Bending rules for animal propulsion

A 3-DOF caudal fin for precise maneuvering of thunniform-inspired unmanned underwater vehicles

Unmanned underwater vehicles (UUVs) will see increased use in scientific research, military operations and maintenance of industrial infrastructure. Many of these applications require that the vehicle possess a long range while retaining precise maneuvering or station-keeping capabilities. Both current UUVs and biological swimmers, often considered the basis for the next generation of UUVs, face a trade-off between the two characteristics. Here, we introduce a novel hybrid propeller concept that enables thunniform-inspired vehicles, which imitate nature's most efficient swimmers, to also achieve high maneuverability. The propeller can produce enhanced three-dimensional kinematics of the caudal fin. An optimization procedure based on real-time experimental data is used to obtain the best kinematics to maneuver the vehicle, and a 4-step strategy is uncovered that results in a 49% increase in maneuverability with respect to conventional 2-D kinematics. The proposed mechanism is shown to be effective for a wide range of fin geometries and stiffness values.

Comparing age- and bone-related differences in collagen fiber orientation: A case study of bats and laboratory mice using quantitative polarized light microscopy

As bones age in most mammals, they typically become more fragile. This state of bone fragility is often associated with more homogenous collagen fiber orientations (CFO). Unlike most mammals, bats maintain mechanically competent bone throughout their lifespans, but little is known of positional and age-related changes in CFO within wing bones. This study tests the hypothesis that age-related changes in CFO in big brown bats (Eptesicus fuscus) differ from those of the standard mammalian model for skeletal aging, the C57BL/6 laboratory mouse. We used data from quantitative polarized light microscopy (qPLM) to compare CFO across the lifespan of long-lived big brown bats and age matched C57BL/6 mice. Eptesicus and C57BL/6 mice displayed idiosyncratic patterns of CFO. Consistent age-related changes were only apparent in the outer cortical bone of Eptesicus, where bone tissue is more longitudinally arranged and more anisotropic in older individuals. Both taxa displayed a ring of more transversely oriented bone tissue surrounding the medullary cavity. In Eptesicus, this tissue represents a greater proportion of the overall cross-section, and is more clearly helically aligned (arranged at 45° to the bone long axis) than similar bone tissue in mice. Bat wing bones displayed a proximodistal gradient in CFO anisotropy and longitudinal orientation in both outer and inner cortical bone compartments. This study lays a methodological foundation for the quantitative evaluation of bone tissue architecture in volant and non-volant mammals that may be expanded in the future.

The spatiotemporal richness of hummingbird wing deformations

Animals exhibit an abundant diversity of forms, and this diversity is even more evident when considering animals that can change shape on demand. The evolution of flexibility contributes to aspects of performance from propulsive efficiency to environmental navigation. It is, however, challenging to quantify and compare body parts that, by their nature, dynamically vary in shape over many time scales. Commonly, body configurations are tracked by labelled markers and quantified parametrically through conventional measures of size and shape (descriptor approach) or non-parametrically through data-driven analyses that broadly capture spatiotemporal deformation patterns (shape variable approach). We developed a weightless marker tracking technique and combined these analytic approaches to study wing morphological flexibility in hoverfeeding Anna's hummingbirds (Calypte anna). Four shape variables explained >95% of typical stroke cycle wing shape variation and were broadly correlated with specific conventional descriptors such as wing twist and area. Moreover, shape variables decomposed wing deformations into pairs of in-plane and out-of-plane components at integer multiples of the stroke frequency. This property allowed us to identify spatiotemporal deformation profiles characteristic of hoverfeeding with experimentally imposed kinematic constraints, including through shape variables explaining <10% of typical shape variation. Hoverfeeding in front of a visual barrier restricted stroke amplitude and elicited increased stroke frequencies together with in-plane and out-of-plane deformations throughout the stroke cycle. Lifting submaximal loads increased stroke amplitudes at similar stroke frequencies together with prominent in-plane deformations during the upstroke and pronation. Our study highlights how spatially and temporally distinct changes in wing shape can contribute to agile fluidic locomotion.

Design and build of small-scale magnetic soft-bodied robots with multimodal locomotion

Small-scale magnetic soft-bodied robots can be designed to operate based on different locomotion modes to navigate and function inside unstructured, confined and varying environments. These soft millirobots may be useful for medical applications where the robots are tasked with moving inside the human body. Here we cover the entire process of developing small-scale magnetic soft-bodied millirobots with multimodal locomotion capability, including robot design, material preparation, robot fabrication, locomotion control and locomotion optimization. We describe in detail the design, fabrication and control of a sheet-shaped soft millirobot with 12 different locomotion modes for traversing different terrains, an ephyra jellyfish-inspired soft millirobot that can manipulate objects in liquids through various swimming modes, a larval zebrafish-inspired soft millirobot that can adjust its body stiffness for efficient propulsion in different swimming speeds and a dual stimuli-responsive sheet-shaped soft millirobot that can switch its locomotion modes automatically by responding to changes in the environmental temperature. The procedure is aimed at users with basic expertise in soft robot development. The procedure requires from a few days to several weeks to complete, depending on the degree of characterization required.

Escape performance in the cyclopoid copepod Oithona davisae

Escaping a predator is one of the keys to success for any living creature. The performance of adults (males, females, and ovigerous females) of the cyclopoid copepod Oithona davisae exposed to an electrical stimulus is analysed as a function of temperature by measuring characteristic parameters associated with the escape movement (distance covered, duration of the appendage movement, mean and maximum escape speeds, Reynolds number). In addition, as a proxy for the efficiency of the motion, the Strouhal number was calculated. The escape performance showed temperature-dependent relationships within each adult state, as well as differences between sexes; additionally, changes owing to the presence of the egg sac were recorded in females. In a broader perspective, the results collected reveal the occurrence of different behavioural adaptations in males and females, adding to the comprehension of the mechanisms by which O. davisae interacts with its environment and shedding new light on the in situ population dynamics of this species.

The hydrodynamics and kinematics of the appendicularian tail underpin peristaltic pumping

Planktonic organisms feed while suspended in water using various hydrodynamic pumping strategies. Appendicularians are a unique group of plankton that use their tail to pump water over mucous mesh filters to concentrate food particles. As ubiquitous and often abundant members of planktonic ecosystems, they play a major role in oceanic food webs. Yet, we lack a complete understanding of the fluid flow that underpins their filtration. Using high-speed, high-resolution video and micro particle image velocimetry, we describe the kinematics and hydrodynamics of the tail in Oikopleura dioica in filtering and free-swimming postures. We show that sinusoidal waves of the tail generate peristaltic pumping within the tail chamber with fluid moving parallel to the tail when filtering. We find that the tail contacts attachment points along the tail chamber during each beat cycle, serving to seal the tail chamber and drive pumping. When we tested how the pump performs across environmentally relevant temperatures, we found that the amplitude of the tail was invariant but tail beat frequency increased threefold across three temperature treatments (5°C, 15°C and 25°C). Investigation into this unique pumping mechanism gives insight into the ecological success of appendicularians and provides inspiration for novel pump designs.

