Bioinspiration & Biomimetics

Large commercial and military aircraft can operate in a wide range of turbulent conditions, except during extreme weather events such as cyclones. Smaller man-made vehicles, such as micro aerial vehicles (MAVs) and nano aerial vehicles (NAVs), are significantly more sensitive to routine environmental wind fluctuations, making them difficult to control. In contrast, insects exhibit remarkable stability in naturally gusty conditions. Despite this, few studies have systematically investigated the impact of gusts and turbulence on insect flight performance. To address this gap and to gain fundamental insights into insect flight stability under gusty conditions, we examined the flight of freely flying black soldier flies subjected to a discrete head-on aerodynamic gust in a controlled laboratory environment. Flight motions were recorded using two high-speed cameras, and body and wing kinematics were analyzed across 14 distinct cases. In response to the gust, we observed consistent features across the cases: (1) asymmetry in wing stroke amplitude, (2) large changes in body roll angle--up to 160{degrees}--occurring over approximately two wing beats ([~]20 ms) with recovery over [~]9 wing beats, (3) transient pitch-down attitude, and (4) deceleration in the flight direction. These rapid responses, combining passive and active control mechanisms, provide insight into the flight control strategies employed by insects. The findings offer valuable guidance for the design of MAVs and NAVs capable of robustly responding to gusts and unsteady airflow in natural environments.

Despite its ubiquity in natural flows, the effects of turbulence on fish locomotion and behavior remain poorly understood. The prevailing hypothesis is that these effects depend on the spatial and temporal scales of the turbulence relative to the fishs size and swimming speed. But in conventional facilities, turbulence usually increases with mean flow, which forces higher swimming speeds and can leave these relative scales unchanged. We therefore present a novel experimental facility that leverages a jet array to decouple the turbulence from the mean flow and systematically control its scales. This approach allows the ratio of turbulent to fish inertial scales to be varied over an order of magnitude, providing a controlled framework for quantifying fish-turbulence interactions. The facility also supports experiments probing strategies fish may use to cope with turbulence, including collective behaviors. Insights from this work have broader implications for ecological studies and engineering applications, including the design of effective fishways and bio-inspired underwater vehicles.

AO_SCPLOWBSTRACTC_SCPLOWMuscle efficiency decreases with increasing size, largely due to a relative decrease in its mechanical output. Muscle mechanical output depends on its activation, strain, and strain rate and thus varies between different muscles within a limb during locomotion. Distinct muscle coordination patterns are required for efficient cycling, and so we would expect that the coordination patterns for efficient cycling or indeed locomotion would change across animal sizes. We tested whether muscle coordination would change with muscle size using data derived from human cycling: this paradigm allowed for controlled changes in both crank torque and cadence, allowing the multifactorial problem of muscle power output to be decomposed. We used kinematic and pedal data from 12 cyclists undergoing steady pedalling at cadences from 80 to 140 r.p.m. and generated musculoskeletal simulations of their movements. We introduced novel multisegment muscle models in the simulation that incorporated the internal muscle mass and thus accounted for the scaling effects of muscle tissue inertia. We solved the simulations for the muscle activity that was required to minimise the metabolic cost during cycling for each condition. The masses of the muscle models were scaled across five orders of magnitude. The predicted muscle activations were classified by Principal Component analysis to identify whether the coordination of muscle activity was modulated across models with different sized muscles. Analysis of variance revealed significant changes in coordination at the large-scale factors. This study shows how the coordination of muscle activity during locomotion will likely change across a range of body sizes due to the non-linear effects of the inertial mass within the muscle tissues.

