Multibody Mechanical Systems Research Articles

A Variational-Vector Calculus Approach to Machine Dynamics

A variational-vector calculus approach is presented to define virtual displacements and rotations and position, velocity, and acceleration of individual components of a multibody mechanical system. A two-body subsystem with both Cartesian and relative coordinates is used to illustrate a systematic method of exploiting the linear structure of both vector and differential calculus, in conjunction with a variational formulation of the equations of motion of rigid bodies, to derive the matrix structure of governing multibody system equations of motion. A pattern for construction of the system mass matrix and generalized force terms is developed and applied to derivation of the equations of motion of a vehicle system. The development demonstrates an approach to multibody machine dynamics that closely parallels methods used in finite-element structural analysis.

A Covariance Method for Identification of Linear Time-Continuous Systems

Abstract A method for the parameter identification of linear, time-invariant systems under stationary, gaussian coloured excitation is presented. The input-and output signals of the considered system are processed in known linear filters. Stationary covariance relations between these signals allow identification of unknown system parameters. The method is developed in detail for mechanical multibody systems and single-input single-output systems.

Induction motors in electromechanical systems with a periodical moment of inertia — Analytical calculation of forced oscillations and test. Part 1

Induction motors driving mechanical multibody systems with periodical motion (i.e. mechanisms, looms etc.) are subjected to a forced oscillation. This is due to the resulting moment of inertia and the imposed torque: Both of them are periodical functions of the rotation angle. The oscillation is approximated by a finite Fourier series satisfying a linearized system of equations. The comparison to simulation results and measurements for a real system (squirrel cage motor, shuttleless loom) proves the accuracy of the presented analytical method. The latter only requires 3% of the computing time which the numerical method does. Part 1 includes the description of the system, the non-linear equations and their linearization. Part 2 includes the concrete calculation of the forced oscillation as well as the example.

A state-space dynamical representation for multibody mechanical systems part I: Systems with tree configuration

The dynamical equations of motion of a multibody system with closed loops are reduced to state space equations within the framework of the computer-oriented Roberson/Wittenburg multibody formalism. First, that formalism is reviewed. One obtains unreduced equations of motion for systems with tree configuration as well as systems with closed loops. The constraint equations are discussed next, formulated in terms of variables representing the relative motion of contiguous interacting bodies. For systems with tree configurations, such constraint equations can be used without further modification to reduce the dynamical equations to state space form, by applying methods of linear algebra. Modes of motion are derived from the constraints and the interaction forces and torques between the bodies are separated into generalized applied and constraint forces. The latter are eliminated, thus reducing the dynamical equations to state space form. Finally, the relations for the determination of the generalized constraint forces are given, assuming that the motion of the system has been determined from its state space representation.

A state-space dynamical representation for multibody mechanical systems part II: Systems with closed loops

In Part I the state space equations for systems with tree configurations are developed. Part II turns to systems with closed loops, for which one also must consider the consistency equations on the motions of bodies forming closed loops. Introducing all the constraint equations on the relative motion of contiguous bodies in the loops into the consistency equations and generalizing the procedure used in Part I, a state-space representation of the dynamical equations is obtained.

Dynamic Analysis of Multirigid‐Body System Based on the Gauss Principle

AbstractThis paper on the basis of the Gauss principle an efficient computer oriented algorithm for solving the equations of motion of multibody mechanical system. No constraints on the type of the kinematic chain of the system are imposed, i.e. the system may contain an arbitrary number of “closed loops”. In the context of the investigation of the dynamics of the industrial manipulators, robots and similar mechanisms, the mechanical systems considered are linked rigid bodies with joints permitting relative rotation or translation. The successive computation is due to a suitable expression of the Gauss “leas constraint” and using of the powerful recently developed iterative programming methods for constraint and unconstrain minimization of a functional.

Multi-body dynamics including the effects of flexibility and compliance

New and recently developed concepts and ideas useful in obtaining efficient computer algorithms for solving the equations of motion of multi-body mechanical systems with flexible links are presented and discussed. These ideas include the use of Euler parameters, Lagrange's form of d'Alembert's principle, generalized speeds, quasi-coordinates, relative coordinates, and structural analysis techniques. The mechanical systems considered are linked bodies forming a tree structure, but with no “closed loops” permitted. An explicit formulation of the governing equations is presented.

Multibody structural dynamics including translation between the bodies

New and recently developed concepts useful for obtaining and solving equations of motion of multibody mechanical systems with translation between the respective bodies of the system, is presented. The incorporation of translation effects make the analysis applicable to a much broader class of problems than was possible with previous analyses which are restricted to linked multibody systems. The concepts developed in the analysis include the use of Euler parameters, Lagrange's form of d'Alembert's principle, quasi-coordinates, relative coordinates, and body connection arrays. Procedures for the development of efficient computer algorithms for evaluating the coefficients of the governing equations of motion are outlined. The methods presented are directly applicable in the analysis of biodynamic and human models, finite segment cable models, mechanisms, manipulators and robots.

Dynamics of Multirigid-Body Systems

New and recently developed concepts and ideas useful in obtaining efficient computer algorithms for solving the equations of motion of multibody mechanical systems are presented and discussed. These ideas include the use of Euler parameters, Lagrange’s form of d’Alembert’s principle, quasi-coordinates, relative coordinates, and body connection arrays. The mechanical systems considered are linked rigid bodies with adjoining bodies sharing at least one point, and with no “closed loops” permitted. An explicit formulation of the equations of motion is presented.