Computational Study of Stiffness-Tuning Strategies in Anguilliform Fish

Biological evidence demonstrates that fish can tune their body stiffness to improve thrust and efficiency during swimming locomotion. However, the stiffness-tuning strategies that maximize swimming speed or efficiency are still unclear. In the present study, a musculo-skeletal model of anguilliform fish is developed to study the properties of variable stiffness, in which the planar serial-parallel mechanism is used to model the body structure. The calcium ion model is adopted to simulate muscular activities and generate muscle force. Further, the relations among the forward speed, the swimming efficiency, and Young's modulus of the fish body are investigated. The results show that for certain body stiffness, the swimming speed and efficiency are increased with the tail-beat frequency until reaching the maximum value and then decreased. The peak speed and efficiency are also increased with the amplitude of muscle actuation. Anguilliform fish tend to vary their body stiffness to improve the swimming speed and efficiency at a high tail-beat frequency or small amplitude of muscle actuation. Furthermore, the midline motions of anguilliform fish are analyzed by the complex orthogonal decomposition (COD) method, and the discussions of fish motions associated with the variable body stiffness and the tail-beat frequency are also presented. Overall, the optimal swimming performance of anguilliform fish benefits from the matching relationships among the muscle actuation, the body stiffness, and the tail-beat frequency.

Ultrafast Miniature Robotic Swimmers with Upstream Motility

With the development of materials science and micro-nano fabrication techniques, miniature soft robots at millimeter or submillimeter size can be manufactured and actuated remotely. The small-scaled robots have the unique capability to access hard-to-reach regions in the human body in a noninvasive manner. To date, it is still challenging for miniature robots to accurately move in the diverse and dynamic environments in the human body (e.g., in blood flow). To effectively locomote in the vascular system, miniature swimmers with upstream swimming capability are required. Herein, we design and fabricate a miniature robotic swimmer capable of performing ultrafast swimming in a fluidic environment. The maximum velocity of the swimmer in water is 30 cm/s, which is 60 body lengths. Moreover, in a tubular environment, the swimmer can still obtain a swimming velocity of 17 cm/s. The swimmer can also perform upstream swimming in a tubular environment with a velocity of 5 cm/s when the flow speed is 10 cm/s. The ultrasound-guided navigation of the swimmer in a phantom mimicking a blood vessel is also realized. This work gives insight into the design of agile undulatory milliswimmers for future biomedical applications.

The effect of dynamic twisting on the flow field and the unsteady forces of a heaving flat plate

Many marine animals can dynamically twist their pectoral fins while swimming. The effects of such dynamic twisting on the unsteady forces on the fin and its surrounding flow field are yet to be understood in detail. In this paper, a flat plate executing a heaving maneuver is subjected to a similar dynamic twisting. In particular, the effects of the direction of twist, non-dimensional heaving amplitude, and reduced frequency are studied using a force sensor and particle image velocimetry (PIV) measurements. Two reduced frequencies,k=0.105, and0.209, and two twisting modes are investigated. In the first twisting mode, the plate is twisted in the direction of the heave (forward-twist), and in the second mode, the plate is twisted opposite to the direction of the heave (backward-twist). Force sensor measurements show that the forward-twist recovers some of the lift that is usually lost during the upstroke of flapping locomotion. Additionally, the forward-twist maintains a near-constant lift coefficient during the transition between downstroke and upstroke, suggesting a more stable form of locomotion. PIV results show that forward-twist limits circulation and leading-edge vortex growth during the downstroke, keepingCd≈0at the cost of the reduced lift. By contrast, backward-twist increases the circulation during the downstroke, resulting in large increases in both lift and drag coefficients. Force sensor data also showed that this effect on the lift is reversed during the upstroke, where the backward-twist causes a negative lift. The effects of each twisting mode are mainly caused by the changes in the shear layer velocity that occur as a result of twisting about the spanwise axis along the mid-chord. The twisting performed by forward-twist reduces the effective angle of attack through the upstroke and downstroke, resulting in a reduced shear layer velocity and lower circulation. The twisting performed by backward-twist does the exact opposite, increasing the effective angle of attack through the upstroke and downstroke and consequently increasing the shear layer velocity and circulation.

Deep-time invention and hydrodynamic convergences through amniote flipper evolution

The diapsid plesiosaurs were pelagic and inhabited the oceans from the Triassic to the Cretaceous. A key evolutionary character of plesiosaurs is the four wing-like flippers. While it is mostly accepted that plesiosaurs were underwater fliers like marine turtles, penguins, and maybe whales, other swimming styles have been suggested in the past. These are rowing and a combination of rowing and underwater flight (e.g., pig-nosed turtle, sea lion). Underwater fliers use lift in contrast to rowers that employ drag. For efficiently profiting of lift during underwater flying, it is necessary that plesiosaurs twisted their flippers by muscular activity. To research the evolution of flipper twisting in plesiosaurs and functionally analogous taxa, including turtles, we used anatomical network analysis (AnNA) and reassessed distal flipper muscle functions. We coded bone-to-bone and additionally muscle-to-bone contacts in N × N matrices for foreflippers of the plesiosaur, the loggerhead sea turtle, the pig-nosed turtle, the African penguin, the California sea lion, and the humpback whale based on literature data. In "R," "igraph" was run by using a walktrap algorithm to obtain morphofunctional modules. AnNA revealed that muscle-to-bone contacts are needed to detect contributions of modules to flipper motions, whereas only-bone matrices are not informative for that. Furthermore, the plesiosaur, the marine turtles, the seal, and the penguin flipper twisting mechanisms, but the penguin cannot actively twist the flipper trailing edge. Finally, the foreflipper of the pig-nosed turtle and of the whale is not actively twisted during swimming.

Snapping for high-speed and high-efficient butterfly stroke-like soft swimmer

Natural selection has tuned many flying and swimming animals to share the same narrow design space for high power efficiency, e.g., their dimensionless Strouhal numbers St that relate flapping frequency and amplitude and forward speed fall within the range of 0.2 < St < 0.4 for peak propulsive efficiency. It is rather challenging to achieve both comparably fast-speed and high-efficient soft swimmers to marine animals due to the naturally selected narrow design space and soft body compliance. Here, bioinspired by the flapping motion in swimming animals, we report leveraging snapping instabilities for soft flapping-wing swimmers with comparable high performance to biological counterparts. The lightweight, butterfly stroke-like soft swimmer (2.8 g) demonstrates a record-high speed of 3.74 body length/s (4.8 times faster than the reported fastest flapping soft swimmer), high power efficiency (0.2 < St = 0.25 < 0.4), low energy consumption cost, and high maneuverability (a high turning speed of 157°/s).