Body orientation is a key variable in the analysis of insect flight behavior, yet it remains difficult to measure across the full extent of a trajectory in most experimental settings. Although modern tracking systems reliably capture the position and velocity of the center of mass, resolving body yaw orientation typically requires dedicated hardware confined to a small, purpose-built volume, and is impractical for large-scale or long-duration studies. Here, we develop a data-driven estimator that predicts body yaw orientation directly from translational flight trajectory data. We trained a fully connected feed-forward artificial neural network (ANN) on a dataset in which both flight trajectory and body orientation were recorded simultaneously in freely flying Drosophila, using a time-delay embedding of ground velocity, air velocity, and inferred thrust vectors as input features. To improve generalization across arbitrary coordinate frames, we augmented the training data with random rotational transformations. Evaluated on a withheld test set of 3,313 trajectories (101,576 frames), the rotation-augmented model achieved a median mean absolute angular error of 10.51{degrees}, with accurate heading recovery across the full [-{pi}, {pi}) range. The estimator provides a practical tool for recovering body orientation information from existing trajectory datasets in which only center- of-mass motion was recorded, extending the behavioral and computational analysis of insect navigation to previously inaccessible data.

Take-off is a fast and energy-efficient strategy for bipedal animals, such as birds, to achieve rapid movement; however, how muscle physiology scales to govern this universal behavior remains unresolved. Research in other species physiologies is not readily applicable. As a result, important questions, whether theropod dinosaurs such as Tyrannosaurus rex were capable of jumping, remain unanswered. In this article, we coupled Lagrangian dynamics with Hills muscle equations and developed new experimental methods to quantify joint rotational stiffness and damping, thereby enabling a systematic description of lower-limb mechanics. The approach establishes a novel kinetic framework that links muscle contractile properties to lower-limb performance without invoking control optimization. Animal observations and tabletop mechanisms validate the framework. The mechanics model reveals that the take-off time of about 0.1 s across body masses of 0.003 to 90 kg is achievable, as heavier birds generate proportionally higher reaction forces. Additionally, Tyrannosaurus rex should be capable of jumping, based on the available physiology data. Beyond evolutionary insights, our framework provides a new methodology for analyzing the mechanical properties of biological joints and informing the design of scalable bio-inspired robots.

Nocturnal migration is a remarkable phenomenon observed in many insect species, including moths. Migratory moths are capable of maintaining precise directional orientation during migration, as demonstrated in both laboratory and field studies, suggesting that they use multiple environmental cues for orientation and navigation. Recent studies on Australian Bogong moths revealed that these animals can use stellar cues and likely the geomagnetic field (in conjunction with local visual cues) to select and maintain population-specific migratory direction. However, the underlying orientation mechanisms used by most other migratory moths are still largely unresolved. Further, it remains unclear whether migratory moths can adjust their orientation using Earths magnetic field parameters for determining their position relative to the goal (i.e. location or map information) - an ability clearly shown in some migratory birds which respond to virtual magnetic displacements by correcting their orientation (experiments when animals are exposed to magnetic cues corresponding to other geographic locations). Here, we present results from virtual magnetic displacement experiments conducted on red underwings (Catocala nupta). In addition, we tested their orientation under simulated overcast conditions and in a vertical magnetic field to get indications whether this species relies on geomagnetic or celestial cues to maintain its population-specific migratory direction. Our results show that (1) red underwings did not compensate for virtual magnetic displacement, indicating the absence of a magnetic map; (2) they remained significantly oriented in the absence of geomagnetic information, suggesting the use of a stellar compass; and (3) there was no evidence of magnetic compass orientation in absence of any visual cues.

Head rotation is the leading cause of diffuse brain injuries from cycling accidents, with severe, long-term or even fatal consequences. Here, we present a novel helmet safety technology, the Release Layer System (RLS), designed to enhance conventional helmets and reduce the likelihood of such injuries. RLS is located on the outer side of the helmet and thus gets impacted first. The force of the impact activates a rolling mechanism triggering the release of an outer polycarbonate panel, thereby dispersing and transforming a substantial portion of the incident rotational energy. To evaluate the effectiveness of the technology, we conducted oblique impact tests on three popular helmet types, in conventional and RLS-equipped configurations, at three impact locations. RLS-equipped helmets reduced Peak Angular Velocity (PAV) by 57-66%, averaged across impact locations, compared to their conventional counterparts. This corresponds to a 68-86% reduction in the probability of an AIS2+ brain injury, as estimated by the Brain Injury Criterion. The most notable improvement was observed at the pYrot location (front impacts, mid-sagittal plane), with up to 85% PAV reduction. Testing across headforms further demonstrated the effectiveness of the technology in mitigating head rotation irrespective of variations in evaluation setups. This work introduces a novel mechanism for rotational impact mitigation and provides evidence of its potential benefits compared with conventional helmets. As an outer-layer approach, RLS may offer an alternative pathway for managing rotational kinematics in future helmet designs.

