Propulsive Force Research Articles

Haptiknit: Distributed stiffness knitting for wearable haptics.

Haptic devices typically rely on rigid actuators and bulky power supply systems, limiting wearability. Soft materials improve comfort, but careful distribution of stiffness is required to ground actuation forces and enable load transfer to the skin. We present Haptiknit, an approach in which soft, wearable, knit textiles with embedded pneumatic actuators enable programmable haptic display. By integrating pneumatic actuators within high- and low-stiffness machine-knit layers, each actuator can transmit 40 newtons in force with a bandwidth of 14.5 hertz. We demonstrate the concept with an adjustable sleeve for the forearm coupled to an untethered pneumatic control system that conveys a diverse array of social touch signals. We assessed the sleeve's performance for discriminative and affective touch in a three-part user study and compared our results with those of prior electromagnetically actuated approaches. Haptiknit improves touch localization compared with vibrotactile stimulation and communicates social touch cues with fewer actuators than pneumatic textiles that do not invoke distributed stiffness. The Haptiknit sleeve resulted in similar recognition of social touch gestures compared to a voice-coil array but represented a more portable and comfortable form factor.

Design of an Underactuated, Flexure-Based Gripper, Actuated Through a Push–Pull Flexure

Abstract The design of grippers for the agro-industry is challenging. To be cost-effective, the picked object should be moved around fast requiring a firm grip on the fruit of different hardnesses, shapes, and sizes without causing damage. This article presents a self-adaptive flexure-based gripper design optimized for high acceleration loads. A main novelty is that it is actuated through a push–pull flexure that is loaded in tension when the gripper closes, allowing it to handle high actuation forces without the risk of buckling. To create a robust gripper that can handle relatively high loads, flexures are used that are reinforced and have a thickness variation over the length. The optimal thickness distribution of these flexures is derived analytically to facilitate the design process. The derived principles are generally applicable to flexure hinges. The resulting advanced cartwheel flexure joint, as used in this gripper, has a 2.5 times higher support stiffness and a 1.5 times higher buckling load when compared to a conventional cartwheel joint of the same size and actuation stiffness. The PP-gripper is numerically optimized for a high pull-out force, using analytical design insights as a starting point. The gripper can grip circular objects with radii between 30 and 40 mm. The pull-out force is 21.4 N, with a maximum actuation force of 100 N. Good correspondence is found between the geometric design approach, the numerically optimized design, and the results of the experimental validation.

Design and Prototype Testing of a Smart SMA Actuator for UAV Foldable Tail Wings

The foldable tail wing system of UAVs offers advantages such as reducing the envelope size and improving storage space utilization. However, due to the compact tail wing space, achieving multi-modal locking and unlocking functionality presents significant challenges. This paper designs a new smart SMA actuator for the use of UAV foldable tail wings. The prototype testing demonstrated the advantages and engineering practicality of the actuator. The core content includes three main parts: thermomechanical testing of the SMA actuation performance, structural design of the actuator, and the fabrication and actuation testing of the prototype. The key parameters related to actuation performance, such as phase transformation temperature and actuation force, were determined through DSC and tensile testing. The geometric parameters of the tail wing were determined through kinetics and kinematic analyses. Through the linkage design of two kinematic pairs, the SMA actuator enables both the deployment and locking of the tail wing. The prototype testing results of the folding tail wing show that, after vibration and temperature variation tests, the SMA actuator is still able to output an actuation stroke of 2.15 mm within 20 ms. The SMA actuator integrates locking for both modes of the tail wing and unlocking during mode transitions, offering advantages such as fast response and minimal space requirements. It provides an effective solution tailored to the needs of the foldable tail wing system.

Does chronic ankle instability affect side-cutting in female soccer players?

Lateral ankle sprains have a high recurrence rate, often developing into chronic ankle instability (CAI). CAI affects movement strategy during side-cutting maneuvers, with inconsistent results in many studies. This study aimed to clarify the characteristics of movement strategies during side-cutting maneuvers in female soccer players with and without CAI. Thirteen female soccer players with CAI and twelve healthy controls performed 10 successful trials of side-cutting maneuvers in three directions (anterolateral, lateral, and posterolateral) under unanticipated conditions. Compared to the control group, the CAI group displayed an increased stance time in the lateral and posterolateral side-cutting maneuvers (lateral: p = .021, effect size = 0.97, posterolateral: p = .014, effect size = 1.00). In posterolateral side-cutting maneuvers, the CAI group displayed a decreased posterior ground reaction force at 19-30 % and 42-54 % of the entire stance phase compared with the control group (p = .001, effect size = 1.30-1.42). Female soccer players with CAI may display increased stance time to compensate for self-reported ankle instability and may also exhibit decreased braking and propulsive force when side-cutting to sharper angles. These observations suggest a hypothesis that could help in the assessment of cutting maneuvers under unanticipated conditions after ankle sprains.