A tale of two fish tails: does a forked tail really perform better than a truncate tail when cruising?

Many fishes use their tail as the main thrust producer during swimming. This fin's diversity in shape and size influences its physical interactions with water as well as its ecological functions. Two distinct tail morphologies are common in bony fishes: flat, truncate tails which are best suited for fast accelerations via drag forces, and forked tails that promote economical, fast cruising by generating lift-based thrust. This assumption is based primarily on studies of the lunate caudal fin of Scombrids (i.e. tuna, mackerel), which is comparatively stiff and exhibits an airfoil-type cross-section. However, this is not representative of the more commonly observed and taxonomically widespread flexible forked tail, yet similar assumptions about economical cruising are widely accepted. Here, we present the first comparative experimental study of forked versus truncate tail shape and compare the fluid mechanical properties and energetics of two common nearshore fish species. We examined the hypothesis that forked tails provide a hydrodynamic advantage over truncate tails at typical cruising speeds. Using experimentally derived pressure fields, we show that the forked tail produces thrust via acceleration reaction forces like the truncate tail during cruising but at increased energetic costs. This reduced efficiency corresponds to differences in the performance of the two tail geometries and body kinematics to maintain similar overall thrust outputs. Our results offer insights into the benefits and tradeoffs of two common fish tail morphologies and shed light on the functional morphology of fish swimming to guide the development of bio-inspired underwater technologies.

How Non-Uniform Stiffness Affects the Propulsion Performance of a Biomimetic Robotic Fish

Live fish in nature exhibit various stiffness characteristics. The anguilliform swimmer, like eels, has a relatively flexible body, while the thunniform swimmer, like the swordfishes, has a much stiffer body. Correspondingly, in the design of biomimetic robotic fish, how to balance the non-uniform stiffness to achieve better propulsion performance is an essential question needed to be answered. In this paper, we conduct an experimental study on this question. First, a customized experimental platform is built, which eases the adjustment of the non-uniform stiffness ratio, the stiffness of the flexible part, the flapping frequency, and the flapping amplitude. Second, extensive experiments are carried out, finding that to maximize the propulsion performance of the biomimetic robotic fish, the non-uniform stiffness ratio is required to adapt to different locomotor parameters. Specifically, the non-uniform stiffness ratio needs to be reduced when the robotic fish works at low frequency, and it needs to be increased when the robotic fish works at high frequency. Finally, detailed discussions are given to further analyze the experimental results. Overall, this study can shed light on the design of a non-uniform biomimetic robotic fish, which helps to increase its propulsion performance.

Tailoring the bending pattern of non-uniformly flexible pitching hydrofoils enhances propulsive efficiency

We present new measurements of non-uniformly flexible pitching foils fabricated with a rigid leading section joined to a flexible trailing section. This construction enables us to vary the bending pattern and resonance condition of the foils independently. A novel effective flexibility, defined as the ratio of added mass forces to elastic forces, is proposed and shown to provide a scaling for the natural frequencies of the fluid-structural system. Foils with very flexible trailing sections ofEI< 1.81 × 10^-5N m²do not show a detectable resonance and are classified as 'non-resonating' as opposed to 'resonating' foils. Moreover, the non-resonating foils exhibit a novel bending pattern where the foil has a discontinuous hinge-like deflection instead of the smooth beam-like deflection of the resonating foils. Performance measurements reveal that both resonating and non-resonating foils can achieve high propulsive efficiencies of around 50% or more. It is discovered that non-uniformly flexible foils outperform their rigid and uniformly flexible counterparts, and that there is an optimal flexion ratio from 0.4 ⩽λ⩽ 0.7 that maximizes the efficiency. Furthermore, this optimal range coincides with the flexion ratios observed in nature. Performance is also compared under the same dimensionless flexural rigidity,R*, which highlights that at the same flexion ratio more flexible foils achieve higher peak efficiencies. Overall, to achieve high propulsive efficiency non-uniformly flexible hydrofoils should (1) oscillate above their first natural frequency, (2) have a flexion ratio in the range of 0.4 ⩽λ⩽ 0.7 and (3) have a small dimensionless rigidity at their optimal flexion ratio. Scaling laws for rigid pitching foils are found to be valid for non-uniformly flexible foils as long as the measured amplitude response is used and the deflection angle of the trailing sectionβ is < 45°. This work provides guidance for the development of high-performance underwater vehicles using simple purely pitching bio-inspired propulsive drives.

Fluid-structure interaction of bio-inspired flexible slender structures: a review of selected topics

Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.

Effects of Bionic Pectoral Fin Rays’ Spanwise Flexibility on Forwarding Propulsion Performance

Oscillating pectoral fins’ spanwise flexibility is a key factor influencing the forwarding propulsion performance of bionic cownose rays, including thrust and heave-pitch stability. This study explores the effects of the bionic pectoral fin ray’s spanwise flexibility on its propulsion performance via experiments. Inspired by the cownose ray, a pair of bionic pectoral fins with fin rays and fabric skin was designed, and two motors drive the controllable flapping motion. The bionic pectoral fins’ flexibility can be quantified by using fin rays’ bending stiffness. The experiments were carried out in a water tank to measure the thrust, the lift force, and the pitch moment of the bionic cownose ray. The fin rays are divided into plastic sheets of five thicknesses and three fin rays with more obvious stiffness variations. The movement parameters included the following: the flapping frequency of 0.3–0.7 Hz, the flapping amplitude of 20–40°, and the phase difference of 20–40°. The experimental results show that the stiffness of the bionic pectoral fin rays plays an important role in the thrust, lift force, and pitch moment. The fin rays with high stiffness root segment and low stiffness tip segment have lower lift and pitch moment while maintaining a high thrust. This shows that the pectoral fins’ flexible characteristics of the cownose ray are of great significance to the design of the bionic prototype.

Eulerian simulation of complex suspensions and biolocomotion in three dimensions

Fluid–structure interactions are ubiquitous in many natural and man-made environments. They are difficult to study analytically, and therefore accurate and flexible computational methods are an indispensable tool in the field. Typically, fluids are simulated with a fixed background computational mesh, whereas a solid is simulated with a mesh that moves with it, making it challenging to couple the two. Here we develop a three-dimensional computational method where both fluid and solid can be represented on a fixed computational grid, which simplifies the coupling between the two phases considerably. Our method can simulate scenarios that are difficult to do with other methods, such as complex suspensions containing soft particles that are both heavier and lighter than the fluid.

