Solvability of reactions in rigid multibody systems with redundant nonholonomic constraints

Wojtyra, Marek; Frączek, Janusz

doi:10.1007/s11044-013-9352-0

Cited by 28 publications

(17 citation statements)

References 31 publications

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“…Main ideas: The judgments of the independent and dependent rows of the constraint Jacobian matrix are used to find which joint reactions of a mechanism with redundant constraints can be uniquely determined [17,[49][50][51][52]. Generally, a kinematic joint imposes a certain number of constraints on the relative motion between the two bodies it connects.…”

Section: Methods Based On the Judgment Of Constraint Jacobian Matrixmentioning

confidence: 99%

“…The independent rows of U q q ð Þ can be identified by a variety of mathematical methods [17,[49][50][51][52], such as the concept of direct sum, the singular value decomposition, the QR decomposition. For an overconstrained rigid body mechanism, the reaction forces/moments corresponding to the independent constraint equations are unique, despite that all joint reactions cannot be uniquely determined.…”

Section: Methods Based On the Judgment Of Constraint Jacobian Matrixmentioning

confidence: 99%

“…This method is computationally intensive because of the high-rank coefficient matrix of the simultaneous equations. Wojtyra et al [17,[49][50][51][52], proposed several mathematical and simulation methods to find the reactions for which joints can be uniquely determined. The corresponding physical interpretation is not considered in those methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Methods for Force Analysis of Overconstrained Parallel Mechanisms: A Review

Liu

Yao

et al. 2017

Chin. J. Mech. Eng.

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The force analysis of overconstrained PMs is relatively complex and difficult, for which the methods have always been a research hotspot. However, few literatures analyze the characteristics and application scopes of the various methods, which is not convenient for researchers and engineers to master and adopt them properly. A review of the methods for force analysis of both passive and active overconstrained PMs is presented. The existing force analysis methods for these two kinds of overconstrained PMs are classified according to their main ideas. Each category is briefly demonstrated and evaluated from such aspects as the calculation amount, the comprehensiveness of considering limbs' deformation, and the existence of explicit expressions of the solutions, which provides an important reference for researchers and engineers to quickly find a suitable method. The similarities and differences between the statically indeterminate problem of passive overconstrained PMs and that of active overconstrained PMs are discussed, and a universal method for these two kinds of overconstrained PMs is pointed out. The existing deficiencies and development directions of the force analysis methods for overconstrained systems are indicated based on the overview.

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Section: Methods Based On the Judgment Of Constraint Jacobian Matrixmentioning

confidence: 99%

Section: Methods Based On the Judgment Of Constraint Jacobian Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Methods for Force Analysis of Overconstrained Parallel Mechanisms: A Review

Liu

Yao

et al. 2017

Chin. J. Mech. Eng.

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“…The prob-lems with matrix inversions may arise when the system passes near or through the singular configuration or/and the system is redundantly constrained. The redundancy results in problems of joint reactions solvability [37,38]. Nevertheless, let us assume that the boundary loads impulses have been successfully evaluated at this phase.…”

Section: Assembly Phasementioning

confidence: 99%

A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

2016

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This paper presents a novel recursive divide-and-conquer formulation for the simulation of complex constrained multibody system dynamics based on Hamilton's canonical equations (HDCA). The systems under consideration are subjected to holonomic, independent constraints and may include serial chains, tree chains, or closed-loop topologies. Although Hamilton's canonical equations exhibit many advantageous features compared to their acceleration based counterparts, it appears that there is a lack of dedicated parallel algorithms for multi-rigid-body system dynamics based on the Hamiltonian formulation. The developed HDCA formulation leads to a two-stage procedure. In the first phase, the approach utilizes the divide and conquer scheme, i.e., a hierarchic assembly-disassembly process to traverse the multibody system topology in a binary tree manner. The purpose of this step is to evaluate the joint velocities and constraint force impulses. The process exhibits linear O(n) (n -number of bodies) and logarithmic O(log 2 n) numerical cost, in serial and parallel implementations, respectively. The time derivatives of the total momenta are directly evaluated in the second parallelizable step of the algorithm. Sample closed-loop test cases indicate very small constraint violation errors at the position and velocity level as well as marginal energy drift without any additional form of constraint stabilization techniques involved in the solution process. The results are comparatively set against more standard acceleration based Featherstone's DCA approach to indicate the performance of the HDCA algorithm.

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“…Methods described in Refs. [30][31][32] may be employed to obtain precise information on constraint reactions solvability during the stiction occurrence. Note that, since constraints of Eq.…”

Section: Constraints Addition-deletion Approachmentioning

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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Solvability of reactions in rigid multibody systems with redundant nonholonomic constraints

Cited by 28 publications

References 31 publications

Methods for Force Analysis of Overconstrained Parallel Mechanisms: A Review

Methods for Force Analysis of Overconstrained Parallel Mechanisms: A Review

A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

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

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