Bipedal Walking and Autobalancing

This thesis explores the dynamics of two mechanical systems capable of performing their tasks without the use of active control. The first system is an autobalancer, which can continuously balance rotating machinery. This is accomplished by using compensating masses that move in a viscous media about the axis of rotation. The second system is a passive bipedal walker, capable of human like gait in the absence of external active control. Since there is no control system to suppress errors in the mechanisms it is important to have a detailed knowledge of how parameters influence on these systems. The dynamics of mechanical models, such as the three dimensional passive walker and autobalancer, are explored and understood using standard dynamical systems methods. This includes calculating the stability of equilibrium positions and limit cycles and creating bifurcation diagrams as parameters of the system are varied. In the case of the autobalancer it is possible to analytically solve for the equilibrium positions. In the passive walker the stability of limit cycles, which corresponds to periodic gaits, are studied. To find these limit cycles a Newton-Raphson root solving scheme is implemented. The model for the autobalancer results in a smooth dynamical system whereas the passive walker includes different kinds of discontinuities. These discontinuities are taken care of by introducing suitable mappings. Results for the autobalancer include suggestions on how to choose parameters of the systems and how to avoid possible dangerous parameter combinations. It also explains some experimentally observed limit cycles. In the case of the passive walker, it is shown how the planar passive walker can be extended into a fully three dimensional walker having dynamics in all spatial directions. Many parameter studies are reported which give an insight to the dynamics of the system. The thesis ends with an report on the search for an implementable passive walker. The methods introduced in this thesis are not limited to the study of autobalancing and passive bipedal walking but are applicable to many mechanical systems with or without discontinuities. autobalancing, bipedal walking, multibody systems, nonlinear dynamics, stability, bifurcations, limit cycles, variational equations, discontinuities Descriptors: