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. We hypothesized that snakes can generate propulsion using a similar mechanism of posteriorly propagating vertical waves pressing against suitably oriented environmental asperities. Using an array of horizontally oriented cylinders, one of which was equipped with force sensors, and a motion capture system, we found snakes generated substantial propulsive force and propulsive impulse with minimal contribution from lateral undulation. Additional tests showed that snakes could propel themselves via vertical undulations from a single suitable contact point, and this mechanism was replicated in a robotic model. Vertical undulations can provide snakes a valuable locomotor tool for taking advantage of vertical asperities in a variety of habitats, potentially in combination with lateral undulation, to fully exploit the 3D structure of the habitat.

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. We recorded the angular ROM while manipulating the models in yaw (lateral bending), pitch (dorsoventral bending) and roll (axial torsion). Removing the zygosphene typically increased yaw and dorsal pitch ROM. In the normal vertebrae, roll was <2.5 deg for all combinations of pitch and yaw. Roll increased in altered vertebrae but only for combinations of high yaw and ventral pitch that were near or beyond the limits of normal vertebra ROM. In the prairie rattlesnake and brown tree snake, roll in the altered vertebrae was always limited by bony processes other than the zygosphene, whereas in the altered vertebrae of the corn snake and boa constrictor, roll ROM was unconstrained when the pre-and post-zygapophyses no longer overlapped. The zygosphene acts as a bony limit for yaw and dorsal pitch, indirectly preventing roll by precluding most pitch and yaw combinations where roll could occur and potentially allowing greater forces to be applied across the vertebral column than would be possible with only softtissue constraints.

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

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