632


JOHN A. FRONIMOS ET AL.


test, the free element was supported by a tensile element consisting of twisted, 19-strand steel wire with 0.027cm thick strands. A loop was made at each end of the wire by bending the wire back on itself twice; joining the overlapping segments with two copper crimp sleeves created a strong connection that resisted slipping. This setup being irreversible, a different wire was measured out for each test to provide the correct angle of insertion and angle of rotation, within a margin of error of 2° under the maximum load. The proximal end of the wire was attached to the wooden frame by the movable metal hook described previously. Weights were suspended from the hook on the bottom of the free element by a loop of wire held shut in the manner detailed above. Using iron dumbbell plates in increments of 1.13 kg (2.5 lb), weights of up to 4.54 kg (10 lb) were applied. For each of the two polarities, tests were conducted at two insertion angles (0°, 55°), two angles of rotation (15°, 25°), and four applied weights (0 kg, 1.13 kg, 2.27 kg, 4.54 kg). Two different cotyle depth-to-height ratios (0.3, 0.4) were used for the lower angle of rotation; only the shallower cotyle was used with the 25° angle. After the models were suspended and loaded, polarizing film was placed behind and in front of the models, with the polarization directions of the films perpendicular to one another. The models were backlit with a light source behind and slightly to the left of themodeled joint. The results were photographed with a Nikon D810 DSLR digital camera and a 60mm Micro Nikkor lens. The camera was placed at a distance of 26cm from the models and manually focused, with a 1/1.6 second exposure time and an aperture of F22. For each configuration, the resulting strain distributions were compared with one another and with the predictions of the hypothesis put forward by Troxell (1925). The hypothesis that joints between


proximally concave centra are significantly more resistant to failure by rotation was tested by measuring how much weight applied to the proximal end of the free element was necessary for joint failure (Supplementary Fig. 2). The experimental design had several additional parameters (Fig. 5) that were varied


to determine how different combinations affected the joint integrity. The tensile element supporting the free centrum, representing ligament, tendon, and muscle, was modeled as a piece of string, the length of which was varied to allow different insertion angles of the tensile element (20°, 45° to the horizontal; Fig. 5, α) and different angles of rotation of the free centrum(0°,15°,25°,35°;Fig. 5, β). The insertion angles reflect uncertainty as to whether sauro- pods had a crocodylian-style supraspinal ligament that spanned each joint at a low angle (e.g., Schwarz et al. 2007) or an avian- or ungulate-style nuchal ligament spanning multiple segments at higher angles (e.g., Tsuihiji 2004). The tensile element was attached with tape to the free centrum at one of three possible insertion sites: proximal to the joint (0.50 cm from the COR; Fig. 5, P), middle (3.25 cm from the COR; Fig. 5, M), or distal to the joint (6.00cmfromthe COR; Fig. 5, D). These permitted assessment of the hypothesis that dis- tal insertion sites result in medial rotation of the proximal end of the free element, as proposed by Fick (1890). Two different concavity depths were used (depth:heightratiosof0.2,0.3;Fig.5,c). The deepest concavity (depth:height ratio of 0.4) was not used because it only permitted rotation up to 15°; the intermediate-depth concavity, though designed to permit rotation up to 25°,


FIGURE 5. Model parameters that were varied during the rotational stability experiments, depicted on a schematic proximally concave joint with the free centrum supported by a tensile element. The alternative, proximally convex polarity, is not pictured. The parameters are the insertion angle of the tensile element (α), the angle of rotation of the free element (β), the depth of the cotyle relative to its height (c), and the insertion site of the tensile element (black crosses). Another variable, the addition of weight to the distal end of the free element, is not shown. The white circle represents the center of rotation. D, distal to the joint; M, middle; P, proximal to the joint.


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