Aspects of Efficient and Reliable Multibody System Simulation

Multibody system equations can be generated in various forms. All of these may be interpreted as results of two basic approaches, the augmentation- and the elimination-method. The former method yields the descriptor form of the system motion, a set of differential-algebraic equations (DAE), and the latter the state space representation, a minimal set of ordinary differential equations (ODE). Both of these methods are surveyed. Particular emphasis is on the discussion of recursive computational schemes, generating the equations of motion with a number of operations, which is proportional to the number N of system bodies (O(N)-formulations).

[1]  C Fuhrer.  ON THE DESCRIPTION OF CONSTRAINED MECHANICAL SYSTEMS BY DIFFERENTIAL ALGEBRAIC EQUATIONS , 1985 .

[2]  F. Pfeiffer.  Über unstetige, insbesondere stosserregte Schwingungen , 1988 .

[3]  R. Jones,et al.  High speed simulation of multi-flexible-body systems with large rotations , 1987 .

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

[5]  R. Featherstone.  The Calculation of Robot Dynamics Using Articulated-Body Inertias , 1983 .

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

[7]  E. Haug,et al.  A recursive formulation constrained mechanical system dynamics. I: Open loop systems , 1987 .

[8]  R. Schwertassek,et al.  Recursive Generation of Multibody System Equations in Terms of Graph Theoretic Concepts , 1989 .

[9]  R. Roberson,et al.  A dynamical formalism for an arbitrary number of interconnected rigid bodies, with reference to the problem of satellite attitude control. , 1966 .

[10]  Ronald L. Huston,et al.  Dynamics of Multibody Systems , 1988 .

[11]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .

[12]  R. Roberson.  The path matrix of a graph, its construction and its use in evaluating certain products , 1984 .

[13]  T. R. Kane,et al.  Dynamics of a cantilever beam attached to a moving base , 1987 .

[14]  R. Schwertassek,et al.  Representation of Joints in Multibody Systems , 1988 .

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

[16]  Manfred Hiller,et al.  The characteristic pair of joints-an effective approach for the inverse kinematic problem of robots , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

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

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

[19]  Takeo Kanade,et al.  Control of a Direct-Drive Arm , 1983 .

[20]  R. Schwertassek.  Multibody Kinematical Equations in Terms of Relative Variables , 1988 .

[21]  Werner Schiehlen,et al.  A Review of: Dynamics of Multibody Systems R. E. ROBERSON and R. SCHWERTASSEK Berlin/ …: Springer-Verlag 1988 , 1990 .

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

[23]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[24]  Thomas R. Kane,et al.  THEORY AND APPLICATIONS , 1984 .