Data from: Polarity of concavo-convex intervertebral joints in the necks and tails of sauropod dinosaurs

The highly elongated necks, and often tails, of sauropod dinosaurs are composed of concavo-convex vertebrae that provided stability without compromising mobility. Polarities of these concavo-convex joints in the neck and tail are anatomically opposite one another but mechanically equivalent. Opisthocoelous cervical vertebrae and procoelous caudal vertebrae have the convex articular face directed away from the body and the concave articular face directed towards the body. This “sauropod-type” polarity is hypothesized to be (1) more resistant to fracturing of the cotylar rim and (2) better stabilized against joint failure by rotation than the opposite polarity. We used physical models to test these two functional hypotheses. Photoelastic analysis of model centra loaded as cantilevers reveals that neither polarity better resists fracture of the cotylar rim; strain magnitude and localization are similar in both polarities. We assessed the rotational stability of concavo-convex joints using pairs of concavo-convex centra loaded near the joint. “Sauropod-type” joints withstood significantly greater weight before failure occurred, a pattern we interpret to be dependent on the position of the center of rotation, which is always within the convex part of the concavo-convex joint. In “sauropod-type” joints, the free centrum rotates about a center of rotation that lies within the more stable proximal centrum. In contrast, the opposite polarity results in a free centrum that rotates about an internal point; when the condyle rotates down and out of joint, the distal end rotates back toward the body, unopposed by ligamentous support. “Sauropod-type” joints remained stable with greater mobility, more mechanically-advantageous tensile element insertions, and greater distal loads than the opposite polarity. The advantages conferred by this joint polarity would have facilitated the evolution of hyperelongated necks and tails by sauropods. Polarity of concavo-convex joints of the appendicular skeleton (e.g., hip, shoulder) is also consistent with the demands of rotational stability.

蜥脚类恐龙（sauropod dinosaurs）极长的颈部，以及多数情况下伴随的超长尾部，其骨骼由凹凸椎骨（concavo-convex vertebrae）构成，这类椎骨可在不降低活动性的同时提升结构稳定性。颈部与尾部的这类凹凸关节的极性（polarity）在解剖学上呈相反状态，但力学性能等效。后凸型颈椎（opisthocoelous cervical vertebrae）与前凸型尾椎（procoelous caudal vertebrae）的凸状关节面均朝向远离躯干的方向，凹状关节面则朝向躯干。这种“蜥脚类型”关节极性被提出存在两项功能优势：其一，更能抵御关节盂缘（cotylar rim）的断裂；其二，相较于相反极性的关节，其可更好地抵御旋转导致的关节失效。我们通过物理模型对这两项假说展开验证。对作为悬臂梁加载的模型椎体开展光弹性分析（photoelastic analysis）后发现，两种极性的关节盂缘抗断裂性能并无显著差异；二者的应变幅值与应变集中位置均较为相似。我们通过成对设置于关节附近的凹凸椎体，评估了凹凸关节的旋转稳定性。“蜥脚类型”关节在发生失效前可承受显著更大的载荷，我们认为这一现象取决于旋转中心的位置——旋转中心始终位于凹凸关节的凸状部分内部。在“蜥脚类型”关节中，活动椎体围绕更稳定的近端椎体内部的旋转中心转动。与之相反，相反极性的关节会使得活动椎体围绕内部一点转动：当髁突（condyle）向下转动并脱离关节时，远端会向躯干方向回摆，且无韧带支撑提供阻力。相较于相反极性的关节，“蜥脚类型”关节可在保持更高活动性的前提下维持结构稳定，其力学优势更利于受拉结构的附着，且可承受更大的远端载荷。这类关节极性所带来的优势，或曾助力蜥脚类恐龙演化出超伸长的颈部与尾部。附肢骨骼（appendicular skeleton，如髋部、肩部）的凹凸关节极性，同样契合旋转稳定性的功能需求。