J. García de Jalón

Natural coordinates for the computer analysis of multibody systems

Abstract 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 and the motion of the system. Angular coordinates are not used. The kinematic constraint equation comes in two ways, from the rigid-body condition for each element and from the joints or kinematic pairs. The consideration of unitary vectors facilitates considerably the formulation of pair constraints when the pair is associated with a particular direction, as is the case with revolute (R), cylindrical (C), or prismatic (P) pairs. The constraint equations are quadratic in the problem coordinates and they never involve transcendental functions. The dynamic differential equations are obtained in a very simple and effective way from the theorem of virtual power. Finally, two examples will be presented.

A simple and highly parallelizable method for real-time dynamic simulation based on velocity transformations

Abstract 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 transformation matrix, which relates body translational and rotational velocities to joint relative velocities, is computed in parallel using an extremely simple and intuitive idea. Similarly, the open-loop projected mass matrix is computed in parallel. Fine grain parallelization and optimum use of the cache memory are achieved by using a body-by-body procedure for the computation of vectors and matrices. Closed-loop systems are transformed into open-loop systems through the penalty formulation. The performance of the method is tested through an arithmetic operation count of a 45 degree of freedom open-loop model of a human body and an 18 degree of freedom closed-loop model of a heavy truck.

A fairly general method for optimum synthesis of planar mechanisms

Abstract 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 minimization process is carried out on two levels, and techniques which have been proved efficient for the problem under consideration are described. Finally, the article presents several examples which have been solved by the proposed method.

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.

Kinematic and Dynamic Simulation of Rigid and Flexible Systems with Fully Cartesian Coordinates

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.

A new direct method for the simple and efficient reanalysis of structures

Abstract This article describes a new direct method for linear static reanalysis of structures, based on the displacement method. The modifications introduced can take the form of adding, eliminating, or substituting one or more elements. It is not necessary to maintain the total number of degrees of freedom. This new method is based on the introduction of the modifications as constraints on the original system by means of the Lagrange multipliers. As a direct result of reanalysis, the nodal forces on the modified section are also obtained. This method is simpler and more efficient than previous ones, requiring only the software necessary for the modified Crout method. The corresponding FORTRAN 77 subroutines are included in an Appendix.

An Efficient Implementation of the Velocity Transformation Method for Real-Time Dynamics with Illustrative Examples

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 well suited for parallel processing. The most computationally demanding tasks are matrix and vector products that may be computed in parallel for each body. Four examples are presented that illustrate the performance of the method.

Computer Analysis of Multibody Systems with »Natural Coordinates«

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 determine the position and the motion of the multi-rigid-body system. The constraint equations arise from the rigid body condition of each element and from the constraints introduced by the joints. In the 3-D case, the inclusion of unitary vectors as mechanism coordinates allows an easy formulation of pair constraints when the pair is related to a particular direction, as in revolute (R), cylindrical (C), or prismatic (P) pairs. The constraint equations are always linear or quadratic in the problem coordinates. The differential equations of motion are obtained easily through the application of the Theorem of Virtual Power. Some examples of dynamic analysis of planar and three-dimensional multibody systems are presented.

COMPUTER SIMULATION OF THE DYNAMIC BEHAVIOUR OF ROAD VEHICLES

This paper presents the application of a computer method developed by the authors and their colleagues for the kinematic and dynamic analysis of plane mechanism, to the analysis and simulation of road vehicle suspensions. For this purpose, some improvements and new capabilities have been added to the original method described previously. In the follow-up a very general description of the method is given, and after that, these particular new characteristics are described in greater detail. Finally, an example of a car suspension is presented.

A Theoric-Experimental Computer Aided Method for the Prediction of Overhead Line Dynamic Behaviour at High Speed

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.