INTERVERTEBRAL JOINT POLARITY IN SAUROPODS


635


FIGURE 7. Stability differences between proximally concave and proximally convex joints across a range of biologically plausible loading conditions. Each cell indicates how much more weight (in grams) was required for joint failure to occur in the proximally concave joint than the proximally convex one. Warm colors indicate differences that exceeded the model uncertainty, and cool colors indicate differences that did not exceed the model uncertainty. The columns and rows indicate five additional variables: the insertion site of the tensile element (proximal, middle, distal), the insertion angle of the tensile element (α), the angle of rotation of the free element (β), the depth of the concavity relative to its height (c), and the addition of weight to the distal end of the free element (+ ). A > sign indicates that the measured value is a minimum because the proximally concave joint did not fail at the maximum applied weight (250g with no distal loading or 230g with distal loading). Values ≥0 are those for which neither polarity failed at the maximum load.


As seen in the epoxy models (Fig. 6), the cotylar rim is strained regardless of joint polarity, and no significant difference in the magnitude or distribution of strain is detected within the sensitivity of the photoelastic analysis. Troxell (1925) assumed that forces acting along a series of procoelous caudal vertebrae would be parallel to the distal element in any given joint, and this assumption guided the experiment of Gosnold and Slaughter (1977). The observed strain distribution in joints loaded as cantilevers indicates that forces act oblique to the free element, rather than parallel to it. This orientation is consistent with the resultant vector of the applied forces (i.e., gravity and tensile support). When the tensile element is horizontal, the resultant vector has a 45° angle to the ground. This is approximately orthogonal to the joint surface of the ventral cotylar rim for proximally convex centra and of the dorsal cotylar rim for proximally concave centra. When the tensile


element is steeply angled, the resultant vector will have a shallower angle and a smaller magnitude, hence the lower observed strain in the models. Therefore, the strongly conserved pattern of cervical opisthocoely and caudal procoely in sauropods is not well explained by a differential vulnerability to cotylar rim fractures. The only instance in which the strain


magnitude differed between joint polarities occurred with a high angle of rotation, a horizontal insertion, and a shallow cotyle; in this case, the proximally convex joint experienced much greater strain. Observation of this joint revealed that the joint surfaces had lost contact with each other dorsally, creating a narrow gape. This gape appears to have resulted from the distal and ventral rotation and translation of the condyle, as discussed with regard to rotational in- stability. This outcome is unsurprising in a proximally convex joint having this angle of


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