机械专业相关英语期刊46

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机械专业相关英语期刊46Multibody System Dynamics 2: 49–69， 1998.
© 1998 Kluwer Academic Publishers. Printed in the Netherlands.
An Improved Formulation for
Constrained Mechanical Systems
ARA ARABYAN and FEI WU
Department of Aerospace and Mechanical Engineering， The University of Arizona，
Tucson， AZ 85721， U.S.A.
(Received: 19 June 1997; accepted in revised form: 18 February 1998)
Abstract. This paper presents an investigation of the advantages of a new formulation in the stu
of mechanical systems with holonomic and nonholonomic constraints. The formulation， origina
proposed for systems of constrained particles， provides an efficient and robust means of simulat
general multibody systems in the presence of redundant， degenerate and intermittent constraints. T
structure of the formulation also allows the use of a dynamics code for pure kinematics analysis w
a simple substitution. In addition， the formulation separates applied and constraint forces explici
allowing recovery of constraint forces by straightforward means. Several examples are given
demonstrate the effectiveness of the formulation in special circumstances.
Key words: generalized inverse， redundancy， degeneracy， inconsistency， dynamics， kinematics， f
mulation， algorithm.
1. Introduction
The development of versatile and efficient formulations for constrained dynamic
systems has been an area of active research in recent years. Important advanc
may be found in the field of robotics， large space structures， and automatica
controlled machinery. These practical problems share the attributes of having
formulate equations of motion with appropriate constraint equations and to sol
them numerically using computer codes devised for generic classes of problems
Various approaches to formulating equations of motion for complex constrain
mechanical systems have been proposed in the literature [1， 3， 12， 16]. Simi
efforts to produce efficient on-line computation of the dynamics of robot manip
lators were made out of the need for real-time feedback control [14， 28].
The formulations enumerated above cannot be applied very efficiently in t
presence of changeable degrees of freedom or mathematical singularities becau
the classical iteration of integration and matrix inversion fail when the matr
comprised of the inertial matrix and the Jacobian matrix of constraints becom
singular or ill-conditioned. In the case of singularities， some methods can im
prove the results to a certain degree [13， 22]， but they cannot handle cases wh
a zero eigenvalue occurs or the condition number of a matrix to be inverted b