Geometric phase predicts locomotion performance in undulating living systems across scales.

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.

Functional diversity of snake locomotor behaviors: A review of the biological literature for bioinspiration.

Organismal solutions to natural challenges can spark creative engineering applications. However, most engineers are not experts in organismal biology, creating a potential barrier to maximally effective bioinspired design. In this review, we aim to reduce that barrier with respect to a group of organisms that hold particular promise for a variety of applications: snakes.

The relative contributions of multiarticular snake muscles to movement in different planes.

Muscles spanning multiple joints play important functional roles in a wide range of systems across tetrapods; however, their fundamental mechanics are poorly understood, particularly the consequences of anatomical position on mechanical advantage. Snakes provide an excellent study system for advancing this topic. They rely on the axial muscles for many activities, including striking, constriction, defensive displays, and locomotion.

Corn Snakes Show Consistent Sarcomere Length Ranges Across Muscle Groups and Ontogeny.

The force-generating capacity of muscle depends upon many factors including the actin-myosin filament overlap due to the relative length of the sarcomere. Consequently, the force output of a muscle may vary throughout its range of motion, and the body posture allowing maximum force generation may differ even in otherwise similar species. We hypothesized that corn snakes would show an ontogenetic shift in sarcomere length range from being centered on the plateau of the length-tension curve in small individuals to being on the descending limb in adults.

Snakes combine vertical and lateral bending to traverse uneven terrain.

Terrestrial locomotion requires generating appropriate ground reaction forces which depend on substrate geometry and physical properties. The richness of positions and orientations of terrain features in the 3D world gives limbless animals like snakes that can bend their body versatility to generate forces from different contact areas for propulsion. Despite many previous studies of how snakes use lateral body bending for propulsion on relatively flat surfaces with lateral contact points, little is known about whether and how much snakes use vertical body bending in combination with lateral bending in 3D terrain.

Testing the effects of body depth on fish maneuverability via robophysical models.

Fish show a wide diversity of body shapes which affect many aspects of their biology, including swimming and feeding performance, and defense from predators. Deep laterally compressed bodies are particularly common, and have evolved multiple times in different families. Functional hypotheses that explain these trends include predator defense and increased maneuverability.

Generation of propulsive force via vertical undulations in snakes.

Lateral undulation is the most widespread mode of terrestrial vertebrate limbless locomotion, in which posteriorly propagating horizontal waves press against environmental asperities (e.g. grass, rocks) and generate propulsive reaction forces.

Defibrillate You Later, Alligator: Q10 Scaling and Refractoriness Keeps Alligators from Fibrillation.

Effective cardiac contraction during each heartbeat relies on the coordination of an electrical wave of excitation propagating across the heart. Dynamically induced heterogeneous wave propagation may fracture and initiate reentry-based cardiac arrhythmias, during which fast-rotating electrical waves lead to repeated self-excitation that compromises cardiac function and potentially results in sudden cardiac death. Species which function effectively over a large range of heart temperatures must balance the many interacting, temperature-sensitive biochemical processes to maintain normal wave propagation at all temperatures.

Comparing the turn performance of different motor control schemes in multilink fish-inspired robots.

Fish robots have many possible applications in exploration, industry, research, and continue to increase in design complexity, control, and the behaviors they can complete. Maneuverability is an important metric of fish robot performance, with several strategies being implemented. By far the most common control scheme for fish robot maneuvers is an offset control scheme, wherein the robot's steady swimming is controlled by sinusoidal function and turns are generated biasing bending to one side or another.

Side-impact collision: mechanics of obstacle negotiation in sidewinding snakes.

Snakes excel at moving through cluttered environments, and heterogeneities can be used as propulsive contacts for snakes performing lateral undulation. However, sidewinding, which is often associated with sandy deserts, cuts a broad path through its environment that may increase its vulnerability to obstacles. Our prior work demonstrated that sidewinding can be represented as a pair of orthogonal body waves (vertical and horizontal) that can be independently modulated to achieve high maneuverability and incline ascent, suggesting that sidewinders may also use template modulations to negotiate obstacles.

Long Limbless Locomotors Over Land: The Mechanics and Biology of Elongate, Limbless Vertebrate Locomotion.

Elongate, limbless body plans are widespread in nature and frequently converged upon (with over two dozen independent convergences in Squamates alone, and many outside of Squamata). Despite their lack of legs, these animals move effectively through a wide range of microhabitats, and have a particular advantage in cluttered or confined environments. This has elicited interest from multiple disciplines in many aspects of their movements, from how and when limbless morphologies evolve to the biomechanics and control of limbless locomotion within and across taxa to its replication in elongate robots.

The control of routine fish maneuvers: Connecting midline kinematics to turn outcomes.

Maneuverability is an important factor in determining an animal's ability to navigate its environment and succeed in predator-prey interactions. Although fish are capable of a wide range of maneuvers, most of the literature has focused on escape maneuvers while less attention has been paid to routine maneuvers, such as those used for habitat navigation. The quantitative relationships between body deformations and maneuver outcomes (displacement of the center of mass and change in trajectory) are fundamental to understanding how fish control their maneuvers, yet remain unknown in routine maneuvers.