Research on Fuzzy PID Compliant Grinding Control Based on DBO Algorithm Optimization

In order to achieve the requirements of high precision, fast response and low overshoot in the robot grinding process. An active compliant actuator at the end of the robot is designed, and a fuzzy PID constant force control method based on dung beetle optimizer (DBO) optimization is proposed. The force and gas flow model of the compliant actuator are analyzed, and the mathematical model of the actuator is established. On the basis of fuzzy PID algorithm, the fuzzy PID parameters optimized by DBO algorithm are adopted. The simulation system model is established by MATLAB, and the performance of PID control, fuzzy PID control and fuzzy PID control method optimized by DBO algorithm is compared. The simulation results show that the fuzzy PID control based on DBO algorithm has faster response speed, reaches stability in 0.5s, no overshoot, and the system is more stable.

Training techniques and enhanced kinematic modeling for extended range twisted string actuators

As a linear actuator, the twisted string actuator (TSA) offers ease of miniaturization, flexibility, and the capability to exert a strong actuation force, due to its large gear ratio. Owing to these characteristics, TSA has recently gained attention as a suitable small actuator for wearable devices, and surgical robots. However, the operating range relative to its size has been reported as limited. This study aims to overcome this limitation by extending the operating range of TSA using the coiling phase, following the twisting phase. To achieve this, we first analyze the training process to effectively mitigate the irregular overlapping phenomena in the coiling stage of TSA, considering the hysteresis and the training effect of TSA under different loads. Second, we address the limitations of conventional TSA kinematic models and propose an improved kinematic model for the extended operating range of TSA. Specifically, this study presents the precise transition points between the twisting and coiling phases of TSA and proposes enhanced analytical models for each phase. Finally, through various experiments, we validate the proposed training process and kinematic model for extended TSA operation. It is expected that the proposed training process and kinematic model for TSA will enable precise actuation within the extended operating range, facilitating a wider array of applications.

Chatter suppression in robotic milling using active contact force actuator

Chatter during the robotic milling process is an obstacle to achieving high milling performance in the field of intelligent manufacturing. Chatter in robotic milling occurs due to low stiffness, resulting in low milling efficiency and poor surface quality. To enhance the stability of the robotic milling, we introduce a novel active contact force actuator, which can improve the milling process stiffness by actively applying the force between the robot and the workpiece. The actuator can adapt to different machining conditions, and provide different sizes of active contact force by controlling the cylinder pressure, and does not interfere with the machining process. The principle of milling stability improvement with the novel actuator is proved, then the equivalent stability prediction diagram is derived to verify the effectiveness of the actuator. The performance of the actuator is finally verified through robotic milling experiments, the results show that the actuator can effectively suppress low-frequency chatter in the robotic milling, and maintain effective chatter suppression capabilities even under the high spindle-speed and feed- speed condition.

Integrated responses of the SIP syncytium generate a major motility pattern in the colon.

