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

Authors: Piiroinen, P T, Dankowicz, H., Nordmark, A.
Document Type: Article
Pubstate: Accepted
Journal: Multibody System Dynamics
Year: 2002


The inherent dynamics of bipedal, passive mechanisms are studied to investigate the relation between motions constrained to two-dimensional planes and those free to move in a three-dimensional 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 two-dimensional analysis to predict the dynamics in the three-dimensional 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.