Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraint forces

Jalón, Javier García de; Gutiérrez-López, Marı́a Dolores

doi:10.1007/s11044-013-9358-7

Cited by 61 publications

(40 citation statements)

References 22 publications

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“…the velocities that belong to the tangent cone) are not in ker(M(q)), consequently they produce positive kinetic energy. These are observations similar to those made in [21] for bilateral constraints (end of Sect. 2 in that paper).…”

Section: Remarksupporting

confidence: 89%

“…If in addition the constraints are functionally independent, then both the acceleration and the multipliers can be calculated uniquely. In the case of bilateral constraints, this boils down to solving a linear equation obtained with the Karush-Kuhn-Tucker matrix, stemming from the so-called index-1 DAE formulation [21,27,39]:…”

Section: M(q)q + F (Qq T) = ∇H(q)λmentioning

confidence: 99%

“…When M(q) and/or ∇h(q) become singular, uniqueness ofq and of ∇h(q)λ is guaranteed for any F (q,q, t) if and only if [21]:…”

Section: M(q)q + F (Qq T) = ∇H(q)λmentioning

confidence: 99%

“…However, the case of interest here is when r < n. Using results from [2], we are going to characterize the existence (solvability) and uniqueness of solutions to (21). Let us first recall the following result, where we concatenate Theorem 3 and Corollary 4 in [2] (Corollary 5 in [2] cannot be applied unless H (q,q) = 0 in which case Φ is a closed convex cone).…”

Section: Well-posedness Of the Mlcpmentioning

confidence: 99%

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Singular mass matrix and redundant constraints in unilaterally constrained Lagrangian and Hamiltonian systems

Brogliato

Goeleven²

2014

Multibody Syst Dyn

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This article deals with the analysis of the contact complementarity problem for Lagrangian systems subjected to unilateral constraints, and with a singular mass matrix and redundant constraints. Previous results by the authors on existence and uniqueness of solutions of some classes of variational inequalities are used to characterize the well-posedness of the contact problem. Criteria involving conditions on the tangent cone and the constraints gradient are given. It is shown that the proposed criteria easily extend to the case where the system is also subjected to a set of bilateral holonomic constraints, in addition to the unilateral ones. In the second part, it is shown how basic convex analysis may be used to show the equivalence between the Lagrangian and the Hamiltonian formalisms when the mass matrix is singular.

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Section: Remarksupporting

confidence: 89%

Section: M(q)q + F (Qq T) = ∇H(q)λmentioning

confidence: 99%

“…When M(q) and/or ∇h(q) become singular, uniqueness ofq and of ∇h(q)λ is guaranteed for any F (q,q, t) if and only if [21]:…”

Section: M(q)q + F (Qq T) = ∇H(q)λmentioning

confidence: 99%

Section: Well-posedness Of the Mlcpmentioning

confidence: 99%

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Singular mass matrix and redundant constraints in unilaterally constrained Lagrangian and Hamiltonian systems

Brogliato

Goeleven²

2014

Multibody Syst Dyn

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“…It is known that flexibility of bodies or joints is one of the main factors deciding on the distribution of reactions in overconstrained mechanisms [19,36]. Similarly, an important role of flexibility may be expected when redundant constraints are introduced to represent locking of the mechanism due to friction.…”

Section: The Role Of Flexibility In Joint Forces Distributionmentioning

confidence: 99%

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Wojtyra

2016

Multibody Syst Dyn

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Problems with uniqueness and high parametric sensitivity of the solution of equations of motion, encountered in the static friction regime, are addressed. Friction in joints of a multibody system with closed-loop kinematic chains is discussed. Three different models of friction are studied: the discontinuous Coulomb model with stiction regime represented in terms of additional constraints; the approximate Coulomb model, smoothed in the vicinity of zero relative velocity; and the LuGre model with presliding displacements represented in terms of auxiliary state variables. Firstly, a rigid body model is investigated. It is shown that in the case of constraint addition approach, problems with uniqueness of solution emerge in the static friction regime. In the case of continuous models of friction, the solution in the stiction regime and its vicinity is highly sensitive to some hardly measurable or arbitrarily chosen parameters of the model of friction. Origins of nonuniqueness and high sensitivity are investigated, and the questionable credibility of the stiction regime simulation results is discussed. Secondly, a simplified model of body and joint elasticity is introduced to investigate the impact of flexibility on the mechanism frictional behavior. It is shown that taking the flexibility into consideration may eliminate the uniqueness and sensitivity problems. Moreover, the quantities that represent flexibility may be regarded as the key factors influencing the results of stiction regime simulation. Five examples are provided to illustrate the presented considerations.

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Dissipative Physical Systems

Brogliato

Lozano

Maschke

et al. 2019

Dissipative Systems Analysis and Control

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Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraint forces

Cited by 61 publications

References 22 publications

Singular mass matrix and redundant constraints in unilaterally constrained Lagrangian and Hamiltonian systems

Singular mass matrix and redundant constraints in unilaterally constrained Lagrangian and Hamiltonian systems

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Dissipative Physical Systems

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