Javier Cuadrado

Modeling and Solution Methods for Efficient Real-Time Simulation of Multibody Dynamics

Current simulation tools for multibody dynamics arenot problem dependent, they use the same modelingprocess to all cases regardless of theircharacteristics. In addition, real-time simulation ofsmall multibody systems is achievable by existingsimulation tools, however, real-time simulation oflarge and complex systems is not possible withexisting methods. This is a challenge that needs to beaddressed before further advances in mechanicalsimulation with hardware-in-the-loop andman-in-the-loop, as well as virtual prototyping aremade possible.This paper addresses the issue of how the modelingprocess – dependent versus independent co-ordinates, anddescriptor form versus state-space form of theequations of motion – affects the dynamic simulation ofmultibody systems and how it could be taken intoaccount to define the concept of intelligentsimulation. With this new concept all the factorsinvolved in the simulation process – modeling,equations, solution, etc. – are chosen and combineddepending upon the characteristics of the system to besimulated. It is envisioned that this concept willlead to faster and more robust real-time simulators.

Intelligent Simulation of Multibody Dynamics : Space-State and Descriptor Methods in Sequential and Parallel Computing Environments

Real-time dynamic simulation of large, realistic and complexmultibody systems is essential in developing modern technologies such asvirtual prototyping, man-in-the-loop simulators and intelligent vehiclecontrol systems. In order to achieve real-time performance, currentcommercial codes require the use of large costly computers, thuslimiting the number of potential users.This paper shows thatreal-time can be achieved on medium-size workstations if, on the onehand, an adequate combination of modeling, dynamic formulation, andnumerical integration scheme is selected and, on the other hand,advantage is taken of sparse matrix technology and parallel computing. Astudy of space-state and descriptor methods involving the dynamics of awhole vehicle model is carried out and in conclusion, two methods areproposed as the best candidates for real-time simulation.

An efficient computational method for real time multibody dynamic simulation in fully cartesian coordinates

Abstract 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 accelerations — as primary variables. The new method is very systematic and general, and shows very good convergence characteristics even for large time steps. The facts that the Jacobian is linear, that the mass matrix is constant, and that neither Coriolis nor centrifugal terms are present in this formulation make the algorithm be very efficient computationally and therefore suitable for real time simulations. A series of numerical simulations are performed which demonstrate the capabilities of the proposed method.

A simple and general method for kinematic synthesis of spatial mechanisms

In this paper a simple and efficient method for optimum kinematic synthesis of multibody systems is presented. The proposed formulation is based on the use of a set of fully Cartesian coordinates. Using the coordinates, the system is described by a set of geometric constraints and the design requirements are introduced by a set of functional constraints. An objective function is defined and minimized to obtain the values for design parameters. Finally, some planar and three-dimensional examples are presented that illustrate the application of the method.

A combined penalty and recursive real-time formulation for multibody dynamics

The continuously improved performance of personal computers enables the real-time motion simulation of complex multibody systems, such as the whole model of an automobile, on a conventional PC, provided the adequate formulation is applied. There exist two big families of dynamic formulations, depending on the type of coordinates they use to model the system: global and topological. The former leads to a simple and systematic programming while the latter is very efficient. In this work, a hybrid formulation is presented, obtained by combination of one of the most efficient global formulations and one of the most systematic topological formulations. It shows, at the same time, easiness of implementation and a high level of efficiency. In order to verify the advantages that the new formulation has over its predecessors, the following four examples are solved using the three formulations and the corresponding results are compared: a planar mechanism which goes through a singular position, a car suspension with stiff behavior, a 6-dof robot with changing configurations, and the full model of a car vehicle. Furthermore, the last example is also analyzed using a commercial tool, so as to provide the readers with a well-known reference for comparison.

Real Time Simulation of Complex 3-D Multibody Systems With Realistic Graphics

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 coordinates of a point and Euler angles or Euler parameters, this method uses the cartesian coordinates of two or more points and the cartesian components of one or more unit vectors rigidly attached to the body. Points and vectors can be shared between contiguous elements, keeping the number of variables moderate and contributing to the definition of pair constraints. With these coordinates the formulation has important advantages: constant mass matrix in the global reference frame, absence of Coriolis and centrifugal inertia forces in the dependent coordinates and a jacobian matrix much more easy to evaluate. The result is a very general and very efficient dynamic formulation.