We present a numerical method specifically designed for simulating three-dimensional fluid–structure interaction (FSI) problems based on the reference map technique (RMT). The RMT is a fully Eulerian FSI numerical method that allows fluids and large-deformation elastic solids to be represented on a single fixed computational grid. This eliminates the need for meshing complex geometries typical in other FSI approaches and greatly simplifies the coupling between fluid and solids. We develop a three-dimensional implementation of the RMT, parallelized using the distributed memory paradigm, to simulate incompressible FSI with neo-Hookean solids. As part of our method, we develop a field extrapolation scheme that works efficiently in parallel. Through representative examples, we demonstrate the method’s suitability in investigating many-body and active systems, as well as its accuracy and convergence. The examples include settling of a mixture of heavy and buoyant soft ellipsoids, lid-driven cavity flow containing a soft sphere, and swimmers actuated via active stress.

Tunable stiffness in fish robotics: mechanisms and advantages

One of the emerging themes of fish-inspired robotics is flexibility. Adding flexibility to the body, joints, or fins of fish-inspired robots can significantly improve thrust and/or efficiency during locomotion. However, the optimal stiffness depends on variables such as swimming speed, so there is no one 'best' stiffness that maximizes efficiency in all conditions. Fish are thought to solve this problem by using muscular activity to tune their body and fin stiffness in real-time. Inspired by fish, some recent robots sport polymer actuators, adjustable leaf springs, or artificial tendons that tune stiffness mechanically. Models and water channel tests are providing a theoretical framework for stiffness-tuning strategies that devices can implement. The strategies can be thought of as analogous to car transmissions, which allow users to improve efficiency by tuning gear ratio with driving speed. We provide an overview of the latest discoveries about (1) the propulsive benefits of flexibility, particularlytunableflexibility, and (2) the mechanisms and strategies that fish and fish-inspired robots use to tune stiffness while swimming.

Kinematics and hydrodynamics analyses of swimming penguins: wing bending improves propulsion performance

Penguins are adapted to underwater life and have excellent swimming abilities. Although previous motion analyses revealed their basic swimming characteristics, the details of the 3D wing kinematics, wing deformation and thrust generation mechanism of penguins are still largely unknown. In this study, we recorded the forward and horizontal swimming of gentoo penguins (Pygoscelis papua) at an aquarium with multiple underwater action cameras and then performed a 3D motion analysis. We also conducted a series of water tunnel experiments with a 3D printed rigid wing to obtain lift and drag coefficients in the gliding configuration. Using these coefficients, the thrust force during flapping was calculated in a quasi-steady manner, where the following two wing models were considered: (1) an 'original' wing model reconstructed from 3D motion analysis including bending deformation and (2) a 'flat' wing model obtained by flattening the original wing model. The resultant body trajectory showed that the penguin accelerated forward during both upstroke and downstroke. The motion analysis of the two wing models revealed that considerable bending occurred in the original wing, which reduced its angle of attack during the upstroke in particular. Consequently, the calculated stroke-averaged thrust was larger for the original wing than for the flat wing during the upstroke. In addition, the propulsive efficiency for the original wing was estimated to be 1.8 times higher than that for the flat wing. Our results unveil a detailed mechanism of lift-based propulsion in penguins and underscore the importance of wing bending.

Tunable stiffness enables fast and efficient swimming in fish-like robots

Fish maintain high swimming efficiencies over a wide range of speeds. A key to this achievement is their flexibility, yet even flexible robotic fish trail real fish in terms of performance. Here, we explore how fish leverage tunable flexibility by using their muscles to modulate the stiffness of their tails to achieve efficient swimming. We derived a model that explains how and why tuning stiffness affects performance. We show that to maximize efficiency, muscle tension should scale with swimming speed squared, offering a simple tuning strategy for fish-like robots. Tuning stiffness can double swimming efficiency at tuna-like frequencies and speeds (0 to 6 hertz; 0 to 2 body lengths per second). Energy savings increase with frequency, suggesting that high-frequency fish-like robots have the most to gain from tuning stiffness.

High-Efficiency Can Be Achieved for Non-Uniformly Flexible Pitching Hydrofoils via Tailored Collective Interactions

New experiments examine the interactions between a pair of three-dimensional (AR = 2) non-uniformly flexible pitching hydrofoils through force and efficiency measurements. It is discovered that the collective efficiency is improved when the follower foil has a nearly out-of-phase synchronization with the leader and is located directly downstream with an optimal streamwise spacing of X*=0.5. The collective efficiency is further improved when the follower operates with a nominal amplitude of motion that is 36% larger than the leader’s amplitude. A slight degradation in the collective efficiency was measured when the follower was slightly-staggered from the in-line arrangement where direct vortex impingement is expected. Operating at the optimal conditions, the measured collective efficiency and thrust are ηC=62% and CT,C=0.44, which are substantial improvements over the efficiency and thrust of ηC=29% and CT,C=0.16 of two fully-rigid foils in isolation. This demonstrates the promise of achieving high-efficiency with simple purely pitching mechanical systems and paves the way for the design of high-efficiency bio-inspired underwater vehicles.

Metachronal motion across scales: current challenges and future directions

Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Lastly, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.

Effect of body stiffness distribution on larval fish-like efficient undulatory swimming

Energy-efficient propulsion is a critical design target for robotic swimmers. Although previous studies have pointed out the importance of nonuniform body bending stiffness distribution (k) in improving the undulatory swimming efficiency of adult fish-like robots in the inertial flow regime, whether such an elastic mechanism is beneficial in the intermediate flow regime remains elusive. Hence, we develop a class of untethered soft milliswimmers consisting of a magnetic composite head and a passive elastic body with different k These robots realize larval zebrafish-like undulatory swimming at the same scale. Investigations reveal that uniform k and high swimming frequency (60 to 100 Hz) are favorable to improve their efficiency. A shape memory polymer-based milliswimmer with tunable k on the fly confirms such findings. Such acquired knowledge can guide the design of energy-efficient leading edge-driven soft undulatory milliswimmers for future environmental and biomedical applications in the same flow regime.