The Biomechanics of Multi-articular Muscle-Tendon Systems in Snakes.

The geometry of the musculoskeletal system, such as moment arms and linkages, determines the link between muscular functions and external mechanical results, but as the geometry becomes more complex, this link becomes less clear. The musculoskeletal system of snakes is extremely complex, with several muscles that span dozens of vertebrae, ranging from 10 to 45 vertebrae in the snake semispinalis-spinalis muscle (a dorsiflexor). Furthermore, this span correlates with habitat in Caenophidians, with burrowing and aquatic species showing shorter spans while arboreal species show longer spans.

Experimental modification of morphology reveals the effects of the zygosphene-zygantrum joint on the range of motion of snake vertebrae.

Variation in joint shape and soft tissue can alter range of motion (ROM) and create trade-offs between stability and flexibility. The shape of the distinctive zygosphene-zygantrum joint of snake vertebrae has been hypothesized to prevent axial torsion (twisting), but its function has never been tested experimentally. We used experimental manipulation of morphology to determine the role of the zygosphene-zygantrum articulation by micro-computed tomography (μCT) scanning and 3D printing two mid-body vertebrae with unaltered shape and with the zygosphene digitally removed for four species of phylogenetically diverse snakes.

Surprising simplicities and syntheses in limbless self-propulsion in sand.

Animals moving on and in fluids and solids move their bodies in diverse ways to generate propulsion and lift forces. In fluids, animals can wiggle, stroke, paddle or slap, whereas on hard frictional terrain, animals largely engage their appendages with the substrate to avoid slip. Granular substrates, such as desert sand, can display complex responses to animal interactions.

Comparative and functional analysis of the digital mucus glands and secretions of tree frogs.

Background: Mucus and mucus glands are important features of the amphibian cutis. In tree frogs, the mucus glands and their secretions are crucial components of the adhesive digital pads of these animals. Despite a variety of hypothesised functions of these components in tree frog attachment, the functional morphology of the digital mucus glands and the chemistry of the digital mucus are barely known.

Morphological and kinematic specializations of walking frogs.

The anuran body plan is defined by morphological features associated with saltatory locomotion, but these specializations may have functional consequences for other modes of locomotion. Several frog species use a quadrupedal walking gait as their primary mode of locomotion, characterized by limbs that move in diagonal pairs. Here, we examine how walking species may deviate from the ancestral body plan and how the kinematics of a quadrupedal gait are modified to accommodate the anuran body plan.

The diversity and evolution of locomotor muscle properties in anurans.

Anuran jumping is a model system for linking muscle physiology to organismal performance. However, anuran species display substantial diversity in their locomotion, with some species performing powerful leaps from riverbanks or tree branches, while other species move predominantly via swimming, short hops or even diagonal-sequence gaits. Furthermore, many anurans with similar locomotion and morphology are actually convergent (e.

Fluoromicrometry: A Method for Measuring Muscle Length Dynamics with Biplanar Videofluoroscopy.

Accurate measurements of muscle length changes are essential for understanding the biomechanics of musculoskeletal systems, and can provide insights into muscular work, force, and power. Muscle length has typically been measured in vivo using sonomicrometry, a method that measures distances by sending and receiving sound pulses between piezoelectric crystals. Here, we evaluate an alternative method, fluoromicrometry, which measures muscle length changes over time by tracking the three-dimensional positions of implanted, radio-opaque markers via biplanar videofluoroscopy.

Tail use improves performance on soft substrates in models of early vertebrate land locomotors.

In the evolutionary transition from an aquatic to a terrestrial environment, early tetrapods faced the challenges of terrestrial locomotion on flowable substrates, such as sand and mud of variable stiffness and incline. The morphology and range of motion of appendages can be revealed in fossils; however, biological and robophysical studies of modern taxa have shown that movement on such substrates can be sensitive to small changes in appendage use. Using a biological model (the mudskipper), a physical robot model, granular drag measurements, and theoretical tools from geometric mechanics, we demonstrate how tail use can improve robustness to variable limb use and substrate conditions.

Robust jumping performance and elastic energy recovery from compliant perches in tree frogs.

Arboreal animals often move on compliant branches, which may deform substantially under loads, absorbing energy. Energy stored in a compliant substrate may be returned to the animal or it may be lost. In all cases studied so far, animals jumping from a static start lose all of the energy imparted to compliant substrates and performance is reduced.

Modulation of orthogonal body waves enables high maneuverability in sidewinding locomotion.

Many organisms move using traveling waves of body undulation, and most work has focused on single-plane undulations in fluids. Less attention has been paid to multiplane undulations, which are particularly important in terrestrial environments where vertical undulations can regulate substrate contact. A seemingly complex mode of snake locomotion, sidewinding, can be described by the superposition of two waves: horizontal and vertical body waves with a phase difference of ± 90°.