Locating, tracking, and intercepting objects is a fundamental behavior for many organisms. For instance, predators must track and capture erratically moving prey for their survival. Using the echolocating bat as a model species, we investigate how short-term changes in target motion predictability affect longer-term motor plans when tracking a prey item. We used a paradigm where prey motion is under experimental control, and then applied computational methods to characterize how target motion predictability influences short- and long-term behavioral control. We find that target motion predictability during the tracking phase of insect capture influences both short-term changes in sonar call control, as well as longer-term behavioral control for transitioning between hunting phases. For changes in immediate behavioral control, bats produce more bursts of calls at a higher rate when tracking unpredictable moving prey, an indication that the bat is collecting more information about the targets motion for unpredictable than predictable trials. In terms of longer-term behavioral control, target motion unpredictability delays the transition from tracking to capture phase behaviors. We suggest that the bat does this to collect more information about target motion to time the transition from tracking to capture behaviors for hunting success. Additionally, we find the effects of target motion unpredictability are first seen as changes in the vocal motor plan and then the auditory motor plan (ear motion), hinting at a sequencing of motor changes that warrant further investigation. SummaryWhen presented with a more challenging hunting task, bats will increase their production of bursts of calls at a higher rate and delay their transition into capture behaviors.

Understanding how biological shape and movement interact with surrounding fluids represents a fundamental challenge at the intersection of biology, physics, and engineering. Fish locomotion exemplifies this challenge: body morphology and swimming kinematics together determine the hydrodynamic forces and flow structures that enable efficient propulsion and maneuverability. Whereas biologists have long sought to connect morphological variation to swimming performance, traditional morphometric approaches provide limited insight into the fluid mechanical consequences of shape differences. Similarly, although computational fluid dynamics can reveal detailed flow physics, simulating hydrodynamics across diverse and dynamic morphologies remains prohibitively expensive for systematic investigation. To bridge this gap, we introduce a data-driven framework that connects fish body shape dynamics to hydro-dynamic performance through compact morphospace parameterization and reduced-order modeling. Using CFD simulations of 15 fish species from the Digital Life Project database (www.digitallife3d.org/3d-model), we generate hydrodynamic datasets capturing the shape-flow relationship. Principal Component Analysis (PCA) extracts four dominant shape parameters from dorsal body profiles, which are then integrated into an Inverse-Design with Dynamic Mode Decomposition (ID-DMD) framework to model the resulting fluid dynamics. The resulting modal analysis suggests that locomotion strategies emerge from specific shape-flow interactions. We further demonstrate the frameworks utility through single- and multi-objective shape optimization, showing how it enables efficient exploration of the morphology-hydrodynamics relationship. This approach offers a novel analysis and design tool for understanding how biological form and motion interact with fluid mechanics, with applications ranging from bio-inspired vehicle development to evolutionary biomechanics.