The peristaltic reflex has been a central concept in gastrointestinal motility; however, evidence was published recently suggesting that post-stimulus responses that follow inhibitory neural responses provide the main propulsive force in colonic motility. This new concept was based on experiments on proximal colon where enteric inhibitory neural inputs are mainly nitrergic. However, the nature of inhibitory neural inputs changes from proximal to distal colon where purinergic inhibitory regulation dominates. In spite of the transition from nitrergic to purinergic regulation, post-stimulus responses and propulsive contractions were both blocked by antagonists of a conductance (ANO1) exclusive to interstitial cells of Cajal (ICC). How purinergic neurotransmission, transduced by PDGFRα+ cells, can influence ANO1 in ICC is unknown. We compared neural responses in proximal and distal colon. Post-stimulus responses were blocked by inhibition of nitrergic neurotransmission in proximal colon, but P2Y1 receptor antagonists were more effective in distal colon. Ca2+ entry through voltage-dependent channels (CaV3) enhances Ca2+ release in ICC. Thus, we reasoned that hyperpolarization caused by purinergic responses in PDGFRα+ cells, which are electrically coupled to ICC, might decrease inactivation of CaV3 channels and activate Ca2+ entry into ICC via anode-break upon cessation of inhibitory responses. Post-stimulus responses in distal colon were blocked by MRS2500 (P2Y1 receptor antagonist), apamin (SK channel antagonist) and NNC55-0396 (CaV3 antagonist). These compounds also blocked propagating contractions in mid and distal colon. These data provide the first clear demonstration that integration of functions in the smooth muscle-ICC-PDGFRα+ cell (SIP) syncytium generates a major motility behaviour. KEY POINTS: Propagating propulsive contractions initiated by the enteric nervous system are a major motility behaviour in the colon. A major component of contractions, necessary for propulsive contractions, occurs at cessation of enteric inhibitory neurotransmission (post-stimulus response) and is generated by interstitial cells of Cajal (ICC), which are electrically coupled to smooth muscle cells. The nature of enteric inhibitory neurotransmission shifts from proximal colon, where it is predominantly due to nitric oxide, to distal colon, where it is predominantly due to purine neurotransmitters. Different cells transduce nitric oxide and purines in the colon. ICC transduce nitric oxide, but another type of interstitial cell, PDGFRα+ cells, transduces input from purinergic neurons. However, the post-stimulus responses in proximal and distal colon are still generated in ICC. This paper explores how integrated behaviours of ICC, PDGFRα+ cells and smooth muscle cells accomplish propulsive motility in the colon.

Optimal crawling: From mechanical to chemical actuation.

Taking inspiration from the crawling motion of biological cells on a substrate, we consider a physical model of self-propulsion where the spatiotemporal driving can involve both a mechanical actuation by active force couples and a chemical actuation through controlled mass turnover. When the material turnover is slow and the mechanical driving dominates, we find that the highest velocity at a given energetic cost is reached when the actuation takes the form of an active force configuration propagating as a traveling wave. As the rate of material turnover increases, and the chemical driving starts to dominate the mechanical one, such a peristalsis-type control progressively loses its efficacy, yielding to a standing-wave-type driving which involves an interplay between the mechanical and chemical actuation. Our analysis suggests a paradigm for the optimal design of crawling biomimetic robots where the conventional purely mechanical driving through distributed force actuators is complemented by a distributed chemical control of the material remodeling inside the force-transmitting machinery.

Analysis of the Radial Force of a Piezoelectric Actuator with Interdigitated Spiral Electrodes.

The actuator is a critical component of the micromanipulator. By utilizing the properties of expansion and contraction, the piezoelectric actuator enables the manipulator to handle and grasp miniature objects during micromanipulation. However, in piezoelectric ceramic disc actuators with conventional surface electrode configurations, the actuating force generated in the radial direction is relatively limited. When used as the actuation element of the manipulator, achieving regulation over a wide range of operating strokes becomes challenging. Therefore, altering the electrode structure is necessary to generate a greater radial force, thus enhancing the positioning and grasping capabilities of the operating arm. This paper investigates a piezoelectric actuator with interdigitated spiral electrodes, featuring a constant pitch between adjacent electrodes. The radial force was tested under mechanical clamping conditions, and the influence of the electrical signal was examined. The characteristics of the electrode structure were described, and the working principles of the piezoelectric actuators were analyzed. Theoretical equations were derived for the macroscopic characterization of the radial clamping force of the actuator, based on the piezoelectric constitutive equation, geometric principles, and Bond matrix transformation relationships. A finite element model was developed, reflecting the features of the electrode structure, and finite element simulations were employed to verify the theoretical equations for radial force. To prepare the samples, encircled interdigitated spiral electrode lines were printed on the PZT-52 piezoelectric ceramic disc using a screen printing method. The clamping force experimental platform was established, and experiments on the clamping radial force were conducted with electrical signals of varying waveforms, frequencies, and voltages. The experimental results show that the piezoelectric ceramic disc actuator with an interdigitated spiral electrode line structure, when excited by a stable sine wave operating at 200 V and 0.2 Hz, generated a peak force of 0.37 N. It was 1.76 times greater than that produced by a previously utilized piezoelectric disc with conventional electrode structures.

Does the flutter kick increase hand propulsion in front crawl swimming?

