Passive double pendulum in the wake of a cylinder forced to rotate emulates a cyclic human walking gait

Abstract

The goal of this work is to present a method based on fluid-structure interactions to enforce a desired trajectory on a passive double pendulum. In our experiments, the passive double pendulum represents human thigh and shank segments, and the interaction between the fluid and the structure comes from a hydrofoil attached to the double pendulum and interacting with the vortices that are shed from a cylinder placed upstream. When a cylinder is placed in flow, vortices are shed in the wake of the cylinder. When the cylinder is forced to rotate periodically, the frequency of the vortices that are shed in its wake can be controlled by controlling the frequency of cylinder's rotation. These vortices exert periodic forces on any structure placed in the wake of this cylinder. In our system, we placed a double pendulum fitted with a hydrofoil at its distal end in the wake of a rotating cylinder. The vortices exerted periodic forces on this hydrofoil which then forced the double pendulum to oscillate. We controlled the cylinder to rotate periodically, and measured the displacement of the double pendulum. By comparing the joint positions of the double pendulum with those of human hip, knee and ankle joint positions during walking, we show how the system is able to generate a human walking gait cycle on the double pendulum only using the interactions between the vortices and the hydrofoil.

Special issue: bioinspired fluid-structure interaction

“…The flag's piezoelectric power harvesting capability is investigated numerically and experimentally for varying geometrical and electrical parameters associated with two conditions that depend on the distance between the cylinder and flag. Carleton et al [13] present a method based on FSIs to enforce the trajectory of a passive double pendulum that represents human thigh and shank segments in a walking gait. The interaction between the fluid and the structure comes from a hydrofoil attached to the double pendulum and interacting with the vortices that are shed from a cylinder placed upstream.…”

Numerical simulation of flow around the legs during walking in water with implications for hydrotherapeutic exercise

“…By controlling this cylinder's rotation, we controlled the vortices that were shed in its wake. These vortices then interacted with hydrofoils that were attached to the passive leg and imposed a walking gait trajectory on the legs 21 . The success of our approach, as well as any other approach in imposing desired walking gait trajectories on patients in water-based exercises, depends on a proper understanding of the flow forces that act on the legs during such exercises.…”