A tail's tale: Biomechanical roles of dorsal thoracic spine of barnacle nauplii

Many marine invertebrates have complex life histories that begin with a planktonic larval stage. Similar to other plankton, these larval invertebrates often possess protruding body extensions, but their function beyond predator deterrence is not well-documented. For example, the planktonic nauplii of crustaceans have spines. Using the epibiotic pedunculate barnacle Octolasmis spp., we investigated how the dorsal thoracic spine affects swimming and fluid disturbance by comparing nauplii with their spines partially removed against those with intact spines. Our motion analysis showed that amputated Octolasmis spp. swam slower, in jerkier trajectories, and were less efficient per stroke cycle than those with intact spines. Amputees showed alterations in limb beat pattern: larger beat amplitude, increased phase lag, and reduced contralateral symmetry. These changes might partially help increase propulsive force generation and streamline the flow, but were insufficient to restore full function. Particle image velocimetry further showed that amputees had a larger relative area of influence, implying elevated risk by rheotactic predator. Body extensions and their interactions with limb motion play important biomechanical roles in shaping larval performance, which likely influences the evolution of form.

Effects of root chord movement on thrust generation of oscillatory pectoral fins

Fin kinematics is the key to thrust generation of oscillatory pectoral fins of manta rays. This could be one of the main reasons that fin designs of robotic manta rays are becoming more complex to simulate the fin kinematics more closely so as to generate high thrusts. However, as the trend suggests, the extent of improvement to thrust generation might not be worth the complexities added to the designs. Out-of-the-box design changes that favour the simplicity and yet improve the fin performance can be a sound replicate for the complicated fin design features. One aspect of manta rays' pectoral fins that influences the fin kinematics is the constraint imposed on the movement of their particularly long root chord that is entirely attached to the body of manta rays. Hypothetically, reducing such a constraint can promote the angle-of-attack during flapping, which can improve thrust generation. This paper aims to study if the simple idea of disengagement of the fin root chord from the body, which is obviously a deviation from the nature, can improve thrust generation. An experiment was conducted on thrust generation of four basic fin designs, where different portions of their chord was disengaged from the body step-by-step. The disengagement occurred for each quarter of the chord, starting from the trailing edge towards the leading edge. It was found that the fins with free root chord (minimal attachment to the body) could generate thrust slightly less than the fully constrained fins (full attachment). In addition, it was shown that thrust generation efficiency kept increasing while disengaging the chord further, and reached the maximum for free root chord. This may show that a powerful and yet more efficient fin can be produced with such a deviation from the nature.

The role of suction thrust in the metachronal paddles of swimming invertebrates

An abundance of swimming animals have converged upon a common swimming strategy using multiple propulsors coordinated as metachronal waves. The shared kinematics suggest that even morphologically and systematically diverse animals use similar fluid dynamic relationships to generate swimming thrust. We quantified the kinematics and hydrodynamics of a diverse group of small swimming animals who use multiple propulsors, e.g. limbs or ctenes, which move with antiplectic metachronal waves to generate thrust. Here we show that even at these relatively small scales the bending movements of limbs and ctenes conform to the patterns observed for much larger swimming animals. We show that, like other swimming animals, the propulsors of these metachronal swimmers rely on generating negative pressure along their surfaces to generate forward thrust (i.e., suction thrust). Relying on negative pressure, as opposed to high pushing pressure, facilitates metachronal waves and enables these swimmers to exploit readily produced hydrodynamic structures. Understanding the role of negative pressure fields in metachronal swimmers may provide clues about the hydrodynamic traits shared by swimming and flying animals.

A novel cylindrical overlap-and-fling mechanism used by sea butterflies

The clap-and-fling mechanism is a well-studied, unsteady lift generation mechanism widely used by flying insects and is considered obligatory for tiny insects flying at low to intermediate Reynolds numbers, Re However, some aquatic zooplankters including some pteropod (i.e. sea butterfly) and heteropod species swimming at low to intermediate Re also use the clap-and-fling mechanism. These marine snails have extremely flexible, actively deformed, muscular wings which they flap reciprocally to create propulsive force, and these wings may enable novel lift generation mechanisms not available to insects, which have less flexible, passively deformed wings. Using high-speed stereophotogrammetry and micro-particle image velocimetry, we describe a novel cylindrical overlap-and-fling mechanism used by the pteropod species Cuvierina atlantica In this maneuver, the pteropod's wingtips overlap at the end of each half-stroke to sequentially form a downward-opening cone, a cylinder and an upward-opening cone. The transition from downward-opening cone to cylinder produces a downward-directed jet at the trailing edges. Similarly, the transition from cylinder to upward-opening cone produces downward flow into the gap between the wings, a leading edge vortex ring and a corresponding sharp increase in swimming speed. The ability of this pteropod species to perform the cylindrical overlap-and-fling maneuver twice during each stroke is enabled by its slender body and highly flexible wings. The cylindrical overlap-and-fling mechanism observed here may inspire the design of new soft robotic aquatic vehicles incorporating highly flexible propulsors to take advantage of this novel lift generation technique.

Enhanced flight performance in non-uniformly flexible wings

The flexibility of biological propulsors such as wings and fins is believed to contribute to the higher performance of flying and swimming animals compared with their engineered peers. Flexibility seems to follow a universal design rule that induces bending patterns at about one-third from the distal tip of the propulsor’s span. However, the aerodynamic mechanisms that shaped this convergent design and the potential improvement in performance are not well understood. Here, we analyse the effect of heterogeneous flexibility on the flight performance (range and descent angle) of passively tumbling wings. Using experiments, numerical simulations, and scaling analysis, we demonstrate that spanwise tip flexibility that follows this empirical rule leads to improved flight performance. Improvement in flight range seems to be related to flutter-induced drag reduction. This mechanism is independent of the wing’s auto-rotation and represents a more general trait of wings with non-uniform tip flexibility.

Octopus Arm-Inspired Tapered Soft Actuators with Suckers for Improved Grasping

Octopuses can employ their tapered arms to catch prey of all shapes and sizes due to their dexterity, flexibility, and gripping power. Intrigued by variability in arm taper angle between different octopus species, we explored the utility of designing soft actuators exhibiting a distinctive conical geometry, compared with more traditional cylindrical forms. We find that these octopus-inspired conical-shaped actuators exhibit a wide range of bending curvatures that can be tuned by simply altering their taper angle and they also demonstrate greater flexibility compared with their cylindrical counterparts. The taper angle and bending curvature are inversely related, whereas taper angle and applied bending force are directly related. To further expand the functionality of our soft actuators, we incorporated vacuum-actuated suckers into the actuators for the production of a fully integrated octopus arm-inspired gripper. Notably, our results reveal that because of their enhanced flexibility, these tapered actuators with suckers have better gripping power than their cylindrical-shaped counterparts and require significantly larger forces to be detached from both flat and curved surfaces. Finally, we show that by choosing appropriate taper angles, our tapered actuators with suckers can grip, move, and place a remarkably wide range of objects with flat, nonplanar, smooth, or rough surfaces, as well as retrieve objects through narrow openings. The results from this study not only provide new design insights into the creation of next-generation soft actuators for gripping a wide range of morphologically diverse objects but also contribute to our understanding of the functional significance of arm taper angle variability across octopus species.