ABSTRACT This study aimed to investigate the effect of the flutter kick on the propulsive force generated by a stroke. Eight male swimmers performed 20 m front crawl trials under two conditions: the Whole Condition, involving maximum effort (T100%) and stroke frequencies at 70, 80, and 90% of T100%, and the Arm Condition, which excluded the flutter kick and matched stroke frequencies with the Whole Condition. Various parameters, including swimming velocity, stroke frequency, stroke length, three-dimensional (3D) resultant hand speed, and hand propulsion were calculated based on underwater 3D motion analysis and hand pressure distribution measurements. A two-way repeated-measures ANOVA was conducted to assess differences, considering the conditions and instructed frequencies as the two factors. There was no significant interaction between the condition and intensity for any of the variables. There was a significant main effect of condition on swimming velocity and stroke length, with these variables being 16.9–18.5% higher and 17.3–19.5% longer, respectively, in the Whole Condition compared to the Arm Condition. However, there was no difference in hand propulsion between the conditions, and it was clarified that the flutter kick did not affect hand propulsion at any swimming velocity.

A model for micro-scale propulsion using flexible rotating flagella

Micro-scale propulsion by rotating helical flagella is of interest for the study of bacteria and robotic micro-swimmers. The propulsive thrust and torque produced by the rotating flagella are usually estimated assuming that they are rigid. In this paper we assume the flagella to be deformable elastic rods and compute propulsive forces and torques by enforcing local equilibrium of the rod within the context of resistive force theory. The torque–speed characteristics of the flagellar motor driving the rotation are taken into account. We show that the problem can be cast as a system of algebraic equations if the flagella are assumed to be helical before and after deformation when no spontaneous curvature is included. If the assumption of helical shape is dropped then we show that the propulsion problem can be cast as a system of first order differential equations that can be solved numerically. Our results in both cases agree reasonably well with experimental observations of bacterial propulsion and deviate from the predictions of Purcell depending on the mechanical properties of the flagellum.

Course control in a self-consistent model of cuttlefish movement

We developed a simulation model to mimic cuttlefish movement. We developed a simulation model to mimic cuttlefish movement, representing an elongated body with two undulatory fins that generate propulsive forces for underwater movement. Our mathematical model concurrently solved equations for both body mechanics and fluid dynamics, using the Navier–Stokes equations to describe the latter. To implement this self-consistent model, we utilized deformable mesh techniques. This enabled us to compute both the apparatus’s movement performance characteristics and hydrodynamic flow parameters, such as vorticity and pressure fields. Our study focused on examining how oscillations of the left and right fins, each with different parameters, impact the apparatus’s maneuverability. We found that differences in frequencies between the left and right fins resulted in a peak turning angle velocity. We also explored how the interplay between hydrodynamic forces influences the apparatus’s course control.

Feeders and expellers, two types of animalcules with outboard cilia, have distinct surface interactions

Within biological fluid dynamics, it is conventional to distinguish between “puller” and “pusher” microswimmers on the basis of the forward or aft location of the flagella relative to the cell body: typically, bacteria are pushers and algae are pullers. Here we note that since many pullers have “outboard” cilia or flagella displaced laterally from the cell centerline on both sides of the organism, there are two important subclasses whose far-field is that of a stresslet, but whose nearfield is qualitatively more complex. The ciliary beat creates not only a propulsive force but also swirling flows that can be represented by paired rotlets with two possible senses of rotation, either “feeders” that sweep fluid toward the cell apex, or “expellers” that push fluid away. Experimental studies of the rotifer in combination with earlier work on the green algae show that the two classes have markedly different interactions with surfaces. When swimming near a surface, expellers such as scatter from the wall, whereas a feeder like stably attaches. This results in a stochastic “run-and-stick” locomotion, with periods of ballistic motion parallel to the surface interrupted by trapping at the surface. Published by the American Physical Society 2024

Asymmetric Charge Distribution in One-dimensional Metal-Organic Assemblies to Promote Photocatalytic Hydrogen Evolution.

The local charge distribution of photocatalyst is crucial to the catalytic activity due to its influence on the charge separation process. Herein, we report two one-dimensional Ni-based metal-organic assemblies for efficient photocatalytic hydrogen evolution without using noble-metal cocatalysts. By adjusting the aromatic ring in the center of the tricarboxylic ligand, the photocatalytic hydrogen evolution activity was increased from 1715 to 2652 μmol h-1 g-1. The detailed mechanism study shows that the introduced nitrogen atoms in the ligands of the metal-organic coordination assembly could modulate the local charge distribution, and yielding a significant enhancement of the molecular dipole moment which engenders a propulsive force for the effective separation and transport of photoinduced charge carriers. This work provides insights into the local charge distribution via ligand modulation for enhancing the activity of photocatalysts.

