Low effective mechanical advantage of giraffes’ limbs during walking reveals trade-off between limb length and locomotor performance

Basu, Christopher; Hutchinson, John R.

doi:10.1073/pnas.2108471119

Cited by 5 publications

(8 citation statements)

References 62 publications

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“…2 and refs. 40 – 43 ]. The Hill-number then predicts , in close agreement with scaling coefficients reported for mammals [ v ∝ m 0.17 and v ∝ m 0.16 , see refs.…”

Section: Resultsmentioning

confidence: 99%

“… 10 muscle lengths s −1 111 , 112 Faster strain rates have been reported, but likely represent extreme specialisation. G 0.3 41 – 43 , 107 Arithmetic average; see text and Fig. 2 .…”

Section: Methodsmentioning

confidence: 99%

“…

Fig. 2 The variation of the musculoskeletal gear ratio, G , with size across 42 vertebrate species varying by five orders of magnitude in mass 40 – 43 , 107 . In the initial across-clade analysis of the allometry of maximum running speed—which included invertebrates much smaller than 0.01 kg and vertebrates heavier than 2 t—an average gear ratio, G = 0.3 (solid line) was used, because it complies with the parsimonious assumption of geometric similarity, and because the gear ratio is confounded by evolutionary history, as evidenced by the different slopes for quadrupedal mammals vs. bipedal Macropodoidea, so that extrapolation bears significant risks [dashed vs. dotted line 41 , 107 ].…”

Section: Methodsmentioning

confidence: 99%

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Dynamic similarity and the peculiar allometry of maximum running speed

Labonte,

Bishop,

Dick

et al. 2024

Nat Commun

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Animal performance fundamentally influences behaviour, ecology, and evolution. It typically varies monotonously with size. A notable exception is maximum running speed; the fastest animals are of intermediate size. Here we show that this peculiar allometry results from the competition between two musculoskeletal constraints: the kinetic energy capacity, which dominates in small animals, and the work capacity, which reigns supreme in large animals. The ratio of both capacities defines the physiological similarity index Γ, a dimensionless number akin to the Reynolds number in fluid mechanics. The scaling of Γ indicates a transition from a dominance of muscle forces to a dominance of inertial forces as animals grow in size; its magnitude defines conditions of “dynamic similarity“ that enable comparison and estimates of locomotor performance across extant and extinct animals; and the physical parameters that define it highlight opportunities for adaptations in musculoskeletal “design” that depart from the eternal null hypothesis of geometric similarity. The physiological similarity index challenges the Froude number as prevailing dynamic similarity condition, reveals that the differential growth of muscle and weight forces central to classic scaling theory is of secondary importance for the majority of terrestrial animals, and suggests avenues for comparative analyses of locomotor systems.

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“…2 and refs. 40 – 43 ]. The Hill-number then predicts , in close agreement with scaling coefficients reported for mammals [ v ∝ m 0.17 and v ∝ m 0.16 , see refs.…”

Section: Resultsmentioning

confidence: 99%

“… 10 muscle lengths s −1 111 , 112 Faster strain rates have been reported, but likely represent extreme specialisation. G 0.3 41 – 43 , 107 Arithmetic average; see text and Fig. 2 .…”

Section: Methodsmentioning

confidence: 99%

“…

Section: Methodsmentioning

confidence: 99%

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Dynamic similarity and the peculiar allometry of maximum running speed

Labonte,

Bishop,

Dick

et al. 2024

Nat Commun

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“…For a contraction against the gravitational force, the inertial and the parasitic limit yield the same scaling coefficient, , vs , respectively. As an illustrative example, we directly predict the magnitude of this optimal mechanical advantage for quadrupeds (dark dotted line), and compare it to the result of an ordinary least squares (OLS) regression on the effective mechanical advantage for 16 species covering about six orders of magnitude in body mass (see (Basu and Hutchinson 2022; Biewener 1989b, 2005; Ren et al 2010) and SI for details). For a contraction against a quadratic drag force, the scaling coefficient for G opt should fall between the parasitic limit, , and the inertial limit .…”

Section: Discussionmentioning

confidence: 99%

Optimising the flow of mechanical energy in musculoskeletal systems through gearing

