Breaking Symmetries and Constraints: Transitions from 2D to 3D in Passive Walkers |
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| Authors: | Piiroinen Petri T. Dankowicz Harry J. Nordmark Arne B. |
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| Affiliation: | (1) Department of Engineering Mathematics, University of Bristol, Bristol, BS2 1TR, U.K.;(2) Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, U.S.A;(3) Department of Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden |
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| Abstract: | The inherent dynamics of bipedal, passive mechanisms are studiedto investigate the relation between motions constrained to two-dimensional (2D)planes and those free to move in a three-dimensional (3D) environment. Inparticular, we develop numerical and analytical techniques usingdynamical-systems methodology to address the persistence and stabilitychanges of periodic, gait-like motions due to the relaxation ofconfiguration constraints and the breaking of problem symmetries. Theresults indicate the limitations of a 2D analysis to predictthe dynamics in the 3D environment. For example, it is shownhow the loss of constraints may introduce characteristically non-2Dinstability mechanisms, and how small symmetry-breaking terms may result inthe termination of solution branches. |
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| Keywords: | passive bipedal mechanisms periodic motion symmetries center manifold bifurcations nonlinear dynamics multibody modeling dynamical systems |
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