An object-oriented approach for an effective formulation of multibody dynamics

Abstract This paper describes a new method for the modeling of the kinematics and dynamics of multibody systems, which is based on the responsibility-driven approach for object-oriented design and the concept of ‘kinetostatic transmission elements’ for mechanical modeling. As a result, a highly data-independent formulation is achieved, where the generic operations offer several analogies to general mappings from manifold theory. The implementation of the approach offers a collection of classes which resemble their real-world counterparts and which allow us to develop, by simple assembly of pre-defined objects, ‘hand-tailored’ multibody programs which are fast and can be integrated in other applications. This is illustrated by an example. Although in this paper the mathematical complexity of the underlying equations is held at a low level, it is easy to extend the method to cover graphical rendering, efficient computation techniques, and elasticity effects. These extensions will be described in future publications.

[1]  J. J. Uicker,et al.  IMP (Integrated Mechanisms Program), A Computer-Aided Design Analysis System for Mechanisms and Linkage , 1972 .

[2]  Manfred Hiller,et al.  Automatic closed-form kinematics-solutions for recursive single-loop chains , 1992 .

[3]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[4]  Manfred Hiller,et al.  EQUATIONS OF MOTION OF COMPLEX MULTIBODY SYSTEMS USING KINEMATICAL DIFFERENTIALS , 1989 .

[5]  G. C. Andrews,et al.  Simulating planar systems using a simplified vector-network method , 1975 .

[6]  J. G. Jalón,et al.  Dynamic Analysis of Three-Dimensional Mechanisms in “Natural” Coordinates , 1987 .

[7]  W. Schiehlen.  Dynamics of complex multibody systems , 1984 .

[8]  Alan Kay,et al.  The reactive engine , 1969 .

[9]  Thomas R. Kane,et al.  Symbolic Generation of Efficient Simulation/Control Routines for Multibody Systems , 1986 .

[10]  Bjarne Stroustrup,et al.  C++ Programming Language , 1986, IEEE Softw..

[11]  Robert W. Sebesta,et al.  Concepts of programming languages , 1973 .

[12]  Manfred Hiller,et al.  SIMULATION OF NONLINEAR VEHICLE DYNAMICS WITH THE MODULAR SIMULATION PACKAGE FASIM , 1991 .

[13]  David Robson,et al.  Smalltalk-80: The Language and Its Implementation , 1983 .

[14]  Ahmed A. Shabana,et al.  A Recursive Formulation for the Dynamic Analysis of Open Loop Deformable Multibody Systems , 1988 .

[15]  M. Géradin,et al.  Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra , 1988 .

[16]  M. Berger,et al.  Differential Geometry: Manifolds, Curves, and Surfaces , 1987 .

[17]  Martin Otter,et al.  A very efficient algorithm for the simulation of robots and similar multibody systems without invers , 1986 .

[18]  Rebecca Wirfs-Brock,et al.  Object-oriented design: a responsibility-driven approach , 1989, OOPSLA 1989.

[19]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[20]  M. A. Chace,et al.  A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 1 , 1977 .

[21]  J. Wittenburg,et al.  MESA VERDE Ein Computerprogramm zur Simulation der nichtlinearen Dynamik von Vielkörpersystemen , 1985, Robotersysteme.

[22]  E. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems , 1987 .

[23]  G. C. Andrews,et al.  The vector-network model: A new approach to vector dynamics , 1975 .

[24]  E. Kreuzer,et al.  NEWEUL — Software for the Generation of Symbolical Equations of Motion , 1990 .

[25]  J. Wittenburg,et al.  Dynamics of systems of rigid bodies , 1977 .

[26]  Donald A. Smith,et al.  DAMN - Digital Computer Program for the Dynamic Analysis of Generalized Mechanical Systems , 1971 .

[27]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .