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. Similar multi-articular spans are present in the prehensile tails of primates, the necks of birds, and our own digits. However, no previous analysis has adequately explained the mechanical consequences of these multi-articular spans. This paper uses techniques from the analysis of static systems in engineering to analyze the consequences of multiarticular muscle configurations in cantilevered gap bridging and compares these outcomes to a hypothetical mono-articular system. Multi-articular muscle spans dramatically reduce the forces needed in each muscle, but the consequent partitioning of muscle cross-sectional area between numerous muscles results in a small net performance loss. However, when a substantial fraction of this span is tendinous, performance increases dramatically. Similarly, metabolic cost is increased for purely muscular multi-articular spans, but decreases rapidly with increasing tendon ratio. However, highly tendinous spans require increased muscle strain to achieve the same motion, while purely muscular systems are unaffected. These results correspond well with comparative data from snakes and offer the potential to dramatically improve the mechanics of biomimetic snake robots.