AO_SCPLOWBSTRACTC_SCPLOWMuscle fibre type distribution influences both the metabolic and contractile properties of individual muscles. However, as humans tend to self-optimize their gait pattern to minimize cost of transport, these changes in muscle properties may influence gait biomechanics in manners that are difficult to isolate in in vivo experiments. The purpose of this study was to predict the influence of muscle fibre type distribution on the metabolic cost and biomechanics of simulated walking and running. We implemented a muscle model that could predict recruitment of slow and fast twitch muscle fibres in a framework for predictive musculoskeletal simulation. Subsequently, we employed the framework to investigate how metabolic cost of transport, stride length, stride frequency, and mechanical work performed by slow and fast twich muscle fibres were influenced by fibre type distribution across locomotion speeds from 1.0 to 4.5 m {middle dot} s-1. Our results predict that cost of transport increases as slow twitch area fraction decreases, while stride length and frequency was minimally affected by fibre type distribution at speeds resulting in walking. In contrast, fibre type distribution interacts with locomotion speed at speeds resulting in running. Specifically, we predict the existence of a threshold speed below which cost of transport decreases with an increasing proportion of slow twitch fibres, while cost of transport increases with increasing proportions of slow twitch fibres above it. The shift in fibre type distribution was accompanied by an increase in stride frequency and decrease in stride length. These shifts in spatiotemporal characteristics appear to allow the muscles to operate at speeds close to those that achieve peak mechanical efficiency. Taken together, the results of this study predict that muscle fibre type distribution may influence both the energetics and biomechanics of gait, and that this influence is dependent upon the locomotion speed.

Finding resources for the colony is one of the most difficult and risky tasks for a social insect worker. A worker on a foraging trip can face a number of challenges, including interference from other individuals, her own errors, and environmental disturbances. Collectively, colonies may use a variety of strategies to minimize the impact of such perturbations on the foraging process. Here, we investigated how individual Solenopsis xyloni ant workers react to perturbation of an established pheromone trail. We trained foragers from colonies in the field to either a low or high concentration sucrose solution in a feeder on a T-maze setup, then replaced a section of floor covering, removing a section of the pheromone trail previously laid. We found that while ants made correct choices on the T-maze when the trail was intact, their choices did not differ from chance when the trail was absent, indicating strong reliance on a pheromone trail (and not, for example, memory) to return to the resource. Moreover, when the trail was absent, we found that a majority of ants abandoned the resource, and that even the ants that were able to reach the resource did not repair the perturbed trail. However, with a high-quality resource, more ants persisted in attempting to reach it (instead of abandoning). We interpret these responses in the framework of robustness mechanisms discussed in systems biology. Our study thus links individual and collective responses to perturbations, and provides an empirical example of how information use interacts with system robustness. Statements and declarationsThe authors have no competing interests to declare that are relevant to the content of this article.

A passive device that attaches to the feet, called an exotendon, can reduce the energetic cost of running at moderate speeds, but its efficacy and optimal design parameters at higher speeds are unknown. Identifying optimal parameters at new speeds experimentally would require many experimental trials with different exotendon designs, which is challenging for participants at higher running speeds. We developed a muscle-driven simulation framework to predict the effect of various exotendon designs on the energetic cost of running at an experimentally untested speed (4 m/s). We used these predictions to select four designs, which we evaluated experimentally as users ran at this speed. The framework correctly predicted that an exotendon that reduced energetic cost at 2.7 m/s would also reduce energetic cost at 4 m/s (10% predicted vs. 5.7% measured) and that a short, stiff exotendon and a long, compliant exotendon would not significantly reduce energetic cost. However, exotendon parameters predicted by the simulation to maximize energetic savings did not significantly reduce energetic cost when evaluated experimentally. There was variability between participants in both the magnitude of maximum energy savings and the exotendon condition associated with those savings. In a 5-km time trial performed with and without the exotendon condition that elicited the largest energy savings for each participant during the experiment, we observed a lower average heart rate (-3.9 {+/-} 3.8 beats/min; P=0.03; mean {+/-} standard deviation) and increased cadence (15.9 {+/-} 9.6 steps/min; P=0.002) when participants ran with the exotendon but did not observe a statistically significant difference in finishing time (-13.5 {+/-} 24.6 sec; P=0.3). These results demonstrate exotendons can reduce energetic cost across multiple running speeds and that predictive simulations provide a framework for guiding experiments to evaluate assistive device designs. Author summaryDesigning assistive devices that help people move more efficiently usually requires many experimental trials. These studies can be time-consuming and physically demanding, especially when testing multiple device designs. In this study, we explored whether computer simulations could help guide the design of an assistive device for running called an exotendon. The exotendon is a simple elastic band that connects the feet and can help runners use less energy. Previous experiments showed that the device reduces the energy needed to run at moderate speeds, but it was unclear whether it would also work at faster speeds or which design would lead to energetic savings. We first used simulations of human running to test many possible exotendon designs at a faster speed. These simulations allowed us to identify promising designs before conducting experiments. We then tested a small number of these designs with runners. The experiments confirmed that the exotendon can reduce the energy required to run at faster speeds, although the efficacy of different designs varied between individuals. Our results show that computer simulations can help researchers rapidly evaluate a variety of assistive device ideas and focus experimental testing on the most promising designs.

