Conditions for uniqueness in simultaneous impact with application to mechanical design

Seghete, Vlad; Murphey, Todd D.

doi:10.1109/icra.2012.6224737

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…More recently, it has been shown that even more may sometimes be needed [19], because the normal part of the restitution law may not be sufficient to describe some motions like perfect rocking of a planar block. Recent results on multiple impacts with or without friction have also been obtained in [11,55,65,66,75,[80][81][82]87].…”

Section: Introductionmentioning

confidence: 94%

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Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction

Brogliato

2013

Multibody Syst Dyn

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Quasi-velocities computed with the kinetic metric of a Lagrangian system are introduced, and the quasi-Lagrange equations are derived with and without friction. This is shown to be very well suited to systems subject to unilateral constraints (hence varying topology) and impacts. Energetical consistency of a generalized kinematic impact law is carefully studied, both in the frictionless and the frictional cases. Some results concerning the existence and uniqueness of solutions to the so-called contact linear complementarity problem, when friction is present, are provided.

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Section: Introductionmentioning

confidence: 94%

“…In a more general setting, since the normal cone is closed convex, the projection in (43) (45) is used in [81,82] with e = 1, who study a kind of binary collisions operator associating each constraint with such a linear mapping between post and pre-impact velocities.…”

Section: Moreau's Impact Lawmentioning

confidence: 99%

Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction

Brogliato

2013

Multibody Syst Dyn

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Multiple Debris Impact Loads in Extreme Hydrodynamic Conditions

Stolle

Nistor

Goseberg

et al. 2020

J. Waterway, Port, Coastal, Ocean Eng.

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A Propagative Model of Simultaneous Impact: Existence, Uniqueness, and Design Consequences

Seghete

Murphey

2014

IEEE Trans. Automat. Sci. Eng.

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Abstract-This paper presents existence and uniqueness results for a propagative model of simultaneous impacts that is guaranteed to conserve energy and momentum in the case of elastic impacts with extensions to perfectly plastic and inelastic impacts. A corresponding time-stepping algorithm that guarantees conservation of continuous energy and discrete momentum is developed, also with extensions to plastic and inelastic impacts. The model is illustrated in simulation using billiard balls and a two-dimensional legged robot as examples; the latter is optimized over geometry and gait parameters to achieve unique simultaneous impacts.Note to Practitioners-Simultaneous impacts are a common occurrence in manufacturing and robotic applications. Simulationbased techniques predicting the motion of a mechanical system subject to simultaneous impacts often use numerical routines that make algorithmic assumptions about impact in order to make the simulation more tractable. Such assumptions have the potential to significantly influence the simulation outcome and may even invalidate results. This paper provides tools for simulating simultaneous impacts, verifying a simulation that deals with simultaneous impacts, and designing a system so that the simulation will be less dynamically sensitive to indeterminacy in simultaneous impact.

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Conditions for uniqueness in simultaneous impact with application to mechanical design

Cited by 4 publications

References 16 publications

Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction

Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction

Multiple Debris Impact Loads in Extreme Hydrodynamic Conditions

A Propagative Model of Simultaneous Impact: Existence, Uniqueness, and Design Consequences

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