. As a consequence, more demands are being placed on these systems, such as the need to d...

It was shown in Chapter 5 how the application of the laws of dynamics to constrained multibody systems leads to a set of differential algebraic equations (DAE). These can be transformed to second order ordinary differential equations (ODE) by proper differentiation of the kinematic constraint equations, by use of an independent set of coordinates,...

So far, several approaches to the solution of the kinematics and dynamics of multibody systems have been presented. It has been assumed in these approaches that all the bodies satisfy the rigid body condition. A body is assumed to be rigid if any pair of its material points do not present relative displacements. In practice, bodies suffer some degr...

A semi-recursive and easy-to-parallelize algorithm for real-time dynamic simulation of open- and closed-loop multi-rigid-body systems is presented. The equations of motion are obtained in terms of a minimal set of relative joint coordinates using an efficient implementation of the velocity transformation method. The open-loop velocity transformatio...

In this paper we present an extension to flexible multibody systems of a system of fully cartesian coordinates previously used in rigid multibody dynamics. This method is fully compatible with the previous one, keeping most of its advantages in kinematics and dynamics. The deformation in each deformable body is expressed as a linear combination of...

A formulation for the dynamic analysis of flexible systems, composed of slender bodies that can be accurately modelled by beams is presented in this paper. A new set of state variables, composed of Cartesian co-ordinates of points and unit vectors, is introduced to define the beam with respect to an inertial frame. A non-linear Timoshenko beam fini...

An algorithm is presented for the dynamic analysis of mechanisms that is based on the combination of fully cartesian coordinates for the definition of the mechanism, a penalty and augmented Lagrangian formulation for the satisfaction of the constraint equations and the trapezoidal rule for numerical integration with the positions — rather than acce...

In the last few years a new method for kinematic and dynamic simulation of multibody problems has been developed by the authors at CEIT and University of Navarra. The most distinctive feature of this method is the use of a fully cartesian set of dependent coordinates; instead of describing the spatial position of a rigid body through the cartesian...

The theoretical foundations of a 3-D multibody program called COMPAMM (COM-Puter Analysis of Machines and Mechanisms) are presented. Instead of using Euler angles or Euler parameters in order to define the spatial orientation of a rigid body, COMPAMM uses the cartesian coordinates of two or more points and the cartesian components of one or more un...

A modified Lagrangian formulation is presented for the dynamic analysis of constraint mechanisms. The proposed method is based on a Hamiltonian description of the dynamics which leads to the Lagrange's equations. However, the constraint conditions are not appended to the Lagrange's equations in the form of algebraic or differential constraints, but...

This paper presents a comparative theoretical and numerical study on the efficiency of several numerical methods for the dynamic analysis of constrained mechanical systems, also called in the literature multibody systems. This comparative study has been performed between methods based on the use of 'reference point' coordinates and those based on t...

In this paper a new method for the dynamic analysis of three-dimensional mechanisms is presented. This method is based on the use, as mechanism coordinates, of Cartesian coordinates and components of some points and vectors rigidly attached to every element. With these coordinates the constraint equations are very easily formulated. A constant mass...

In this paper we will describe a new method for the computer kinematic and dynamic analysis of a wide range of three-dimensional mechanisms or multibody systems. This method is based on a new system of non-independent coordinates that use Cartesian coordinates of points and Cartesian components of unitary vectors in order to describe the position a...

This article introduces a new method for optimum synthesis of planar mechanisms with lower pairs. The method uses a single objective function for any mechanism and for any type of synthesis, making it possible to perform even mixed syntheses. It is also possible to consider a wide variety of constraints and initial conditions. The error minimizatio...

In this paper a new method for the numerical analysis of multirigid-body systems is described. This method uses a new system of non independent coordinates formed by the cartesian coordinates of some points of the mechanism, and -in the three dimensional case- by the cartesian components of some unitary vectors fixed to the elements. All of them de...

One of the most relevant problems in high speed trains is the quality of contact between the overhead line and the pantograph. The loss of contact due to dynamic interaction causes damage in power units and wear in the line. A great amount of work has been done during the last two decades by most important railway administrations to predict current...

In this article, we shall present the numerical solution to the dynamic problem of planar mechanisms with lower pairs. This method is based on the basic coordinates and link constraints. We shall begin by describing the matrix formulation of the inertial forces on a link and creating the dynamic equilibrium equations in three different ways: in Lag...

IN THIS PAPER, A NEW METHOD FOR THE NUMERICAL SOLUTION OF THE FINITE DISPLACEMENT PROBLEM IN SPATIAL MECHANISMS WITH REVOLUTE (R), CYLINDRICAL (C), SPHERICAL (S), AND PRISMATIC (P) PAIRS IS PRESENTED. IT IS BASED ON THE USE OF SPECIAL POINTS' COORDIATES AS LAGRANGIAN COORDINATES OF THE MECHANISM. THE KINEMATIC CONSTRAINT EQUATIONS ARE IMPOSED AS CO...

The authors present a new numerical method for the computer analysis of spatial mechanisms. This study is limited to the analysis of velocities and accelerations. Results are obtained in the form of a set of velocities and accelerations of different points of the mechanism. The position of all points of the mechanism is considered as known. The vel...

In the first part of this study, a new method for solving the problem of kinematic analysis was presented, based on the concepts of “basic coordinates” and “link constraint equations”. In this second part, these same concepts are used to solve the problems of initial position, finite displacements and static equilibrium position of a mechanism with...

This work presents a new method for the analysis of lower pair mechanisms with the help of a computer. This method make use of the coordinates of the pairs and of those of other points of interest as Lagrangian coordinates of the problem. It also makes use of link constraint equations. Perhaps, the most attractive features of this method are its co...

The efficiency of the application of mini-computers to the solution of many problems by means of the finite element method is well recognized, and the importance of the percentage of time devoted to the solution of the resultant systems of linear equations is also noteworthy.Here, we present a comparative study of six programs of the solution of sy...

This work describes a topological semi-recursive formulation for multibody dynamics that is very simple and efficient. This formulation is called “semirecursive” because it uses recursivity, but at the end it needs to solve a system of n linear equations, with n the numbers of degrees of freedom. With relative coordinates the formulation shall incl...

Abstract This paper describes MechXML (Mechanism eXtensible Markup Language), an XML-based language to describe multibody systems and their analysis. It has been designed to be highly readable both by humans (using comprensible tags) and by computers (taking advantage of tools available for validating and parsing XML files). The MechXML files are d...

MechML con ADAMS [2] y Mbs3d[3], como casos representativos de programas comerciales y de investigación, respectivamente.

En este artículo se presenta un nuevo método numérico de análisis cinemáticlo y dinámico con computador de sistemas mecánicos formados por varios só!idos rígidos. El método presentado utiliza un nuevo sistema de coordenadas no independientes fonnado por las coordenadas cartesianas de algunos puntos del mecanismo y las componentes cartesiarias de al...

La formación de los futuros ingenieros mecánicos en dinámica de sistemas multicuerpo 3-D rara vez encuentra una materia específica en los planes de estudio, ni siquiera en postgrado. Cuando sólo se dispone de algunas horas (entre 5 y 10 horas de clase y unas 15 de trabajo personal) en el marco de una materia más general, las coordenadas naturales y...

La Diferenciación Automática (DA) es una nueva técnica que permite obtener, de forma au-tomática y exacta, las derivadas de funciones definidas mediante código de ordenador. En este trabajo la DA se ha aplicado al cálculo de las Jacobianas de las ecuaciones de restric-ción. Como ejemplos concretos se presentan los casos de un robot y de un turismo.