Understanding how fish navigate complex natural environments requires bridging fine-scale biomechanics with ecological behavior. We investigated the volitional movement and energetics of wild red drum (Sciaenops ocellatus) across laboratory, mesocosm, and field settings. Using flow-respirometry, we quantified metabolic costs and swimming kinematics under ecologically relevant flow conditions shaped by bluff bodies mimicking mangrove roots and oyster mounds. Fish swimming in turbulent wakes exhibited reduced oxygen consumption and altered tailbeat dynamics, especially at high flow speeds. In a large outdoor mesocosm, dual accelerometers revealed a rich behavioral repertoire, including maneuvering and rest, which is not easily observable in confined lab settings. Spectral analysis and clustering identified eight distinct locomotory states, highlighting the limitations of summed acceleration metrics. Field telemetry tracked wild red drum across a 54 km estuarine corridor for a three-year period through an array of 36 acoustic receivers, revealing movement patterns shaped by tidal flow and physical habitats. Hydrodynamic modeling revealed that while laboratory trials demonstrated substantial energetic savings at high flows (approaching 100 cm/s), wild fish were detected predominantly in low-velocity microhabitats (<30 cm/s) near structurally complex features. This mismatch suggests that habitat selection is an adaptive strategy driven by ecological factors such as foraging opportunities, predation refuge, and site fidelity, rather than hydrodynamic efficiency alone. Our multi-scalar approach demonstrates that while flow-structure interactions can reduce locomotor costs for fish, habitat use in the wild reflects broader ecological constraints, offering a framework for integrating biomechanics, physiology, and ecology in conservation-relevant contexts.

Wearable devices for gravity balancing have high potential for impact across domains, including neuromotor rehabilitation and occupational systems. Devices made from compliant mechanisms, optimized to achieve specific compensation moments at target joints, have proven effective, but thus far have solely been optimized towards gravity compensation and not other wearability criteria. In this work, we propose a multi-objective optimization framework, based on particle swarm optimization, to design a soft, gravity balancing shoulder orthosis, while taking into account wearability constraints such as undesired loading directions and device size. Using this custom framework, we pursued multiple stages of orthosis design and optimization, selecting multiple solutions to be translated to real-world prototypes. These solutions were realized via 3D printing with thermoplastic polyurethane and evaluated for mechanical performance on benchtop and in-vivo. In-vivo testing on 6 healthy individuals demonstrated relative reductions in muscle activity for the anterior deltoid and upper trapezius, by 53 % and 71 % respectively when operating the orthosis for static tasks within functional shoulder ranges of motion. Changes in muscle activation were also were observed across other muscles, including the posterior deltoid, as well as in dynamic tasks at different speeds.

