arXiv subjects

Madhusudhan Venkadesan

Publications and source records attributed to Madhusudhan Venkadesan.

8 recordsLinked to original sources

arXiv2026

Size and shape of terrestrial animals

Natural selection for terrestrial locomotion has yielded unifying patterns in the body shape of legged animals, often manifesting as scaling laws. One such pattern appears in the frontal aspect ratio. Smaller animals like insects typically adopt a landscape frontal aspect ratio, with a wider side-to-side base of support than center of mass height. Larger animals like elephants, however, are taller than wide with a portrait aspect ratio. Known explanations for postural scaling are restricted to animal groups with similar anatomical and behavioural motifs, but the trend in frontal aspect ratio transcends such commonalities. Here we show that vertebrates and invertebrates with diverse body plans, ranging in mass from 28 mg to 22000 kg, exhibit size-dependent scaling of the frontal aspect ratio driven by the need for lateral stability on uneven natural terrain. Because natural terrain exhibit scale-dependent unevenness, and the frontal aspect ratio is important for lateral stability during locomotion, smaller animals need a wider aspect ratio for stability. This prediction is based on the fractal property of natural terrain unevenness, requires no anatomical or behavioural parameters, and agrees with the measured scaling despite vast anatomical and behavioural differences. Furthermore, a statistical phylogenetic comparative analysis found that shared ancestry and random trait evolution cannot explain the measured scaling. Thus, our findings reveal that terrain roughness, acting through natural selection for stability, likely drove the macroevolution of frontal shape in terrestrial animals.

physics.bio-ph↗

arXiv2025

Transverse contributions to the longitudinal stiffness of the human foot

Humans rely on foot stiffness to withstand the propulsive forces of walking and running. Skeletal adaptations that increase foot stiffness include the medial longitudinal arch (MLA) and the transverse tarsal arch (TTA). The TTA has been hypothesized to stiffen the foot through cross-axis coupling of transverse intermetatarsal stiffness with sagittal-plane midfoot stiffness, but this has been tested only in cadaveric specimens. In vivo testing is essential because muscle contraction substantially modulates MLA function and may similarly affect the TTA's cross-axis coupling. Here we provide in vivo evidence for the TTA's contribution to foot stiffness by externally increasing intermetatarsal stiffness and measuring its effects on midfoot elasticity during walking. As predicted by the cross-axis coupling hypothesis, increasing intermetatarsal stiffness with an elastic tape wrapped around the forefoot reduced the energy absorbed in midfoot flattening and increased sagittal-plane midfoot stiffness concomitantly (mean,$\pm$,standard error of the mean (SEM): $13.9\% \pm 3\%$ and $16.8\% \pm 5.8\%$, respectively). However, taping did not change the curvature of the TTA, thereby isolating the effects of cross-axis coupling from morphological changes to the TTA. Thus, forefoot taping modulates midfoot stiffness through cross-axis coupling and could provide a non-invasive means to manage pathological foot flexibility or enhance athletic performance.

physics.bio-ph↗

arXiv2021

Rheological basis of skeletal muscle work loops

Skeletal muscle is subjected to simultaneous time-varying neural stimuli and length changes in vivo. Work loops are experimental representations of these in vivo conditions and exhibit force versus length responses that are not explainable using either soft matter rheology or the classical isometric and isotonic characterizations of muscle. These gaps in our understanding have often prompted the search for new muscle phenomena. However, we presently lack a framework to explain the mechanical origins of work loops that integrates multiple facets of current understanding of muscle, as a rheological material and also a stimulus-responsive actuator. Here we present a new hypothesis that work loops emerge by splicing together force versus length loops corresponding to different constant stimuli. Using published muscle datasets and a detailed sarcomere model, we find that the hypothesis accurately predicts work loops and helps understand them in terms of rheological behaviors measured at fixed-stimuli. Importantly, this framework identifies conditions under which a rheological understanding of muscle fails to explain the emergent work loops, and new muscle phenomena may be necessary to explain its in vivo function.

