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 place a double pendulum fitted with a hydrofoil at its distal end in the wake of a rotating cylinder. The vortices exert periodic forces on this hydrofoil which then forces the double pendulum to oscillate. We control the cylinder to rotate periodically, and measure 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.
more »
« less
This content will become publicly available on July 15, 2025
Force Transmission in Non-Uniform Fluid Flow by Controlling Vortices
This paper investigates the use of imposed rotations of an underwater cylinder reversing direction at a desired frequency in order to transmit vortices in a flow and enable a new method of underwater force transmission. A hydrofoil interacts with controlled vortices, which modulates the forces on the hydrofoil. The motivation is to assist and resist users walking on an underwater treadmill in a continuous-flow aquatic therapy pool used for gait rehabilitation, utilizing buoyancy to reduce apparent limb weight and impact force while walking. Previously, we have shown this concept on a small scale with a passive double pendulum when the incoming fluid flow is highly uniform. This paper shows that force transmission is also possible in such a harsh environment (a continuous-flow aquatic therapy pool) where the incoming flow is highly non-uniform and at a much larger scale. By measuring forces acting on a downstream hydrofoil, we show that the frequency of the vortices generated upstream can be perceived by the downstream hydrofoil.
more »
« less
- Award ID(s):
- 2024409
- PAR ID:
- 10559291
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 979-8-3503-5536-9
- Page Range / eLocation ID:
- 434 to 439
- Format(s):
- Medium: X
- Location:
- Boston, MA, USA
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Synopsis The study of underwater walking presents major challenges because the small forces applied during underwater walking are difficult to measure due to the lack of a sufficiently sensitive force plate that functions underwater. Understanding the force interaction between the underwater walker and the substrate may lead to better understanding of the evolution, ecology, and biomechanics of underwater walking. The shift from aquatic to terrestrial life was a crucial transition in animal evolution where, underwater walking preceded the invasion of land and combines mechanics from terrestrial locomotion (substrate reaction forces) and aquatic swimming (buoyancy and drag). In this work, we describe our design of a low-cost underwater force plate made using 3D printed multi axis load cells equipped with commercial strain gauges amplified with a custom circuit board, and custom code to gather force data. The use of 3D printed sensors allows customization of the material and thickness of the shear beam load cell to accommodate the loads for a wide range of study species. We show that our design can detect loads as small as 1 mN (filtered) with minimal noise and present sample live animal trials of several species. The 3D multiaxial load cells, circuit design, and custom code are open-source and available online.
-
null (Ed.)We present the dynamics of a hydrofoil free to oscillate in a plane as it interacts with vortices that are shed from a cylinder placed upstream. We consider cases where the cylinder is (i) fixed, (ii) forced to rotate constantly in one direction or (iii) forced to rotate periodically. When the upstream cylinder is fixed, at lower reduced velocities, the hydrofoil oscillates with a frequency equal to the frequency of vortices shed from the cylinder, and at higher reduced velocities with a frequency equal to half of the shedding frequency. When we force the cylinder to rotate in one direction, we control its wake and directly influence the response of the hydrofoil. When the rotation rate goes beyond a critical value, the vortex shedding in the cylinder's wake is suppressed and the hydrofoil is moved to one side and remains mainly static. When we force the cylinder to rotate periodically, we control the frequency of vortex shedding, which will be equal to the rotation frequency. Then at lower rotation frequencies, the hydrofoil interacts with one of the vortices in its oscillation path in the positive crossflow (transverse) direction, and with the second vortex in the negative crossflow direction, resulting in a 2:1 ratio between its inline and crossflow oscillations and a figure-eight trajectory. At higher rotation frequencies, the hydrofoil interacts with both shed vortices on its positive crossflow path and again in its negative crossflow path, resulting in a 1:1 ratio between its inline and crossflow oscillations and a linear trajectory.more » « less
-
more » « less
Synopsis Underwater walking was a crucial step in the evolutionary transition from water to land. Underwater walkers use fins and/or limbs to interact with the benthic substrate and produce propulsive forces. The dynamics of underwater walking remain poorly understood due to the lack of a sufficiently sensitive and waterproof system to measure substrate reaction forces (SRFs). Using an underwater force plate (described in our companion paper), we quantify SRFs during underwater walking in axolotls (Ambystoma mexicanum) and Spot prawn (Pandalus platyceros), synchronized with videography. The horizontal propulsive forces were greater than the braking forces in both species to overcome hydrodynamic drag. In axolotls, potential energy (PE) fluctuations were far smaller than kinetic energy (KE) fluctuations due to high buoyant support (97%), whereas the magnitudes were similar in the prawn due to lower buoyant support (93%). However, both species show minimal evidence of exchange between KE and PE, which, along with the effects of hydrodynamic drag, is incompatible with inverted pendulum dynamics. Our results show that, despite their evolutionary links, underwater walking has fundamentally different dynamics compared with terrestrial walking and emphasize the substantial consequences of differences in body plan in underwater walking.
-
more » « less
Abstract Objects moving in water or stationary objects in streams create a vortex wake. An underwater robot encountering the wake created by another body experiences disturbance forces and moments. These disturbances can be associated with the disturbance velocity field and the bodies creating them. Essentially, the vortex wakes encode information about the objects and the flow conditions. Underwater robots that often function with constrained sensing capabilities can benefit from extracting this information from vortex wakes. Many species of fish do exactly this, by sensing flow features using their lateral lines as part of their multimodal sensing capabilities. Besides the necessary sensing hardware, a more important aspect of sensing is related to the algorithms needed to extract the relevant information about the flow. This paper advances a framework for such an algorithm using the setting of a pitching hydrofoil in the wake of a thin plate (obstacle). Using time series pressure measurements on the surface of the hydrofoil and the angular velocity of the hydrofoil, a Koopman operator is constructed that propagates the time series forward in time. Multiple approaches are used to extract dynamic information from the Koopman operator to estimate the plate position and are bench marked against a state-of-the-art convolutional neural network (CNN) applied directly to the time series. We find that using the Koopman operator for feature extraction improves the estimation accuracy compared to the CNN for the same purpose, enabling “blind” sensing using the lateral line.