Studies on active and sedated fish passing through turbines and pumps show different mortality and injury rates for both cases. Consequently, fish behavior appears to play a substantial role in these outcomes. However, direct behavioral observations in hydraulic machines using quantitative parameters to draw conclusions about the underlying mechanisms are hardly possible and remain understudied. In this study, we examined the behavior of adult brown trout (Salmo trutta) in an experimental flume under hydraulic conditions characterized by strong flow acceleration and high velocities typical of turbine and pump intakes. Fish movement behavior was analyzed based on a quantitative approach to enable the analysis of swimming behavior even in flow velocities exceeding the sprint swimming speed of fish. The application of Hidden Markov Models (HMM) to analyze activity states and movement modes of fish from video tracking data demonstrated significant effects of the spatial velocity gradient (SVG) and flow velocity on fish behavior. Notably, SVG emerged as the primary trigger for avoidance reactions when exceeding a threshold of [Formula]. Fish exhibited distinct movement patterns under dark and daylight conditions, with more avoidance reactions in darkness. Whereas a considerable proportion of fish in daylight increased their swimming activity in the zone were flow velocity exceeded sprint swimming speed, in dark conditions no activity peak occurred in the same zone. The results illustrate how hydraulic conditions and lighting influence fish behavior. Integrating the behavioral rules identified in this study into numerical mortality-risk models could substantially improve their predictive accuracy. Thus, the findings allow for the development of less fish harming engineering solutions for hydropower facilities and pumping stations.

Optimizing assistive wearable devices is crucial for their efficacy and user adoption, yet state-of-the-art methods like Human-in-the-Loop Optimization (HILO) and biomechanical modeling face limitations. HILO is time-consuming and often restricted to optimizing control parameters, while inverse dynamics assumes invariant kinematics, which is unreliable for adaptive human-device interaction. Predictive simulation offers a powerful alternative, enabling computational exploration of design spaces. However, existing approaches often lack systematic optimization frameworks and rigorous validation against experimental data. To address this, we developed a Design Optimization Platform that integrates predictive simulations within a two-level optimization structure for personalizing assistive device design. This paper primarily validates the platforms predictive simulations against a publicly available dataset of the passive Biarticular Thigh Exosuit (BATEX), assessing its reliability. Our findings show that the model can sufficiently predict the kinematics and major muscle activations, except for the pelvis tilt and some biarticular muscles. The key finding is that successful identification of personalized optimal BATEX stiffness parameters needs acceptable prediction of metabolic cost trends, not their precise values. Our analysis further reveals that the models accuracy in predicting Vasti muscle activation in the baseline condition is a significant indicator of its success in predicting metabolic cost trends. This demonstrates that accurate prediction of performance trends is more important for effective simulation-based design optimization than perfect biomechanical accuracy, advancing targeted and efficient assistive device development.

Biomechanical simulations of complex hand motions remain scarce, due to challenges that span computation and data acquisition. Using a computer vision-based motion capture approach, a 23-degree of freedom musculoskeletal model, and direct collocation optimization, we performed muscle-driven simulations to track hand kinematics from 7 participants performing American Sign Language gestures. While proximal joints were tracked accurately, interphalangeal joint tracking was significantly worse, with a consistent flexion bias. Modifications to finger extensor muscle paths that incorporated the dual-inserting nature of the extensors improved accuracy, suggesting better representation of extensor force distribution across distal joints may be necessary for accurate hand simulations.