Polet,

Labonte

2024

Preprint

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Movement is integral to animal life, and most animal movement is actuated by the same engine: skeletal muscle. Muscle input is typically mediated by skeletal elements, resulting in musculoskeletal systems that are "geared": at any instant, the muscle force and velocity are related to the output force and velocity only via a proportionality constant G, the "mechanical advantage". The functional analysis of such "simple machines" has traditionally centred around this instantaneous interpretation, such that a small vs large G is thought to reflect a fast vs forceful system, respectively. But evidence is mounting that a complete analysis ought to also consider the mechanical energy output of a complete contraction. Here, we approach this task systematically, and use the theory of physiological similarity to study how gearing affects the flow of mechanical energy in a minimalist model of a musculoskeletal system. Gearing influences the flow of mechanical energy in two key ways: it can curtail muscle work output, because it determines the ratio between the characteristic muscle work and kinetic energy capacity; and it defines how each unit of muscle work is partitioned into different system energies, i.e. into kinetic vs. "parasitic" energy such as heat. As a consequence of both effects, delivering maximum work in minimum time and with maximum transmission efficiency generally requires a mechanical advantage of intermediate magnitude. This optimality condition can be expressed in terms of two dimensionless numbers, which reflect the key geometric, physiological, and physical properties of the interrogated musculoskeletal system, and the environment in which the contraction takes place. Illustrative application to exemplar musculoskeletal systems predicts plausible mechanical advantages in disparate biomechanical scenarios; yields a speculative explanation for why gearing is typically used to attenuate the instantaneous force output (G_opt < 1); and predicts how G needs to vary systematically with animal size to optimise the delivery of mechanical energy, in superficial agreement with empirical observations. A many-to-one-mapping from musculoskeletal geometry to mechanical performance is identified, such that differences in G alone do not provide a reliable indicator for specialisation for force vs speed- neither instantaneously, nor in terms of mechanical energy output. The energy framework presented here can be used to estimate an optimal mechanical advantage across variable muscle physiology, anatomy, mechanical environment and animal size, and so facilitates investigation of the extent to which selection has made efficient use of gearing as degree of freedom in musculoskeletal "design".

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“… Swanstrom et al, 2005 ; Becker et al, 2019 , 2020 ; Harrison et al, 2010 ; Symons et al, 2016 , 2017 ), neuromuscular control in rats and mice (e.g. Johnson et al, 2011 ; Yeo et al, 2011 ; Charles et al, 2018 ), muscle activations in dog forelimbs ( Stark et al, 2021 ), and relative postural leverage or ‘effective mechanical advantage’ across the evolution of giraffids ( Basu and Hutchinson, 2022 ). Neuromechanical analyses of walking in cats have benefitted from integration of empirical- and simulation-based data for the hindlimbs.…”

Section: Spectrum Of Digital Modelling Methods: Toward Theoretical Ap...mentioning

confidence: 99%

Modern three-dimensional digital methods for studying locomotor biomechanics in tetrapods

Demuth

Herbst

Polet

et al. 2023

Journal of Experimental Biology

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Here, we review the modern interface of three-dimensional (3D) empirical (e.g. motion capture) and theoretical (e.g. modelling and simulation) approaches to the study of terrestrial locomotion using appendages in tetrapod vertebrates. These tools span a spectrum from more empirical approaches such as XROMM, to potentially more intermediate approaches such as finite element analysis, to more theoretical approaches such as dynamic musculoskeletal simulations or conceptual models. These methods have much in common beyond the importance of 3D digital technologies, and are powerfully synergistic when integrated, opening a wide range of hypotheses that can be tested. We discuss the pitfalls and challenges of these 3D methods, leading to consideration of the problems and potential in their current and future usage. The tools (hardware and software) and approaches (e.g. methods for using hardware and software) in the 3D analysis of tetrapod locomotion have matured to the point where now we can use this integration to answer questions we could never have tackled 20 years ago, and apply insights gleaned from them to other fields.

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Low effective mechanical advantage of giraffes’ limbs during walking reveals trade-off between limb length and locomotor performance

Cited by 5 publications

References 62 publications

Dynamic similarity and the peculiar allometry of maximum running speed

Dynamic similarity and the peculiar allometry of maximum running speed

Optimising the flow of mechanical energy in musculoskeletal systems through gearing

Modern three-dimensional digital methods for studying locomotor biomechanics in tetrapods

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