Breaking Symmetries and Constraints: Transitions from 2D to 3D in Passive Walkers

Petri T. Piiroinen; Harry J. Dankowicz; Arne B. Nordmark

doi:10.1023/A:1025540401249

Breaking Symmetries and Constraints: Transitions from 2D to 3D in Passive Walkers

Petri T. Piiroinen, Harry J. Dankowicz, Arne B. Nordmark

Research output: Contribution to journal › Article › peer-review

Abstract

The inherent dynamics of bipedal, passive mechanisms are studied to investigate the relation between motions constrained to two-dimensional (2D) planes and those free to move in a three-dimensional (3D) environment. In particular, we develop numerical and analytical techniques using dynamical-systems methodology to address the persistence and stability changes of periodic, gait-like motions due to the relaxation of configuration constraints and the breaking of problem symmetries. The results indicate the limitations of a 2D analysis to predict the dynamics in the 3D environment. For example, it is shown how the loss of constraints may introduce characteristically non-2D instability mechanisms, and how small symmetry-breaking terms may result in the termination of solution branches.

Original language	English (US)
Pages (from-to)	147-176
Number of pages	30
Journal	Multibody System Dynamics
Volume	10
Issue number	2
DOIs	https://doi.org/10.1023/A:1025540401249
State	Published - Sep 2003
Externally published	Yes

Keywords

Bifurcations
Center manifold
Dynamical systems
Multibody modeling
Nonlinear dynamics
Passive bipedal mechanisms
Periodic motion
Symmetries

ASJC Scopus subject areas

Modeling and Simulation
Aerospace Engineering
Mechanical Engineering
Computer Science Applications
Control and Optimization

Online availability

10.1023/A:1025540401249

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title = "Breaking Symmetries and Constraints: Transitions from 2D to 3D in Passive Walkers",

abstract = "The inherent dynamics of bipedal, passive mechanisms are studied to investigate the relation between motions constrained to two-dimensional (2D) planes and those free to move in a three-dimensional (3D) environment. In particular, we develop numerical and analytical techniques using dynamical-systems methodology to address the persistence and stability changes of periodic, gait-like motions due to the relaxation of configuration constraints and the breaking of problem symmetries. The results indicate the limitations of a 2D analysis to predict the dynamics in the 3D environment. For example, it is shown how the loss of constraints may introduce characteristically non-2D instability mechanisms, and how small symmetry-breaking terms may result in the termination of solution branches.",

keywords = "Bifurcations, Center manifold, Dynamical systems, Multibody modeling, Nonlinear dynamics, Passive bipedal mechanisms, Periodic motion, Symmetries",

author = "Piiroinen, {Petri T.} and Dankowicz, {Harry J.} and Nordmark, {Arne B.}",

note = "Funding Information: Acknowledgment is made to the Thomas F. and Kate Miller Jeffress Memorial Trust for the partial support of this research. We also gratefully acknowledge the financial support from the Swedish Foundation for Strategic Research. We would like to thank Jesper Adolfsson for valuable insight and help and for permission to use Figure 1.",

year = "2003",

month = sep,

doi = "10.1023/A:1025540401249",

language = "English (US)",

volume = "10",

pages = "147--176",

journal = "Multibody System Dynamics",

issn = "1384-5640",

publisher = "Springer Netherlands",

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AU - Piiroinen, Petri T.

AU - Dankowicz, Harry J.

AU - Nordmark, Arne B.

N1 - Funding Information: Acknowledgment is made to the Thomas F. and Kate Miller Jeffress Memorial Trust for the partial support of this research. We also gratefully acknowledge the financial support from the Swedish Foundation for Strategic Research. We would like to thank Jesper Adolfsson for valuable insight and help and for permission to use Figure 1.

PY - 2003/9

Y1 - 2003/9

N2 - The inherent dynamics of bipedal, passive mechanisms are studied to investigate the relation between motions constrained to two-dimensional (2D) planes and those free to move in a three-dimensional (3D) environment. In particular, we develop numerical and analytical techniques using dynamical-systems methodology to address the persistence and stability changes of periodic, gait-like motions due to the relaxation of configuration constraints and the breaking of problem symmetries. The results indicate the limitations of a 2D analysis to predict the dynamics in the 3D environment. For example, it is shown how the loss of constraints may introduce characteristically non-2D instability mechanisms, and how small symmetry-breaking terms may result in the termination of solution branches.

AB - The inherent dynamics of bipedal, passive mechanisms are studied to investigate the relation between motions constrained to two-dimensional (2D) planes and those free to move in a three-dimensional (3D) environment. In particular, we develop numerical and analytical techniques using dynamical-systems methodology to address the persistence and stability changes of periodic, gait-like motions due to the relaxation of configuration constraints and the breaking of problem symmetries. The results indicate the limitations of a 2D analysis to predict the dynamics in the 3D environment. For example, it is shown how the loss of constraints may introduce characteristically non-2D instability mechanisms, and how small symmetry-breaking terms may result in the termination of solution branches.

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KW - Center manifold

KW - Dynamical systems

KW - Multibody modeling

KW - Nonlinear dynamics

KW - Passive bipedal mechanisms

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KW - Symmetries

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Breaking Symmetries and Constraints: Transitions from 2D to 3D in Passive Walkers

Abstract

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