626


JOHN A. FRONIMOS ET AL.


and tail suggests there is a functional advantage for centra that are concave toward the body compared with the opposite polarity. Several previous studies sought to identify the factors that determine concavo-convex joint polarity. Early proposals by L. Fick (1845) and Henke and Reyher (1874) assumed that muscles play an active role in developing joint shape during ontogeny, leading those authors to the conclusion that the location of muscle insertion sites on the moremobile bone (i.e., the one farther fromthe body) determines whether its articular surface is convex or concave. This was expanded upon by R. Fick (1890), who, like his predecessors, focused predominately on the concavo-convex joints of the human appendicular skeleton. Summarizing Henke and Reyher (1874), Fick (1890: p. 392) wrote that, “the one articular surface where the muscles insert near the joint will always be ground concave, the joint end with distant muscle attachments, in contrast, will be convex” (translated from the German by J.A.F. and J. Fahlke). In other words, when muscle insertion sites on the free element are located close to the joint, the free element will develop a cotyle, whereas when insertion sites are distally located, it will develop a condyle instead (Fig. 2). The fixed element of the joint will develop a corresponding condyle or cotyle, respectively. Although Fick (1890) described the shaping of the joint surface as a process of abrasion, Fick (1904: pp. 40–44; following Roux 1891) later clarified that the same outcome would result from bone growth being inhibited by pressure at the contact points between joint surfaces. Fick (1890) predicted the relationship


betweenmuscle insertion site and joint polarity based on his reconstruction of the forces acting on the free element in each scenario (Fig. 2). He decomposed the applied muscular force (Fm) into a rotational component (R) that moves the free element and a compressional component parallel to the free element (Cfr). At the joint surface, the compressional force acts oblique to the fixed element and so can be further decomposed into compression acting on the fixed element (Cfx) and a shear component (S) acting along the joint surface. When the site of force application is far from


the joint (Fig. 2A, t1), the opposing rotational and shear components are widely spaced, and there is a center of rotation in between them within the free element; as the distal end rotates laterally, the proximal end rotates medially. Although not clearly stated by Fick (1890), if the muscle originates from the fixed element, its pull will have a greater medial component the farther distally it inserts on the free element, which will also contribute to the described movement. Given the assumption that muscular action determines joint shape, Fick (1890) concluded that the pressure of this movement would abrade or inhibit bone growth at the corners of the free element, eventually rounding its end into a condyle (Fig. 2A, t2); the corresponding pressure on the central part of the fixed element would generate the cotyle. In contrast, when muscles insert on the free element near the joint, the rotational component of the applied force acts close to the articular surface (Fig. 2B, t1). With the rotational force more directly opposed to the shear component, the center of rotation is located at the joint surface, and the proximal end of the free element must rotate laterally, along with the rest of the bone. The pulling muscle may also have a lesser medial component and a shorter moment arm, reducing the magnitude of the shear. As the free element is pulled laterally over the edge of the fixed element, the corners of the fixed element would be rounded off into a condyle, and the free element would bear the cotyle


(Fig. 2B, t2). To test his hypothesis, Fick created flat-ended elements in plaster and attached strings to the free element at insertion sites near to or far from the joint. When the strings were repeatedly pulled side to side by a motor, the articular surfaces were ground into a condyle and cotyle in accordance with the predictions above (see Fick 1890: Fig. 5, reproduced in Supplementary Fig. 1). Although the mechanics described by Fick


(1890) are plausible, the hypothesis presented does not explain the distribution of opisthocoely and procoely in the sauropod spine. Sauropod cervical vertebrae are hyperelongated, displa- cing the ligament and muscle insertions of the neural spine, transverse process, and cervical rib distally. According to the hypothesis, this


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