Canonical description of wing kinematics and dynamics for a straight flying insectivorous bat (Hipposideros pratti)

Bats, with highly articulated wings, are some of the most agile flyers in nature. A novel three-dimensional geometric decomposition framework is developed to reduce the complex kinematics of a bat wing into physical movements used to describe flapping flight: namely flapping, stroke plane deviation and pitching, together with cambering and flexion. The decomposition is combined with aerodynamic simulations to investigate the cumulative effect of each motion on force production, and their primary contribution to the unsteady vortex dynamics. For the nearly straight and level flight of Hipposideros pratti, results show that the flapping motion by itself induced a moderate drag and lift. Stroke plane deviation increased lift, and nullified the drag. With the inclusion of the pitching motion into the kinematics, lift production further increased by a factor of more than 2.5, and exhibited a positive net thrust by virtue of the favorable wing orientation during the upstroke. The primary contribution of cambering, which included a maximum chord line displacement of ≈40% standard mean chord, was the stabilization of the leading edge vortex during the downstroke. This increased mean lift by about 35% at the expense of net thrust. Flexion was perhaps the most complex motion with maximum displacements of 75% standard mean chord. This was instrumental in reducing the negative lift during the upstroke by preventing the formation of strong leading edge vortices. The aerodynamic effective angle of attack emerged as a heuristic parameter to describe lift and net thrust production across movements.

Physics of unsteady thrust and flow generation by a flexible surface flapping in the absence of a free stream

Inspired by the flexible wings and fins of flying and swimming animals, we investigate the flow induced by the interaction between a flapping flexible surface and the surrounding fluid for the limiting case of Strouhal number S t → ∞ (zero free-stream speed). The model selected for this purpose is a two-dimensional sinusoidally pitching rigid symmetric foil to which is attached at the trailing edge a thin chordwise flexible surface (along the chord line). The flow so generated is a coherent jet aligned along the foil centreline, containing a reverse Bénard–Kármán vortex street and delivering a corresponding unidirectional thrust. We analyse the flow and thrust generation process. The measured velocity field suggests that the flow and thrust generation mainly occurs during the phases when the trailing edge is near the centreline. Flexibility of the surface is important in accelerating the near-wake flow and in transferring momentum and energy to the fluid. We present a detailed account of when and where the momentum and energy are added to the fluid. This study shows that the deformations of the flexible surface are responsible for generating a favourable pressure gradient along the jet direction, and for the observed unsteady actuator disc-type action.

Data Management Rubric for Video Data in Organismal Biology

Standards-based data management facilitates data preservation, discoverability, and access for effective data reuse within research groups and across communities of researchers. Data sharing requires community consensus on standards for data management, such as storage and formats for digital data preservation, metadata (i.e., contextual data about the data) that should be recorded and stored, and data access. Video imaging is a valuable tool for measuring time-varying phenotypes in organismal biology, with particular application for research in functional morphology, comparative biomechanics, and animal behavior. The raw data are the videos, but videos alone are not sufficient for scientific analysis. Nearly endless videos of animals can be found on YouTube and elsewhere on the web, but these videos have little value for scientific analysis because essential metadata such as true frame rate, spatial calibration, genus and species, weight, age, etc. of organisms, are generally unknown. We have embarked on a project to build community consensus on video data management and metadata standards for organismal biology research. We collected input from colleagues at early stages, organized an open workshop, “Establishing Standards for Video Data Management,” at the Society for Integrative and Comparative Biology meeting in January 2017, and then collected two more rounds of input on revised versions of the standards. The result we present here is a rubric consisting of nine standards for video data management, with three levels within each standard: good, better, and best practices. The nine standards are: (1) data storage; (2) video file formats; (3) metadata linkage; (4) video data and metadata access; (5) contact information and acceptable use; (6) camera settings; (7) organism(s); (8) recording conditions; and (9) subject matter/topic. The first four standards address data preservation and interoperability for sharing, whereas standards 5–9 establish minimum metadata standards for organismal biology video, and suggest additional metadata that may be useful for some studies. This rubric was developed with substantial input from researchers and students, but still should be viewed as a living document that should be further refined and updated as technology and research practices change. The audience for these standards includes researchers, journals, and granting agencies, and also the developers and curators of databases that may contribute to video data sharing efforts. We offer this project as an example of building community consensus for data management, preservation, and sharing standards, which may be useful for future efforts by the organismal biology research community.

On the diverse roles of fluid dynamic drag in animal swimming and flying

Questions of energy dissipation or friction appear immediately when addressing the problem of a body moving in a fluid. For the most simple problems, involving a constant steady propulsive force on the body, a straightforward relation can be established balancing this driving force with a skin friction or form drag, depending on the Reynolds number and body geometry. This elementary relation closes the full dynamical problem and sets, for instance, average cruising velocity or energy cost. In the case of finite-sized and time-deformable bodies though, such as flapping flyers or undulatory swimmers, the comprehension of driving/dissipation interactions is not straightforward. The intrinsic unsteadiness of the flapping and deforming animal bodies complicates the usual application of classical fluid dynamic forces balance. One of the complications is because the shape of the body is indeed changing in time, accelerating and decelerating perpetually, but also because the role of drag (more specifically the role of the local drag) has two different facets, contributing at the same time to global dissipation and to driving forces. This causes situations where a strong drag is not necessarily equivalent to inefficient systems. A lot of living systems are precisely using strong sources of drag to optimize their performance. In addition to revisiting classical results under the light of recent research on these questions, we discuss in this review the crucial role of drag from another point of view that concerns the fluid-structure interaction problem of animal locomotion. We consider, in particular, the dynamic subtleties brought by the quadratic drag that resists transverse motions of a flexible body or appendage performing complex kinematics, such as the phase dynamics of a flexible flapping wing, the propagative nature of the bending wave in undulatory swimmers, or the surprising relevance of drag-based resistive thrust in inertial swimmers.

A pressure-based force and torque prediction technique for the study of fish-like swimming

Many outstanding questions about the evolution and function of fish morphology are linked to swimming dynamics, and a detailed knowledge of time-varying forces and torques along the animal’s body is a key component in answering many of these questions. Yet, quantifying these forces and torques experimentally represents a major challenge that to date prevents a full understanding of fish-like swimming. Here, we develop a method for obtaining these force and torque data non-invasively using standard 2D digital particle image velocimetry in conjunction with a pressure field algorithm. We use a mechanical flapping foil apparatus to model fish-like swimming and measure forces and torques directly with a load cell, and compare these measured values to those estimated simultaneously using our pressure-based approach. We demonstrate that, when out-of-plane flows are relatively small compared to the planar flow, and when pressure effects sufficiently dominate shear effects, this technique is able to accurately reproduce the shape, magnitude, and timing of locomotor forces and torques experienced by a fish-like swimmer. We conclude by exploring of the limits of this approach and its feasibility in the study of freely-swimming fishes.

