Impulsive motion of multibody systems

Chang, Chau-Chin; Peng, Shou-Tao

doi:10.1007/s11044-007-9035-9

Cited by 19 publications

(7 citation statements)

References 27 publications

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“…Another situation in which impulsive behavior occurs is the sudden application of bilateral constraints on a system, in order to instantaneously block an existing joint, or to model dynamic mass capture and the like. Such types are treated in [12,30,33], all within an equality framework. A more sophisticated approach for such constraint addition or deletion would in the author's opinion be a Coulomb-type impact element, in which the "normal force" is replaced by an impulsive control to turn the constraint on (and off) as needed [25].…”

Section: Energy Preserving Integration In Discrete Mechanicsmentioning

confidence: 99%

“…In [17], this approach is generalized to spatial friction by using Keller's method. Frictionless multicontacts are treated in [11] within the Appellian classification of impulsive constraints. The presence of additional bilateral constraints is explicitly taken into account, and the overall problem is stated in the framework of equalities.…”

Section: Energy Preserving Integration In Discrete Mechanicsmentioning

confidence: 99%

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Energetic consistency conditions for standard impacts

Glocker

2013

Multibody Syst Dyn

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The paper presents a full account of Poisson's impact law in inequality form. Based on an entirely new setting for the decompression phase, impact laws for unilateral and bilateral geometric and kinematic constraints and various friction elements are introduced and equipped with an impact coefficient in the sense of Poisson's impulse ratio. Energetic consistency is proven for small and similar impact coefficients via the condition number of the Delassus operator. Energetic consistency is generally proven for frictionless systems, as well as for systems containing one single frictional contact. A counter-example is developed, which demonstrates a possible energy increase for Poisson impacts in the presence of more than one frictional contact.

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Section: Energy Preserving Integration In Discrete Mechanicsmentioning

confidence: 99%

Section: Energy Preserving Integration In Discrete Mechanicsmentioning

confidence: 99%

Energetic consistency conditions for standard impacts

Glocker

2013

Multibody Syst Dyn

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“…The impact phenomena related to multibody systems have already been well formulated. Chang and Peng (2007) applied the Kane’s method to study the collision between two multibody systems. In their investigations, four diverse types of impulsive constraints were also considered.…”

Section: Introductionmentioning

confidence: 99%

Oblique Impact of Multi-Flexible-Link Systems

Shafei

2016

Journal of Vibration and Control

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The main goal of this paper is to present an automatic approach for the dynamic modeling of the oblique impact of a multi-flexible-link robotic manipulator. The behavior of a multi-flexible-link system confined inside a closed environment with curved walls can be completely expressed by two distinct mathematical models. A set of differential equations is employed to model the system when it has no contact with the curved walls (Flight phase); and a set of algebraic equations is used whenever it collides with the confining surfaces (Impact phase). In this article, in addition to the Assumed Mode Method (AMM), the Euler-Bernoulli Beam Theory (EBBT), and the Newton's kinematic impact law, the Gibbs-Appell (G-A) formulation has been employed to derive the governing equations in both phases. Also, instead of using 3 Â 3 rotational matrices, which involves lengthy kinematic and dynamic formulations for deriving the governing equations, 4 Â 4 transformation matrices have been used. Moreover, for the systematic modeling of flexible multiple links through the space, two virtual links have been added to the n real links of a manipulator. Finally, two case studies have been simulated to demonstrate the validity of the proposed approach.

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“…In the literature several attempts have been made in order to overcome these complexities and many papers deal with procedures that are adapted to computational methods and applications. Some relevant recent references here are Klitsch [19], in connection with the multibody system software SIMPACK ® , Lankarni and Pereira [20] for planar systems, Chang and Peng [21], who use Kane’s method to study impulsive motions for multibody systems, and Chang et al [22] discussing so-called impulsive constraints. Investigations of a more theoretical nature are presented by Glocker and Pfeiffer [23] and Glocker [24].…”

Section: Introductionmentioning

confidence: 99%

Instantaneous impulses in multibody dynamics

Lidström

2015

Mathematics and Mechanics of Solids

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This paper considers instantaneous impulses in multibody dynamics. Instantaneous impulses may act on the multibody from its exterior or they may appear in its interior as a consequence of two of its parts interacting by an impact imposed by a unilateral constraint. The theory is based on the Euler laws of instantaneous impulses, which may be seen as a complement to the Euler laws for regular motions. Based on these laws, and specific continuum properties of the quantities involved, local balance laws for momentum and moment of momentum, involving instantaneous impulses and introducing the Cauchy impulse tensor, are derived. Thermodynamical restrictions on the impulse tensor are formulated based on the dissipation inequality. By stating a principle of virtual work for instantaneous impulses, and demonstrating its equivalence to Euler’s laws, Lagrange’s equations are derived. Lagrange’s equations are convenient to use in the case of multibody dynamics containing rigid as well as flexible parts. A central theme of this paper is the discussion of the interaction between parts of the multibody and their relation to geometrical and kinematical constraints. This interaction is severely affected by the presence of friction, which is notoriously difficult to handle. In a preparation for this discussion we first consider the one-point impact between two rigid bodies. The importance of the so-called impact tensor for this problem is demonstrated. In order to be able to handle the impact laws of Poisson and Stonge, an impact process, governed by a system of ordinary differential equations, is defined. Within this model phenomena, such as slip stop, slip start and slip direction reversal, may be handled. For a multibody with an arbitrary number of parts and multiple impacts, the situation is much more complicated and certain simplifications have to be introduced. Equations of motion for a multibody, consisting of rigid parts and in the presence of ideal bilateral constraints and unilateral constraints involving friction, are formulated. Unique solutions are obtained, granted that the mass matrix of the multibody system is non-singular, the constraint matrices satisfy specific full rank conditions and that the friction is not too high.

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Impulsive motion of multibody systems

Cited by 19 publications

References 27 publications

Energetic consistency conditions for standard impacts

Energetic consistency conditions for standard impacts

Oblique Impact of Multi-Flexible-Link Systems

Instantaneous impulses in multibody dynamics

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