A rotationless formulation of multibody dynamics: Modeling of screw joints and incorporation of control constraints

Uhlar, Stefan; Betsch, Peter

doi:10.1007/s11044-009-9149-3

Cited by 18 publications

(13 citation statements)

References 17 publications

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“…It is worth mentioning, that the present rotationless formulation is closely related to the notion of natural coordinates advocated by García de Jalón and coworkers, see [7,21,20]. The coherence between both formulations is outlined in detail by Uhlar and Betsch in [54]. For the modeling of joint friction, the application of a coordinate augmentation technique, introduced by Betsch and Uhlar [15,54,52], will play a major role.…”

Section: Introductionmentioning

confidence: 94%

“…The coherence between both formulations is outlined in detail by Uhlar and Betsch in [54]. For the modeling of joint friction, the application of a coordinate augmentation technique, introduced by Betsch and Uhlar [15,54,52], will play a major role. The coordinate augmentation technique makes possible the introduction of rotational DOF into the rotationless formulation and finally to apply internal forces which account for the dissipative effects in a straightforward way.…”

Section: Introductionmentioning

confidence: 99%

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On the derivation of energy consistent time stepping schemes for friction afflicted multibody systems

Uhlar

Betsch

2010

Computers & Structures

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

On the derivation of energy consistent time stepping schemes for friction afflicted multibody systems

Uhlar

Betsch

2010

Computers & Structures

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“…Thus, Betsch et al have preferred the representation of 3D rotations by preserving all 9 elements of the rotation matrix as parameters, in the framework of energy-momentum consistent time-stepping schemes for finite-dimensional mechanical systems with holonomic constraints [11][12][13]. The method of using a discrete null space matrix was used to eliminate the discrete Lagrange multipliers [11].…”

Section: Direct Dynamics Of Gough-stewart Hexapod Platforms Using Thementioning

confidence: 99%

Direct Dynamics of Gough-Stewart Hexapod Platforms Using the Redundant Parameterization of Rotations by Full Rotation Matrices

2017

IJOMAM

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-The direct dynamics study of Gough-Stewart hexapod platforms presented in this paper represents a preparatory step towards the direct dynamics study of a double hexapod, i.e., two Gough-Stewart platforms mounted in parallel one above the other. The direct dynamics model used here is based on the redundant parameterization of rotations by full 3 dynamics of each solid of the hexapod platform comprises 12 scalar differential equations (3 for each translation and 9 for each solid rotation) and 6 algebraic scalar orthogonality equations, plus the algebraic constraints characterizing the joints. For the entire hexapod, the overall differentialalgebraic system comprises 156 scalar differential equations and 78+72=150 scalar algebraic equations. Of course, a number of 150 scalar Lagrange multipliers are introduced in association with fulfilling the algebraic equations. So, our dynamic modelling technique involves an increased number of parameters and equations, but this disadvantage is compensated by the fact that the dynamic equations can be written in a systematic way, being structurally similar for each solid of the hexapod multibody system. From the numerical point of view, the differential-algebraic system is solved by an iterative "shooting method", using classical adaptive step size Runge-Kutta integration. No convergence troubles were encountered so far, when studying the direct dynamics of the Gough-Stewart hexapod platform considered as case study.

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“…Please refer to Uhlar and Betsch, 10 Bru¨ls et al, 11 Bru¨ls and Cardona, 12 Celledoni et al, 13 Celledoni and Owren, 14 and Mu¨ller and Terze 34 for some new developments on this topic.…”

Section: A Heavy Topmentioning

confidence: 99%

Dynamical equations of multibody systems on Lie groups

Pan

2015

Advances in Mechanical Engineering

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The Euler-Poinaré principle is a reduced Hamilton's principle under Lie group framework. In this article, it is applied to derive a hybrid set of dynamical equations of rigid multibody systems, which include four parts: the classical Euler-Lagrange equations of rigid bodies in their translational coordinates of mass center; Euler-Poinaré equations via orientation matrices and their related angular velocities; the constraint equations due to different joints in Cartesian coordinates and Lie groups; and the reconstruction equations between special orthogonal groups and their Lie algebras. The generalized mass matrices of dynamical equations are constant, which is computationally efficient. All the equations can be constructed systematically and can be solved easily. The construction equations can be used to design Lie group integrators of multibody system dynamics. The procedure presented in this article can be extended easily to flexible multibody systems, systems with non-holonomic constraints, and so on.

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A rotationless formulation of multibody dynamics: Modeling of screw joints and incorporation of control constraints

Cited by 18 publications

References 17 publications

On the derivation of energy consistent time stepping schemes for friction afflicted multibody systems

On the derivation of energy consistent time stepping schemes for friction afflicted multibody systems

Direct Dynamics of Gough-Stewart Hexapod Platforms Using the Redundant Parameterization of Rotations by Full Rotation Matrices

Dynamical equations of multibody systems on Lie groups

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