Symmetry and Asymmetry in Bouncing Gaits

In running, hopping and trotting gaits, the center of mass of the body oscillates each step below and above an equilibrium position where the vertical force on the ground equals body weight. In trotting and low speed human running, the average vertical acceleration of the center of mass during the lower part of the oscillation equals that of the upper part, the duration of the lower part equals that of the upper part and the step frequency equals the resonant frequency of the bouncing system: we define this as on-offground symmetric rebound. In hopping and high speed human running, the average vertical acceleration of the center of mass during the lower part of the oscillation exceeds that of the upper part, the duration of the upper part exceeds that of the lower part and the step frequency is lower than the resonant frequency of the bouncing system: we define this as on-off-ground asymmetric rebound. Here we examine the physical and physiological constraints resulting in this on-off-ground symmetry and asymmetry of the rebound. Furthermore, the average force exerted during the brake when the body decelerates downwards and forwards is greater than that exerted during the push when the body is reaccelerated upwards and forwards. This landing-takeoff asymmetry, which would be nil in the elastic rebound of the symmetric spring-mass model for running and hopping, suggests a less efficient elastic energy storage and recovery during the bouncing step. During hopping, running and trotting the landing-takeoff asymmetry and the mass-specific vertical stiffness are smaller in larger animals than in the smaller animals suggesting a more efficient rebound in larger animals

Walking dynamics are symmetric (enough)

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a physical system as a modeling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady-state (limit-cycle). Here we adapt statistical cross validation in order to examine whether there are statistically significant asymmetries, and even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modeling convenience---it can produce a better model.Comment: Draft submitted to Journal of the Royal Society Interfac

Running, hopping and trotting: tuning step frequency to the resonant frequency of the bouncing system favors larger animals

A long-lasting challenge in comparative physiology is to understand why the efficiency of the mechanical work done to maintain locomotion increases with body mass. It has been suggested that this is due to a more elastic step in larger animals. Here, we show in running, hopping and trotting animals, and in human running during growth, that the resonant frequency of the bouncing system decreases with increasing body mass and is, surprisingly, independent of species or gait. Step frequency roughly equals the resonant frequency in trotting and running, whereas it is about half the resonant frequency in hopping. The energy loss by elastic hysteresis during loading and unloading the bouncing system from its equilibrium position decreases with increasing body mass. Similarity to a symmetrical bounce increases with increasing body mass and, for a given body mass, seems to be maximal in hopping, intermediate in trotting and minimal in running. We conclude that: (1) tuning step frequency to the resonant frequency of the bouncing system coincides with a lower hysteresis loss in larger, more-compliant animals; (2) the mechanism of gait per se affects similarity with a symmetrical bounce, independent of hysteresis; and (3) the greater efficiency in larger animals may be due, at least in part, to a lower hysteresis loss

The role of biomechanical analysis of horse and rider in equitation science

Equestrian sports are unique in that they involve the participation of two athletes that differ greatly in morphology yet are able to move together harmoniously; experienced riders not only move in phase with the horse, they can even improve the consistency of the horse’s movements. The motion of the horse imposes perturbations on the rider that differ in magnitude and direction according to gait. In faster gaits where suspension phases are present, the rider must accommodate greater vertical and horizontal accelerations of the horse’s trunk through three-dimensional movements of their axial body segments. The rider, in turn, can improve the horse’s performance through correct training, or cause it to deteriorate through faults in the rider’s position or incorrect application of the aids. This review addresses the current state of knowledge of the biomechanics of the horse-rider interaction, with reference to the ways in which the emerging field of equitation science can help to improve equine welfare by enhancing rider awareness of horse behaviour and movement, as well as the impact of the rider on the horse

Exploring Passive Dynamics in Legged Locomotion

A common observation among legged animals is that they move their limbs differently as they change their speed. The observed distinct patterns of limb movement are usually referred to as different gaits. Experiments with humans and mammals have shown that switching between different gaits as locomotion speed changes, enables energetically more economical locomotion. However, it still remains unclear why animals with very different morphologies use similar gaits, where these gaits come from, and how they are related. This dissertation approaches these questions by exploring the natural passive dynamic motions of a range of simplified mechanical models of legged locomotion. Recent research has shown that a simple bipedal model with compliant legs and a single set of parameters can match ground reaction forces of both human walking and running. As first contribution of this dissertation, this concept is extended to quadrupeds. A unified model is developed to reproduce many quadrupedal gaits by only varying the initial states of a motion. In addition, the model parameters are optimized to match the experimental data of real horses, as measured by an instrumented treadmill. It is shown that the proposed model is able to not only create similar kinematic motion trajectories, but can also explain the ground reaction forces of real horses moving with different gaits. In order to reveal the mechanical contribution to gaits, the simplistic bipedal and quadrupedal models are then augmented to have passive swing leg motions by including torsional springs at the hip joints. Through a numerical continuation of periodic motions, this work shows that a wide range of gaits emerges from a simple bouncing-in-place motion starting with different footfall patterns. For both, bipedal and quadrupedal models, these gaits arise along one-dimensional manifolds of solutions with varying total energy. Through breaking temporal and spatial symmetries of the periodic motions, these manifolds bifurcate into distinct branches with various footfall sequences. That is, passive gaits are obtained as different oscillatory motions of a single mechanical system with a single set of parameters. By reproducing a variety of gaits as a manifestation of the passive dynamics of unified models, this work provides insights into the underlying dynamics of legged locomotion and may help design of more economical controllers for legged machines.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147585/1/ganzheny_1.pd