A novel mobile robot with origami wheels designed for navigating sandy terrains

Abstract Sand robots play a vital role as mobile tools for human exploration of desert regions, facilitating resource transportation and exploration. However, desert areas primarily consist of beaches or dunes, resulting in a highly diverse and complex terrain environment that demands enhanced adaptability from sandy mobile robots. Traditional wheeled robots currently face challenges such as skidding, limited climbing ability, and inadequate obstacle avoidance capabilities in sandy environments. To address these issues and enable effective adaptation to the intricate sand environment, we propose a novel sandy mobile robot equipped with Kresling origami wheels. The origami wheel can dynamically adjust its width and morphology through Kresling origami folding. Experimental tests were conducted to illustrate the impact of width variation on the robot’s mobility velocity, propulsive force, climbing performance, and carrying capacity. The self-folding malleability of the origami wheel empowers the robot to efficiently accomplish diverse tasks, including swift movement on flat sand surfaces, seamless crossing of narrow channels, and intelligent obstacle avoidance. By successfully completing these multimodal tasks while adapting to varying requirements, our robot demonstrates promising prospects for practical applications of mobile robots equipped with origami wheels – paving the way for wider adaptation and utilization of sand mobile robots.

A Machine Learning–Based Ergonomic Assessment of Wireless Hand Control System for Lower‐Limb Disabled Tractor Operators and Abled Female Agricultural Workers

ABSTRACTTractor being the most used power source for agricultural operations needs hand control (HC) and foot control (FC) to maneuver it. FCs restrict lower‐limb disabled agricultural workers from participating in tractor operation, and high requirement of actuation forces to operate FCs may create overexertion and early fatigue to female agricultural workers. Therefore, a sensor‐based HC system has been developed to assist them in tractor operation with minimal actuating force. This study focuses on ergonomic assessment of the HC system to assess the suitability for the abled and disabled agricultural workers, including physiological, psychophysical, and muscle fatigue parameters. Heart rate (HR) of abled male and female, and disabled male and female was observed in the range of 83–118, 85–117, 93–118, and 92–114 beats/min, respectively, during tractor operation. Energy expenditure rate (EER) during tractor operation with FCs (9.7–17.4 kJ/min) was observed higher than with the HC system (7.3–16.5 kJ/min). Body parts discomfort was observed highest for the right hand of all the subjects (4.9–5.3) and maximum overall discomfort was experienced by abled females during the operation with FCs (5.4) as they have to exert higher force. The root mean square (RMS) value of the electromyography signal obtained for extensor digitorum muscle was found to be higher for all the subjects and with both HC and FC (abled male, 17.37–40.43 µV; abled female, 14.76–45.29 µV; disabled male, 15.49–40.23 µV; disabled female, 30.32–54.29 µV) than other upper arm muscles middle deltoid, flexor carpi radialis, and brachioradialis. Muscle workload for all the selected muscles of all the subjects was observed within the recommended limit during the tractor operation with a developed HC system (< 30%). Categorization of overall discomfort rating (ODR) of the subjects using HR, EER, and RMS through machine learning algorithms such as k‐nearest neighbor (KNN), random forest classifier, and support vector machine predicted the ODR with accuracies in the range of 77%–83%. KNN algorithm was found to be most accurate with prediction accuracy of 83%. The developed HC system provides assistantship to the lower‐limb disabled agricultural workers (1%–100% disability of lower limbs) and allows female workers to operate the tractor with minimal physical exertion.

Breaststroke and butterfly intercycle kinematic variation according to different competitive levels with Statistical Parametric Mapping analysis