Neural feedback is important for healthy control of movement, and multiple neurological disorders (e.g., stroke, cerebral palsy, Parkinsons disease, incomplete spinal cord injury) can be described by how they impair healthy feedback or induce unhealthy feedback. Researchers have created numerous computational neuromusculoskeletal models controlled by simulated neural feedback mechanisms, but these models rarely represent actual human subjects and thus have not found practical application in treating patients with movement impairments. As a step toward designing patient-specific treatments for individuals with neurological disorders, this study used the Neuromusculoskeletal Modeling Pipeline to develop and evaluate a novel synergy-based feedforward (FF)+feedback (FB) model using a personalized, three-dimensional neuromusculoskeletal walking model of an actual human subject post-stroke. Experimental walking data collected from the subject were used to create the subjects personalized walking model. This model was used to calculate lower body muscle activations consistent with the subjects electromyographic, joint motion, and ground reaction data for 5 calibration walking cycles. Nominal FF synergy controls were calculated by averaging the muscle synergies that closely reconstructed the 5 cycles of muscle activations and associated joint moments simultaneously. These nominal FF controls were then scaled by 0, 25, 50, 75, 100, and 125%, and the gap in reproducing individual cycle muscle activations was filled by fitting FB synergy controls as a function of joint positions, velocities, and moments as surrogates for muscle lengths, muscle velocities, and tendon forces. Finally, the six synergy-based FF+FB models controlled the subjects personalized walking model in predictive simulations performed for 3 testing walking cycles withheld from calibration. The 100% FF model (which still had minimal FB) reproduced the testing walking cycles the most closely, and only the 75%, 100%, and 125% FF models generated near-periodic walking motions using initial conditions consistent with experimental values. The 0, 25, and 50% FF models could generate near-periodic walking motions only when the initial conditions were allowed to diverge substantially from experimental values. Our findings suggest that predictive simulations of walking using real experimental data may require a minimum level of feedforward control and sufficient fitting data to predict a subjects actual dynamically consistent motion.

Escape responses are a critical behavioural mechanism influencing survival during predation events. In most species of teleosts and several other lower vertebrates, these responses are triggered by Mauthner cells (M-cells), which generate faster escapes (characterised by higher turning rates and shorter response latencies) than non-M-cell triggered responses. Most adult elasmobranchs lack M-cells and consequently exhibit slower escape response timing than teleosts. Spotted Ratfish (Hydrolagus colliei) are a notable exception in that adults possess M-cells, yet their escape response performance has not been explored. Here, we quantify the kinematics and timing of ratfish escape responses elicited by a mechano-acoustic stimulus. We show that ratfish exhibit higher turning rates and shorter response latencies than other adult chondrichthyans, though their response latencies are also significantly longer than those of teleosts. These findings suggest that retention of M-cells confers enhanced escape performance in ratfish, with important implications for their vulnerability to predator attacks. Summary statementThis study reveals that adult Spotted Ratfish (Hydrolagus colliei) show fast escape response with a performance that is intermediate between teleosts and previously studied elasmobranchs.

Vertical ground reaction force (vGRF) profiles during walking typically exhibit a double-peaked structure with a mid-stance trough, yet the mechanical conditions governing this morphology remain incompletely defined. In this study, we examined how the balance between push-off and collision impulses during the step-to-step transition influences the temporal and structural characteristics of the vGRF trajectory. Empirical relationships describing push-off and collision work were used to compute transition impulses across walking speeds ranging from 0.8 to 1.4 m{middle dot}s{square}1. A normalized Impulse Balance Index (IBI) was defined to quantify the relative dominance of push-off and collision impulses. The temporal position of the mid-stance trough was quantified using a Trough Deficit Index (TDI) derived from quadratic fits of the vGRF trajectory. Across walking speeds, push-off and collision variations produced step-to-step active work performance imbalance. Push-off and collision became approximately balanced near 1.2 m{middle dot}s{square}1, corresponding to the mechanically preferred walking speed. Deviations from this balanced condition were associated with systematic shifts in trough timing: the trough occurred 1.83% and 1.56% earlier in stance at 0.8 and 1.0 m{middle dot}s{square}1, respectively, and 1.31% later at 1.4 m{middle dot}s{square}1 relative to the reference speed. TDI exhibited a strong inverse relationship with impulse balance (IBI), indicating that vGRF morphology is tightly coupled to the mechanical balance of the step transition. A simplified pendular model further demonstrated that active torque, representing work, during single support shifts the quadratic vertex of the force trajectory by approximately 48.6-51.1% of stance, consistent with the observed trough timing variations. These results show that vertical GRF morphology reflects the imbalance between push-off and collision provides a simple signal of step-to-step transition mechanics, that may be used for rehabilitation and exoskeleton modulation.