Abstract
SynopsisAnimal legs are diverse, complex, and perform many roles. One defining requirement of legs is to facilitate terrestrial travel with some degree of economy. This could, theoretically, be achieved without loss of mechanical energy if the body could take a continuous horizontal path supported by vertical forces only—effectively a wheel-like translation, and a condition closely approximated by walking tortoises. If this is a potential strategy for zero mechanical work cost among quadrupeds, how might the structure, posture, and diversity of both sprawled and parasagittal legs be interpreted? In order to approach this question, various linkages described during the industrial revolution are considered. Watt’s linkage provides an analogue for sprawled vertebrates that uses diagonal limb support and shows how vertical-axis joints could enable approximately straight-line horizontal translation while demanding minimal mechanical power. An additional vertical-axis joint per leg results in the wall-mounted pull-out monitor arm and would enable translation with zero mechanical work due to weight support, without tipping or toppling. This is consistent with force profiles observed in tortoises. The Peaucellier linkage demonstrates that parasagittal limbs with lateral-axis joints could also achieve the zero-work strategy. Suitably tuned four-bar linkages indicate this is feasibly approximated for flexed, biologically realistic limbs. Where “walking” gaits typically show out of phase fluctuation in center of mass kinetic and gravitational potential energy, and running, hopping or trotting gaits are characterized by in-phase energy fluctuations, the zero limb-work strategy approximated by tortoises would show zero fluctuations in kinetic or potential energy. This highlights that some gaits, perhaps particularly those of animals with sprawled or crouched limbs, do not fit current kinetic gait definitions; an additional gait paradigm, the “zero limb-work strategy” is proposed.
Highlights
The Possibility of Zero Limb-Work Gaits in Sprawled and Parasagittal Quadrupeds: Insights from Linkages of the Industrial Revolution
Some form of minimization of mechanical work has been invoked as an account for quadrupedal gaits (Alexander 1980; Ruina et al 2005; Srinivasan and Ruina 2006; Xi et al 2015; Polet and Bertram 2019; Usherwood 2019)
Quadrupedal gaits could, provided appropriate straight-line mechanisms were anatomically realizable, require consistently zero power, at least in terms of the limb mechanical work associated with weight support during steady translation
Summary
The Possibility of Zero Limb-Work Gaits in Sprawled and Parasagittal Quadrupeds: Insights from Linkages of the Industrial Revolution. One defining requirement of legs is to facilitate terrestrial travel with some degree of economy This could, theoretically, be achieved without loss of mechanical energy if the body could take a continuous horizontal path supported by vertical forces only—effectively a wheellike translation, and a condition closely approximated by walking tortoises. If this is a potential strategy for zero mechanical work cost among quadrupeds, how might the structure, posture, and diversity of both sprawled and parasagittal legs be interpreted? 動物使用對角肢體支撐的方法,並展示了垂直軸關節如 何在需要最小機械動力的情況下實現近似直線的水平移 動。每條腿增加壹個垂直軸關節使得安裝在墻上的拉出 監控器手臂可以實現移動,可以實現在重量的支持方面 零機械功的移動,並且不會傾斜或傾倒。這與在烏龜身 上觀察到的力分布相壹致。Peaucellier 聯動裝置顯示, 具有側軸關節的內收直立肢也可以實現零功策略。適當 調整的四桿機構表明這是可行的近似彎曲、生物學上合 理的四肢。“行走”步態壹般表現為質心動能和重力勢能 的非相位漲落,奔跑、跳躍和小跑步態表現為同相位能 量漲落,而陸龜近似的零肢功策略則表現為動能或勢能 的零漲落。這突出表明,某些步態,特別是那些四肢伸 展或蜷曲的動物步態,不符合當前的動態步態定義;這 裏我們提出了壹種新的步態模式——“零肢體-功策 略”。
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