How the bending kinematics of swimming lampreys build negative pressure fields for suction thrust

Swimming animals commonly bend their bodies to generate thrust. For undulating animals such as eels and lampreys, their bodies bend in the form of waves that travel from head to tail. These kinematics accelerate the flow of adjacent fluids, which alters the pressure field in a manner that generates thrust. We used a comparative approach to evaluate the cause-and-effect relationships in this process by quantifying the hydrodynamic effects of body kinematics at the body-fluid interface of the lamprey, Petromyzon marinus, during steady-state swimming. We compared the kinematics and hydrodynamics of healthy control lampreys to lampreys whose spinal cord had been transected mid-body, resulting in passive kinematics along the posterior half of their body. Using high-speed particle image velocimetry (PIV) and a method for quantifying pressure fields, we detail how the active bending kinematics of the control lampreys were crucial for setting up strong negative pressure fields (relative to ambient fields) that generated high-thrust regions at the bends as they traveled all along the body. The passive kinematics of the transected lamprey were only able to generate significant thrust at the tail, relying on positive pressure fields. These different pressure and thrust scenarios are due to differences in how active versus passive body waves generated and controlled vorticity. This demonstrates why it is more effective for undulating lampreys to pull, rather than push, themselves through the fluid.

Propulsion via flexible flapping in granular media

Biological locomotion in nature is often achieved by the interaction between a flexible body and its surrounding medium. The interaction of a flexible body with granular media is less understood compared with viscous fluids partially due to its complex rheological properties. In this work, we explore the effect of flexibility on granular propulsion by considering a simple mechanical model in which a rigid rod is connected to a torsional spring that is under a displacement actuation using a granular resistive force theory. Through a combined numerical and asymptotic investigation, we characterize the propulsive dynamics of such a flexible flapper in relation to the actuation amplitude and spring stiffness, and we compare these dynamics with those observed in a viscous fluid. In addition, we demonstrate that the maximum possible propulsive force can be obtained in the steady propulsion limit with a finite spring stiffness and large actuation amplitude. These results may apply to the development of synthetic locomotive systems that exploit flexibility to move through complex terrestrial media.

Optimal specific wavelength for maximum thrust production in undulatory propulsion

What wavelengths do undulatory swimmers use during propulsion? In this work we find that a wide range of body/caudal fin (BCF) swimmers, from larval zebrafish and herring to fully-grown eels, use specific wavelength (ratio of wavelength to tail amplitude of undulation) values that fall within a relatively narrow range. The possible emergence of this constraint is interrogated using numerical simulations of fluid-structure interaction. Based on these, it was found that there is an optimal specific wavelength (OSW) that maximizes the swimming speed and thrust generated by an undulatory swimmer. The observed values of specific wavelength for BCF animals are relatively close to this OSW. The mechanisms underlying the maximum propulsive thrust for BCF swimmers are quantified and are found to be consistent with the mechanisms hypothesized in prior work. The adherence to an optimal value of specific wavelength in most natural hydrodynamic propulsors gives rise to empirical design criteria for man-made propulsors.

The relationship between pectoral fin ray stiffness and swimming behavior in Labridae: insights into design, performance, and ecology

The functional capabilities of flexible, propulsive, appendages are directly influenced by their mechanical properties. The fins of fishes have undergone extraordinary evolutionary diversification in structure and function, which raises questions of how fin mechanics relate to swimming behavior. In the fish family Labridae, pectoral fin swimming behavior ranges from rowing to flapping. Rowers are more maneuverable than flappers, but flappers generate greater thrust at high speeds and achieve greater mechanical efficiency at all speeds. Interspecific differences in hydrodynamic capability are largely dependent on fin kinematics and deformation, and are expected to correlate with fin stiffness. Here we examine fin ray stiffness in two closely related species that employ divergent swimming behaviors, the flapping Gomphosus varius and the rowing Halichoeres bivittatus. To determine the spatial distribution of flexural stiffness across the fin, we performed three-point bending tests at the center of the proximal, middle, and distal regions of four equally spaced fin rays. Pectoral fin ray flexural stiffness ranged from 0.0001-1.5109 microNewtons•m2, and the proximal regions of G. varius fin rays were nearly an order of magnitude stiffer than those of H. bivittatus. In both species, fin ray flexural stiffness decreased exponentially along the proximo-distal span of fin rays, and flexural stiffness decreased along the fin chord from the leading to trailing edge. Further, the proportion of fin area occupied by fin rays was significantly greater in G. varius than in H. bivittatus, suggesting that the proportion of fin ray to fin area contributes to differences in fin mechanics.

Optimal chordwise stiffness profiles of self-propelled flapping fins

The versatility of fish to adapt to different swimming requirements is attributed to their complex muscular system. Fish modulate their fin stiffness and shape for maximized performance. In this paper, optimal chordwise stiffness profiles that maximize the propulsive performance have been predicted using theoretical studies. An experimental setup has been fabricated to measure the stiffness profiles of real fish caudal fins. Chordwise varying stiffness robotic fins fabricated using carbon fiber reinforced composites (CFRC) have been tested in the water tunnel to evaluate their performance over constant stiffness fins. It is observed that the varying stiffness fins produce larger thrusts and efficiencies compared to constant stiffness fins for all the operating conditions considered in this work. A comparison of the digital image correlation (DIC) measured deformations of the fins showed that the better performance of varying stiffness fins is due to their larger curvatures and trailing edge amplitudes. These theoretical and experimental studies provide a greater understanding of the role of stiffness in fish fins for locomotion.

Veterinary Forensics

Projectile injury represents an estimated 14% of reported animal cruelty cases in the United States. Cases involving projectiles are complicated by gross similarities to other common types of injury, including bite wounds and motor vehicle injuries, by weapons and ammunition not commonly recognized or understood by veterinary medical professionals, and by required expertise beyond that employed in routine postmortem examination. This review describes the common types of projectile injuries encountered within the United States, as well as firearms and ammunition associated with this form of injury. The 3 stages of ballistics—internal, external, and terminal—and wounding capacity are discussed. A general understanding of firearms, ammunition, and ballistics is necessary before pursuing forensic projectile cases. The forensic necropsy is described, including gunshot wound examination, projectile trajectories, different imaging procedures, collection and storage of projectile evidence, and potential advanced techniques for gunpowder analysis. This review presents aspects of projectile injury investigation that must be considered in tandem with standard postmortem practices and procedures to ensure reliable conclusions are reached for medicolegal as well as diagnostic purposes.