cond-mat.soft↗

arXiv2018

How to run on rough terrains

Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with an alternating aerial and stance phase. Stance is modeled as a passive, impulsive collision followed by an active, impulsive push-off that compensates for collisional losses. Such a runner has infinitely many strategies to maintain periodic gaits on flat ground. However, these strategies differ in how perturbations due to terrain unevenness are propagated. Instabilities manifest as tumbling (orientational instability) or failing to maintain a steady speed (translational instability). We find that open-loop strategies that avoid sensory feedback are sufficient to maintain stability on step-like terrains with piecewise flat surfaces that randomly vary in height. However, these open-loop runners lose orientational stability on rough terrains whose slope and height vary randomly. Only by avoiding tangential collisions is orientational stability recovered. Tangential collisions may be avoided through leg-retraction to match foot and ground speed at touch down. By analyzing the propagation of perturbations, we derive a single dimensionless parameter that governs stability and guides the design and control of both biological and robotic runners.

physics.bio-ph↗

arXiv2017

Stiffness of the human foot and evolution of the transverse arch

Foot stiffness underlies its mechanical function, and is central to the evolution of human bipedal locomotion. The stiff and propulsive human foot has two distinct arches, the longitudinal and transverse. By contrast, the feet of non-human primates are flat and softer. Current understanding of foot stiffness is based on studies that focus solely on the longitudinal arch, and little is known about the mechanical function of the transverse arch. However, common experience suggests that transverse curvature dominates the stiffness; a drooping dollar bill stiffens significantly upon curling it along the transverse direction, not the longitudinal. We derive a normalized curvature parameter that encapsulates the geometric principle underlying the transverse curvature-induced stiffness. We show that the transverse arch accounts for almost all the difference in stiffness between human and monkey feet (vervet monkeys and pig-tailed macaques) by comparing transverse curvature-based predictions against published data on foot stiffness. Using this functional interpretation of the transverse arch, we trace the evolution of hominin feet and show that a human-like stiff foot likely predates Homo by $\sim 1.5$ million years, and appears in the $\sim 3.4$ million year old fossil from Burtele. A distinctly human-like transverse arch is also present in early members of Homo, including Homo naledi, Homo habilis, and Homo erectus. However, the $\sim 3.2$ million year old Australopithecus afarensis is estimated to have possessed a transitional foot, softer than humans and stiffer than other extant primates. A foot with human-like stiffness probably evolved around the same time as other lower limb adaptations for regular bipedality, and well before the emergence of Homo, the longitudinal arch, and other adaptations for endurance running.

physics.bio-ph↗

arXiv2017

Curvature-induced stiffening of a fish fin

How fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin's curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness. Using analysis of a 3D reconstruction of a Mackerel (Scomber japonicus) pectoral fin, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The 3D reconstruction shows that, even in its geometrically flat state, a functional curvature is embedded within the fin microstructure owing to the morphology of individual rays. Since the ability of a propulsive surface to transmit force to the surrounding fluid is limited by its stiffness, the fin curvature controls the coupling between the fish and its surrounding fluid. Thereby, our results provide mechanical underpinnings and morphological predictions for the hypothesis that the spanned range of fin stiffnesses correlates with the behaviour and the ecological niche of the fish.

physics.flu-dyn↗

arXiv2015

Polynomial mechanics and optimal control

We describe a new algorithm for trajectory optimization of mechanical systems. Our method combines pseudo-spectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical quantities such as momentum. We thus obtain a global discretization of the Lagrange-d'Alembert variational principle using pseudo-spectral methods. Our proposed scheme inherits the numerical convergence characteristics of spectral methods, yet preserves momentum-conservation and symplecticity after discretization. We compare this algorithm against two other established methods for two examples of underactuated mechanical systems; minimum-effort swing-up of a two-link and a three-link acrobot.

eess.SY↗

arXiv2010

Optimal strategies for throwing accurately

Accuracy of throwing in games and sports is governed by how errors at projectile release are propagated by flight dynamics. To address the question of what governs the choice of throwing strategy, we use a simple model of throwing with an arm modelled as a hinged bar of fixed length that can release a projectile at any angle and angular velocity. We show that the amplification of deviations in launch parameters from a one parameter family of solution curves is quantified by the largest singular value of an appropriate Jacobian. This allows us to predict a preferred throwing style in terms of this singular value, which itself depends on target location and the target shape. Our analysis also allows us to characterize the trade-off between speed and accuracy despite not including any effects of signal-dependent noise. Using nonlinear calculations for propagating finite input-noise, we find that an underarm throw to a target leads to an undershoot, but an overarm throw does not. Finally, we consider the limit of the arm-length vanishing, i.e. shooting a projectile, and find that the most accurate shooting angle bifurcates as the ratio of the relative noisiness of the initial conditions crosses a threshold.

physics.bio-ph↗