Multibody System Dynamics

, Volume 10, Issue 2, pp 147–176

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


  • Petri T. Piiroinen
    • Department of Engineering MathematicsUniversity of Bristol
  • Harry J. Dankowicz
    • Department of Engineering Science and MechanicsVirginia Polytechnic Institute and State University
  • Arne B. Nordmark
    • Department of MechanicsRoyal Institute of Technology

DOI: 10.1023/A:1025540401249

Cite this article as:
Piiroinen, P.T., Dankowicz, H.J. & Nordmark, A.B. Multibody System Dynamics (2003) 10: 147. doi:10.1023/A:1025540401249


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.

passive bipedal mechanismsperiodic motionsymmetriescenter manifoldbifurcationsnonlinear dynamicsmultibody modelingdynamical systems
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© Kluwer Academic Publishers 2003