Evolving soft locomotion in aquatic and terrestrial environments: effects of material properties and environmental transitions

Designing soft robots poses considerable challenges: automated design approaches may be particularly appealing in this field, as they promise to optimize complex multi-material machines with very little or no human intervention. Evolutionary soft robotics is concerned with the application of optimization algorithms inspired by natural evolution in order to let soft robots (both morphologies and controllers) spontaneously evolve within physically-realistic simulated environments, figuring out how to satisfy a set of objectives defined by human designers. In this paper a powerful evolutionary system is put in place in order to perform a broad investigation on the free-form evolution of walking and swimming soft robots in different environments. Three sets of experiments are reported, tackling different aspects of the evolution of soft locomotion. The first two sets explore the effects of different material properties on the evolution of terrestrial and aquatic soft locomotion: particularly, we show how different materials lead to the evolution of different morphologies, behaviors, and energy-performance tradeoffs. It is found that within our simplified physics world stiffer robots evolve more sophisticated and effective gaits and morphologies on land, while softer ones tend to perform better in water. The third set of experiments starts investigating the effect and potential benefits of major environmental transitions (land - water) during evolution. Results provide interesting morphological exaptation phenomena, and point out a potential asymmetry between land-water and water-land transitions: while the first type of transition appears to be detrimental, the second one seems to have some beneficial effects.Comment: 37 pages, 22 figures, currently under review (journal

Landing-Takeoff Asymmetries Applied to Running Mechanics: A New Perspective for Performance

Background:Elastic bouncing is a physio-mechanical model that can elucidate running behavior in different situations, including landing and takeoff patterns and the characteristics of the muscle-tendon units during stretch and recoil in running. An increase in running speed improves the body’s elastic mechanisms. Although some measures of elastic bouncing are usually carried out, a general description of the elastic mechanism has not been explored in running performance. This study aimed to compare elastic bouncing parameters between the higher- and lower-performing athletes in a 3000 m test.Methods:Thirty-eight endurance runners (men) were divided into two groups based on 3000 m performance: the high-performance group (Phigh; n = 19; age: 29 ± 5 years; mass: 72.9 ± 10 kg; stature: 177 ± 8 cm; 3000time: 656 ± 32 s) and the low-performance group (Plow; n = 19; age: 32 ± 6 years; mass: 73.9 ± 7 kg; stature: 175 ± 5 cm; 3000time: 751 ± 29 s). They performed three tests on different days: (i) 3000 m on a track; (ii) incremental running test; and (iii) a running biomechanical test on a treadmill at 13 different speeds from 8 to 20 km h−1. Performance was evaluated using the race time of the 3000 m test. The biomechanics variables included effective contact time (tce), aerial time (tae), positive work time (tpush), negative work time (tbreak), step frequency (fstep), and elastic system frequency (fsist), vertical displacement (Sv) in tce and tae (Sce and Sae), vertical force, and vertical stiffness were evaluated in a biomechanical submaximal test on treadmill.Results:The tae, fsist, vertical force and stiffness were higher (p < 0.05) and tce and fstep were lower (p < 0.05) in Phigh, with no differences between groups in tpush and tbreak.Conclusion:The elastic bouncing was optimized in runners of the best performance level, demonstrating a better use of elastic components

Simple models of legged locomotion based on compliant limb behavior = Grundmodelle pedaler Lokomotion basierend auf nachgiebigem Beinverhalten

In der vorliegenden Dissertation werden einfache Modelle zur Beinlokomotion unter der gemeinsamen Hypothese entwickelt, dass die beiden grundlegenden und als verschieden angesehenen Gangarten Gehen und Rennen auf ein allgemeines Konzept zurückgeführt werden können, welches in den Standphasen allein auf nachgiebigem Beinverhalten beruht. Hierbei wird auf der Ebene der mechanischen Beschreibung der Gangarten nachgiebiges Beinverhalten mittels des vom Rennen bekannten Masse-Feder-Modells abstrahiert. Zunächst wird eine vergleichsweise einfache, analytische Näherungslösung desselben identifiziert; in einem weiteren Schritt wird die charakteristische Geschwindigkeit des Gangartwechsels aus federartigem Beinverhalten erklärt; und schließlich wird ein zweibeiniges Masse-Feder-Modell für Gehen vorgeschlagen, welches die beobachteten Bodenreaktionskräfte dieser Gangart beschreibt. Auf der Ebene der neuromechanischen Beschreibung wird aufgezeigt, wie das mit einer mechanischen Feder abstrahierte Beinverhalten durch eine positive Rückkopplung der Muskelkraft dezentral und autonom innerhalb des Muskelskelettapparats erzeugt werden kann. Schließlich werden die Einzelergebnisse der Arbeit zusammengefasst, wobei die beiden fundamentalen Gangarten Gehen und Rennen innerhalb des zweibeinigen Masse-Feder-Modells vereinigt werden und die Bedeutung dieses, auf nachgiebigem Beinverhalten beruhenden Zusammenschlusses sowohl für die biomechanische und motorische Grundlagenforschung als auch für Anwendungen in der Robotik, Rehabilitation und Prothetik erörtert wird

