Modeling Mechanisms with Nonholonomic Joints Using the Boltzmann-Hamel Equations

Cameron, Jonathan; Book, Wayne J.

doi:10.1177/027836499701600104

Cited by 44 publications

(22 citation statements)

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“…McPhee (1996) showed how to use linear graph theory in multibody system dynamics. Cameron and Book (1997) described a technique based on Boltzmann-Hamel equations to derive dynamic equations of motion. Comprehensive discussion on dynamic formalisms can be found in the seminal text by Roberson and Schwertassek (1988), Schiehlen (1990Schiehlen ( , 1997, Shabana (2001), and Wittenburg (2008).…”

Section: Introductionmentioning

confidence: 99%

Evolution of the DeNOC-based dynamic modelling for multibody systems

2013

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Abstract. Dynamic modelling of a multibody system plays very essential role in its analyses. As a result, several methods for dynamic modelling have evolved over the years that allow one to analyse multibody systems in a very efficient manner. One such method of dynamic modelling is based on the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices. The DeNOC-based methodology for dynamics modelling, since its introduction in 1995, has been applied to a variety of multibody systems such as serial, parallel, general closed-loop, flexible, legged, cam-follower, and space robots. The methodology has also proven useful for modelling of proteins and hyper-degree-of-freedom systems like ropes, chains, etc. This paper captures the evolution of the DeNOC-based dynamic modelling applied to different type of systems, and its benefits over other existing methodologies. It is shown that the DeNOC-based modelling provides deeper understanding of the dynamics of a multibody system. The power of the DeNOC-based modelling has been illustrated using several numerical examples.

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Section: Introductionmentioning

confidence: 99%

Evolution of the DeNOC-based dynamic modelling for multibody systems

2013

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“…Condition (27) geometrically means that each of the column vectors of A (1,2) belongs to the linear space orthogonal to the space generated by the columns of Γ 1 or equivalently, by virtue of (28), that it is a linear combination of the row vectors of α 1 . Owing to Properties 3.1 and 3.2, if assumptions (H1) and (H2) are met, then the matrix of coefficients (20) is simplified into…”

Section: Remark 21mentioning

confidence: 99%

“…and they are totally disentangled from the so called reconstruction equations (30), which play in some sense the same role as (2). The same procedure cannot be employed for nonholonomic systems, because of the kinematics relations: actually, the occurrence of a cyclic coordinate does not entail the constancy of the corresponding momentum, as (9) exhibits.…”

Section: Eliminating Some Of the Coordinatesmentioning

confidence: 99%

An algebraic procedure for reducing the Boltzmann-Hamel equations in nonholonomic systems

Talamucci¹

2015

atam

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Nonholonomic systems are increasingly worth considering, because of their application for a wide class of models in mechanical engineering, joint construction, robotics, control for wheels and many other types of mechanisms. A mathematical method suitable for treating such models is based on the definition of quasi-velocities and the formlation of the Boltzmann-Hamel equations. The paper pursues the aim of discussing the appropriate choice of quasivelocities: the possibility of simplifying the mathematical problem via the definition of specific quasi-velocities is discussed, mainly focussing on the linear structure of part of the system and developing algebraic procedure. The technique formulated in the paper is then applied to some models which are exemplars in literature for nonholonomic constrained systems.

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“…Systems with nonholonomic constraints have been reduced to explicit differential equation in various ways as well, in the context of geometric mechanics and Ehresmann connections [4], and in the context of port-Hamiltonian systems and Poisson brackets [5], [6]. Both holonomic and nonholonomic constraints have been treated in the framework of Kane's equations [7], [8] and Boltzmann-Hamel equations [9], which use a type of quasi-coordinates as we do here, but are nevertheless restricted to joints with a Euclidean joint space. This paper, which is based partially on [10], presents a systematic method that is valid for general non-Euclidean holonomic and nonholonomic joints.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian dynamics of open multibody systems with generalized holonomic and nonholonomic joints

Duindam

2007

2007 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-Standard methods to model multibody systems are aimed at systems with configuration spaces isomorphic to R n . This limitation leads to singularities and other artifacts in case the configuration space has a different topology, for example in the case of ball joints or a free-floating mechanism. This paper discusses an extension of classical methods to allow for a very general class of joints, including all joints with a Lie group structure as well as nonholonomic joints.The model equations are derived using the Boltzmann-Hamel equations and have very similar structure and complexity as obtained using classical methods, but they do not suffer from singularities. Furthermore, the equations are explicit differential equations (both for holonomic and nonholonomic joints) and can be directly implemented in simulation software.

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Modeling Mechanisms with Nonholonomic Joints Using the Boltzmann-Hamel Equations

Cited by 44 publications

References 1 publication

Evolution of the DeNOC-based dynamic modelling for multibody systems

Evolution of the DeNOC-based dynamic modelling for multibody systems

An algebraic procedure for reducing the Boltzmann-Hamel equations in nonholonomic systems

Lagrangian dynamics of open multibody systems with generalized holonomic and nonholonomic joints

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