Performance and Application Criteria of Two Fast Formulations for Flexible Multibody Dynamics

Abstract The performance of the simulation of flexible multibody systems can be improved by means of the use of topological formulations, which have provided good results in the simulation of large rigid multibody systems. In this work, a topological formulation for rigid bodies is extended to the flexible case, and tests are carried out in order to compare its performance with that of a global formulation. Three systems are simulated: a double four-bar mechanism, a vehicle suspension, and a full vehicle. As it happens in the rigid case, the topological formulation is faster than the global one only for large mechanisms.

WEAK COUPLING OF MULTIBODY DYNAMICS AND BLOCK DIAGRAM SIMULATION TOOLS

Dynamic simulation of complex mechatronic systems can be carried out in an efficient and modular way making use of weakly coupled co-simulation setups. When using this approach, multirate methods are often needed to improve the efficiency, since the physical components of the system usually have different frequencies and time scales. However, most multirate methods have been designed for strongly coupled setups, and their application in weakly coupled co-simulations is not straightforward due to the limitations enforced by the commercial simulation tools used for mechatronics design. This work describes a weakly coupled multirate method applied to combine a block diagram simulator (Simulink) with a multibody dynamics simulator in a co-simulation setup. A double-mass triple-spring system with known analytical solution is used as test problem in order to investigate the behavior of the method as a function of the frequency ratio (FR) of the coupled subsystems. Several synchronization schemes (fastest-first and slowest-first) and interpolation/extrapolation methods (polynomials of different order and smoothing) have been tested. Results show that the slowest-first methods deliver the best results, combined with a cubic interpolation (for FR 50, none of the tested methods can deliver precise results, although smoothing techniques can reduce interpolation errors for certain situations.Copyright

Determination of Holonomic and Nonholonomic Constraint Reactions in an Index-3 Augmented Lagrangian Formulation With Velocity and Acceleration Projections

Index-3 augmented Lagrangian formulations with projections of velocities and accelerations represent an efficient and robust method to carry out the forward-dynamics simulation of multibody systems modeled in dependent coordinates. Existing formalisms, however, were only established for holonomic systems, for which the expression of the constraints at the position-level is known. In this work, an extension of the original algorithms for nonholonomic systems is introduced. Moreover, projections of velocities and accelerations have two side effects: they modify the kinetic energy of the system and they contribute to the constraint reaction forces. Although the effects of the projections on the energy have been studied by several authors, their role in the calculation of the reaction forces has not been described so far. In this work, expressions to determine the constraint reactions from the Lagrange multipliers of the dynamic equations and the Lagrange multipliers of the velocity and acceleration projections are introduced. Simulation results show that the proposed strategy can be used to expand the capabilities of index-3 augmented Lagrangian algorithms, making them able to deal with nonholonomic constraints and provide correct reaction efforts.

Efficient and accurate simulation of the rope–sheave interaction in weight-lifting machines

This article presents different approaches that can be used for modelling wire ropes in weight-lifting machines. It is shown that modelling the rope as a linear spring, although very simple and efficient, is energetically inconsistent and produces spurious terms in the equations of motion if the rope deformation along the segment in contact with the sheave is not considered. In order to overcome this problem and obtain an efficient yet accurate method for the simulation of such systems, a semi-analytical method is derived by introducing an analytical model of the rope–sheave interaction in the system, and the obtained results are compared with a finite-element numerical model. The semi-analytical model is based on a continuum mechanics approach of the rope; it assumes Coulomb friction between the sheave and the rope and neglects the centrifugal force of the segment of rope in contact with the sheave while accounting for tangential inertia forces in the rope. The numerical model is based on the Absolute Nodal Coordinate Formulation, and accounts for both the inertia forces and the bending and axial deformation of the rope.