Suction-based propulsion as a basis for efficient animal swimming

A central and long-standing tenet in the conceptualization of animal swimming is the idea that propulsive thrust is generated by pushing the surrounding water rearward. Inherent in this perspective is the assumption that locomotion involves the generation of locally elevated pressures in the fluid to achieve the expected downstream push of the surrounding water mass. Here we show that rather than pushing against the surrounding fluid, efficient swimming animals primarily pull themselves through the water via suction. This distinction is manifested in dominant low-pressure regions generated in the fluid surrounding the animal body, which are observed by using particle image velocimetry and a pressure calculation algorithm applied to freely swimming lampreys and jellyfish. These results suggest a rethinking of the evolutionary adaptations observed in swimming animals as well as the mechanistic basis for bio-inspired and biomimetic engineered vehicles.

Swimming animals are generally assumed to generate forward thrust by pushing surrounding water rearwards. Here, Gemmell et al. show that efficient swimming in lampreys and jellyfish is achieved primarily through suction, as vortex-associated low pressure regions are synchronized by undulations of the body.

Effects of non-uniform stiffness on the swimming performance of a passively-flexing, fish-like foil model

Simple mechanical models emulating fish have been used recently to enable targeted study of individual factors contributing to swimming locomotion without the confounding complexity of the whole fish body. Yet, unlike these uniform models, the fish body is notable for its non-uniform material properties. In particular, flexural stiffness decreases along the fish's anterior-posterior axis. To identify the role of non-uniform bending stiffness during fish-like propulsion, we studied four foil model configurations made by adhering layers of plastic sheets to produce discrete regions of high (5.5 × 10(-5) Nm(2)) and low (1.9 × 10(-5) Nm(2)) flexural stiffness of biologically-relevant magnitudes. This resulted in two uniform control foils and two foils with anterior regions of high stiffness and posterior regions of low stiffness. With a mechanical flapping foil controller, we measured forces and torques in three directions and quantified swimming performance under both heaving (no pitch) and constant 0° angle of attack programs. Foils self-propelled at Reynolds number 21 000-115 000 and Strouhal number ∼0.20-0.25, values characteristic of fish locomotion. Although previous models have emphasized uniform distributions and heaving motions, the combination of non-uniform stiffness distributions and 0° angle of attack pitching program was better able to reproduce the kinematics of freely-swimming fish. This combination was likewise crucial in maximizing swimming performance and resulted in high self-propelled speeds at low costs of transport and large thrust coefficients at relatively high efficiency. Because these metrics were not all maximized together, selection of the 'best' stiffness distribution will depend on actuation constraints and performance goals. These improved models enable more detailed, accurate analyses of fish-like swimming.

Stability versus Maneuvering: Challenges for Stability during Swimming by Fishes

Fishes are well known for their remarkable maneuverability and agility. Less visible is the continuous control of stability essential for the exploitation of the full range of aquatic resources. Perturbations to posture and trajectory arise from hydrostatic and hydrodynamic forces centered in a fish (intrinsic) and from the environment (extrinsic). Hydrostatic instabilities arise from vertical and horizontal separation of the centers of mass (CM) and of buoyancy, thereby creating perturbations in roll, yaw, and pitch, with largely neglected implications for behavioral ecology. Among various forms of hydrodynamic stability, the need for stability in the face of recoil forces from propulsors is close to universal. Destabilizing torques in body-caudal fin swimming is created by inertial and viscous forces through a propulsor beat. The recoil component is reduced, damped, and corrected in various ways, including kinematics, shape of the body and fins, and deployment of the fins. We postulate that control of the angle of orientation, θ, of the trailing edge is especially important in the evolution and lifestyles of fishes, but studies are few. Control of stability and maneuvering are reflected in accelerations around the CM. Accelerations for such motions may give insight into time-behavior patterns in the wild but cannot be used to determine the expenditure of energy by free-swimming fishes.

Predicting propulsive forces using distributed sensors in a compliant, high DOF, robotic fin

Engineered robotic fins have adapted principles of propulsion from bony-finned fish, using spatially-varying compliance and complex kinematics to produce and control the fin's propulsive force through time. While methods of force production are well understood, few models exist to predict the propulsive forces of a compliant, high degree of freedom, robotic fin as it moves through fluid. Inspired by evidence that the bluegill sunfish (Lepomis macrochirus) has bending sensation in its pectoral fins, the objective of this study is to understand how sensors distributed within a compliant robotic fin can be used to estimate and predict the fin's propulsive force. A biorobotic model of a bluegill sunfish pectoral fin was instrumented with pressure and bending sensors at multiple locations. Experiments with the robotic fin were executed that varied the swimming gait, flapping frequency, stroke phase, and fin stiffness to understand the forces and sensory measures that occur during swimming. A convolution-based, multi-input-single-output (MISO) model was selected to model and study the relationships between sensory data and propulsive force. Subsets of sensory data were studied to determine which sensor modalities and sensor placement locations resulted in the best force predictions. The propulsive forces of the fin were accurately predicted using the linear MISO model on intrinsic sensory data. Bending sensation was more effective than pressure sensation for predicting propulsive forces, and the importance of bending sensation was consistent with several results in biology and engineering studies. It was important to have a spatial distribution of sensors and multiple sensory modalities in order to predict forces across large changes to dynamics. The relationship between propulsive forces and intrinsic sensory measures is complex, and good models should allow for temporal lags between forces and sensory data, changes to the model within a fin stroke, and changes to the model through gait transitions.

Convergent evolution of mechanically optimal locomotion in aquatic invertebrates and vertebrates

Examples of animals evolving similar traits despite the absence of that trait in the last common ancestor, such as the wing and camera-type lens eye in vertebrates and invertebrates, are called cases of convergent evolution. Instances of convergent evolution of locomotory patterns that quantitatively agree with the mechanically optimal solution are very rare. Here, we show that, with respect to a very diverse group of aquatic animals, a mechanically optimal method of swimming with elongated fins has evolved independently at least eight times in both vertebrate and invertebrate swimmers across three different phyla. Specifically, if we take the length of an undulation along an animal's fin during swimming and divide it by the mean amplitude of undulations along the fin length, the result is consistently around twenty. We call this value the optimal specific wavelength (OSW). We show that the OSW maximizes the force generated by the body, which also maximizes swimming speed. We hypothesize a mechanical basis for this optimality and suggest reasons for its repeated emergence through evolution.