Towards understanding human locomotion

Die zentrale Frage, die in der vorliegenden Arbeit untersucht wurde, ist, wie man die komplizierte Dynamik des menschlichen Laufens besser verstehen kann. In der wissenschaftlichen Literatur werden zur Beschreibung von Laufbewegungen (Gehen und Rennen) oftmals minimalistische "Template"-Modelle verwendet. Diese sehr einfachen Modelle beschreiben nur einen ausgewählten Teil der Dynamik, meistens die Schwerpunktsbahn. In dieser Arbeit wird nun versucht, mittels Template-Modellen das Verständnis des Laufens voranzubringen. Die Analyse der Schwerpunktsbewegung durch Template-Modelle setzt eine präzise Bestimmung der Schwerpunktsbahn im Experiment voraus. Hierfür wird in Kapitel 2.3 eine neue Methode vorgestellt, welche besonders robust gegen die typischen Messfehler bei Laufexperimenten ist. Die am häfigsten verwendeten Template-Modelle sind das Masse-Feder-Modell und das inverse Pendel, welche zur Beschreibung der Körperschwerpunktsbewegung gedacht sind und das Drehmoment um den Schwerpunkt vernachlässigen. Zur Beschreibung der Stabilisierung der Körperhaltung (und damit der Drehimpulsbilanz) wird in Abschnitt 3.3 das Template-Modell "virtuelles Pendel" für das menschliche Gehen eingeführt und mit experimentellen Daten verglichen. Die Diskussion möglicher Realisierungsmechanismen legt dabei nahe, dass die Aufrichtung des menschlichen Gangs im Laufe der Evolution keine große mechanische Hürde war. In der Literatur wird oft versucht, Eigenschaften der Bewegung wie Stabilität durch Eigenschaften der Template-Modelle zu erklären. Dies wird in modifizierter Form auch in der vorliegen Arbeit getan. Hierzu wird zunächst eine experimentell bestimmte Schwerpunktsbewegung auf das Masse-Feder-Modell übertragen. Anschließend wird die Kontrollvorschrift der Schritt-zu-Schritt-Anpassung der Modellparameter identifiziert sowie eine geeignete Näherung angegeben, um die Stabilität des Modells, welches mit dieser Kontrollvorschrift ausgestattet wird, zu analysieren. Der Vergleich mit einer direkten Bestimmung der Stabilität aus einem Floquet-Modell zeigt qualitativ gute Übereinstimmung. Beide Ansätze führen auf das Ergebnis, dass beim langsamen menschlichen Rennen Störungen innerhalb von zwei Schritten weitgehend abgebaut werden. Zusammenfassend wurde gezeigt, wie Template-Modelle zum Verständnis der Laufbewegung beitragen können. Gerade die Identifikation der individuellen Kontrollvorschrift auf der Abstraktionsebene des Masse-Feder-Modells erlaubt zukünftig neue Wege, aktive Prothesen oder Orthesen in menschenähnlicher Weise zu steuern und ebnet den Weg, menschliches Rennen auf Roboter zu übertragen.Human locomotion is part of our everyday life, however the mechanisms are not well enough understood to be transferred into technical devices like orthoses, protheses or humanoid robots. In biomechanics often minimalistic so-called template models are used to describe locomotion. While these abstract models in principle offer a language to describe both human behavior and technical control input, the relation between human locomotion and locomotion of these templates was long unclear. This thesis focusses on how human locomotion can be described and analyzed using template models. Often, human running is described using the SLIP template. Here, it is shown that SLIP (possibly equipped with any controller) cannot show human-like disturbance reactions, and an appropriate extension of SLIP is proposed. Further, a new template to describe postural stabilization is proposed. Summarizing, this theses shows how simple template models can be used to enhance the understanding of human gait

LEG STIFFNESS ASYMMETRY DURING COUNTERMOVEMENT JUMP

The purpose of this study was to identify whether the value of stiffness during two-legged countermovement jump in dominant lower limb is similar to the one in non-dominant lower limb. The research was conducted on 35 basketball players. Each participant performed three countermovement jumps with arm swing to the maximum height. Measurements employed a two Kistler force plates and a BTS SMART system for motion analysis. Leg stiffness (understood as an inclination of the curve of ground reaction forces vs. height of the greater trochanter of the femur) was computed for these parts of countermovement and take-off phases where its value was relatively constant and forcelength relationship was similar to linear. Statistically significant differences were found during the comparison of the stiffness in the dominant and non-dominant lower limb