Breaststroke and butterfly are complex swimming techniques requiring refined motor skills to perform successfully, with coordinated and consistent interaction between propulsive and resistive forces being decisive when considering swimmers expertise. The current study analysed those techniques intercycle kinematic variation in two swimmers cohorts. Twenty elite and 15 national level swimmers performed one 25 m breaststroke and one 25 m butterfly sprints, with an underwater camera recording images at 120 Hz in the sagittal plane. Mean velocity, maximum and minimum velocities, stroke rate and length, intracycle velocity variation and phases relative duration were calculated for consecutive cycles (elite: five breaststroke/butterfly, national level: eight breaststroke/seven butterfly). The two highest peaks and the lower peak in between in breaststroke were also addressed. Intercycle and inter-groups analysis were performed using ANOVA, ANCOVA and Statistical Parametric Mapping. Elite and national level differed regarding breaststroke mean and maximum velocities, 1st and 2nd peaks and minimum between peaks (1.30 ± 0.02 vs 1.15 ± 0.02 m/s, 2.13 ± 0.05 vs 1.88 ± 0.06 m/s, 1.63 ± 0.05 vs 1.48 ± 0.05 m/s, 2.13 ± 0.05 vs 1.86 ± 0.05 m/s, 1.33 ± 0.04 vs 1.23 ± 0.04 m/s), and butterfly mean, maximum and minimum velocities, stroke rate and intracycle velocity variation, respectively (1.65 ± 0.01 vs 1.50 ± 0.01 m/s, 2.20 ± 0.04 vs 2.09 ± 0.04 m/s, 1.12 ± 0.04 vs 0.79 ± 0.04 m/s, (57.9 ± 0.9 vs 54.9 ± 1.0cycles/min, 18.4 ± 1.3 vs 23.7 ± 1.3 %). Elite and national level swimmers showed consistent breaststroke intercycle kinematic variation, but a butterfly mean velocity decay, with the upper limbs release and recovery, and the outsweep phases originating variability between butterfly cycles. Skill levels contrasted in technical and strategic features at sprint breaststroke and butterfly but showed similar velocity variability between consecutive swimming cycles.

Optimal replicator dynamic controller for semi active control of long span cable stayed bridge with considering special variability of seismic excitations

Cable-stayed bridges are lifeline infrastructures. However, due to their design and structural characteristics, they are sensitive to the vibrations. Thus, vibration control in these structures is essential. Semi-active control systems have gained significant attention due to their high performance and adaptability. However, the implementation of these systems has always faced serious challenges particularly when it comes to developing appropriate control algorithms because semi active devices have complex and non-linear characteristics. Inspired by evolutionary game theory, the author utilizes the replicator dynamic controller concept to optimize the performance of MR dampers to improve the vibration reduction of cable-stayed bridges. Two key parameters in the proposed control methodologies using replicator dynamics are the total population (total available resources or the sum of actuator forces) and the growth rate. Instead of using the sensitivity analysis that has been done in previous studies for vibration reduction of highway bridges using a replicator controller, the author used an evolutionary algorithm named the nondominated sorting genetic algorithm (NSGA-II) to create an optimal replicator dynamic controller for more effective vibration reduction. The proposed methodology is evaluated through its numerical application to a second-generation benchmark example based on the Bill Emerson Memorial Bridge, which considers a more realistic behavior of the cable-stayed bridge by accounting for multiple support excitations. The study indicates that the optimal replicator dynamic controller improves the vibration reduction performance of MR dampers. Specifically, deck displacement is reduced by 46 % compared to passive control system and shear forces at the tower base are reduced by 33 % compared to active control systems for the El Centro earthquake. The results indicate that the proposed Replicator Dynamic Controller optimized through NSGA-II provides a robust and effective solution for improving seismic resilience of cable-stayed bridges.

Submaximal force–velocity relationships during mountain ultramarathon: Data from the field

ABSTRACT This study presents a novel method for evaluating the submaximal velocity-force (V(F)) relationship in mountain ultramarathon races using crowdsourced data from Strava.com. The dataset includes positional data from 408 participants of the 171-km UTMB® 2023 race (9,850-m D+). The race was divided into 100-m segments. The mean net propulsive force and velocity were computed for each segment to describe the submaximal V(F) relationship as a rational function of three parameters. F1: propulsive force at 1 m · s−1; V0: theoretical maximum velocity on flat terrain; C: curvature parameter (the lower C, the more linear the V(F) relationship). The V(F) profile parameters were found to be F1 = 1.80 ± 0.33 N · kg−1, V0 = 2.36 ± 0.42 m · s−1, and C = 0.66 ± 1.81, with good independence between the parameters within a group of homogeneous performance. The best athletes had the highest F1, V0, and C values. V(F) parameters were affected by fatigue during the race, with decreases of 20.9%, 32.0%, and 59.8% between the first and second parts of the race respectively. These findings suggest that the V(F) relationship is an interesting original approach for studying performance and fatigability during mountain ultra-endurance races.