P.Y. Willems

Linearity of Multibody Systems with Respect to Barycentric Parameters: Dynamics and Identification Models Obtained by Symbolic Generation

Abstract The aim of the paper is to produce the equations of motion of a multibody system in symbolic form. The formulation permits emphasis of the linearity of the equation with respect to barycentric parameters. Dynamic and identification models for manipulators are derived in an easy-to-read symbolic form by use of the ROBOTRAN program, which is also described.

On the Attitude Dynamics of Spinning Deformable Systems

A general method for attitude dynamics investigation of spinning deformable systems is presented. The stability of given equilibrium configurations is determined by use of the Liapunov technique. Necessary and sufficient conditions are obtained in most cases. The choice of the body reference frame is considered, and the motion of various frames, such as principal axes frame, mean frame, and Tisserands frame, is investigated.

On the stability of interconnected rigid bodies

SummaryThe aim of this paper is to determine conditions for equilibrium of an orbiting system of interconnected rigid bodies and to find the stability conditions for a given equilibrium configuration. The equations were expressed in a body mean frame and derived from the Roberson-Wittenburg formalism, the combination of the advantages of these methods leading to a rather simple stability analysis by use of the Liapunov technique.ÜbersichtEs werden die Bedingungen für das Gleichgewicht eines Systems von miteinander verbundenen starren Körpern aufgestellt, die sich auf einer Umlaufbahn befinden. Die Stabilitätsbedingungen für eine gegebene Gleichgewichtslage werden berechnet. Die Bewegungsgleichungen werden nach dem Vorbild von Roberson-Wittenburg abgeleitet und in einem körperfesten Zwischensystem ausgedrückt. Dank der Vorteile dieses Vorgehens kann die Stabilitätsanalyse verhältnismäßig einfach nach der Ljapunovschen Methode durchgeführt werden.

AUTODYN & ROBOTRAN — Computer Programmes

This contribution presents the main features of the AUTODYN programme. This programme based on d’Alembert Potential Power Principle, permits to derive the equations of motion of any mechanical system which can be represented by a set of interconnected rigid bodies. In particular, it has important applications in the fields of robotics and vehicle dynamics. The variables of the system are the generalized variables describing the relative motion of the various joints of the system. A joints’ library including surface rolling interconnections (rail-wheel joint) is available. Constraints can be considered and in particular those resulting from loops of bodies are automatically generated. The Lagrange multipliers technique permits to derive the complete set of equations of motion; a system reduction via the elimination of these multipliers and a coordinate partioning method is available. The obtained programme can be used as a sub-routine for any desired application such as numerical integration, stability analysis, control design, numerical linearization, eigenvalues determination.

Determination of three-dimensional joint efforts of a subject walking on a treadmill

Many studies have attempted to determine some joint effort components in the human body in motion. However, it seems that no model has been developed to systematically determine the joint efforts for the whole human body in three dimensions. This research develops a noninvasive method to determine the joint torques for a subject in motion, on the basis of a three-dimensional inverse dynamical model of the human body. This model is applied here to walking on a treadmill.

Multibody Systems With Loops - a Pseudo-constraint Approach

The paper presents an original approach for solving kinematical problems related to constraints, in particular those appearing in multibody systems with loops. This approach uses linear combinations of the time derivatives of the constraints in order to construct a pseudo-gradient which can be computed from straight forward kinematical considerations. Moreover, this method permits avoiding numerical convergence toward undesired solutions.

On the equilibrium configuration of a particular three-body system

SummaryThe equilibrium configurations of a deformable spinning satellite are investigated. The system is modelled by three interconnected rigid bodies, two of them having the characteristics of rigidified cables or beams. The equilibrium conditions and stability criteria of this particular system are provided by the multibody formalism. Using these conditions, all the equilibrium configurations which can not a priori be found to be unstable are determined.ÜbersichtEs werden die Gleichgewichtslagen eines deformierbaren drehenden Satelliten untersucht. Das Modell des Satelliten besteht aus drei miteinander verbundeneu starren Körpern, von denen zwei als erstarrt gedachte Kabel oder Balken betrachtet werden. Die Gleichgewichtsbedingungen und die Stabilitätskriterien dieses Systems werden mit Hilfe des Formalismus der Mehrkörpersystemtheorie abgeleitet. Auf diese Weise werden alle diejenigen Gleichgewichtslagen bestimmt, die nicht von vornherein offensichtlich instabil sind.