THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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Alexander et al. (1 979) rewrded a duty factor $=0.29 at a stride frequency of 2.3 Hz. Such a low duty factw seems unrealistic for G. libratus, a much larger biped than the ostrich. With legs roughly twice as long as those of an ostrich, the tyrannosaurid could conceivably reach fairly high absolute speeds without recourse to a long ballistic suspended phase. Carrano (1998) and Christiansen (1 999) hypothesized that large theropods were unlikely to have employed long suspended phases. These would require the inducement of high potential energies, leading to high (and potentially damaging) bending force about secondary moments when the foot retumed to the ground. These authors did not consider how energy storage by elastic tissues would decrease the rate of strain on bone and distribute footfaIl energies (see Discussion below). Nevertheless, the high number of unknown factors introduced by tendon elasticity, as well as consideration of bone strength (Christiansen 1999), signal caution in ascnbing long ballistic periads to Iarge theropods. A conservatively high duty factor, p=0.45, is therefore estimated for a nrnning Gorgosaurus libratus. b. Forces with the metatarsus normal to the substrate: Substituting these quantities into equation (6): m=2212 kg, g=9.81 rneterdsec?, p=0.45, gives the resulting ground-reaction force FG: (7) FG=37873 N
This quantity approximates the vertical ground-reaction force acting upon the foot during fast linear locomotion, when the metatarsus is perpendicular to the ground (Figure 4.1). With the metatarsus at 90 degrees to the substrate, most of the ground- reaction force would be channeled vertically through the proximal phalanges and metatarsals. The proportion of FG channeled through a given metatarsal is directly proportional to the area of ground undemeath the element. To detemine relative areas, the metatarsus of TMP 94.1 2.602 was inverted, and the distal surface of each metatarsal was photographed from above. A plumb bob, hanging from the camera to the visual center of each distal surface, ensured that the three elements were photographed from the same distance. The photographs were scanned, and the relative areas determined by Object-Image for Macintosh software, from the United States Nationai Institutes of Health. Metatarsal III accounted for 0.4 of the total area; MT II and MT IV accounted for 0.3 each. These quantities and FG from equation 7 were substituted into the following equation: (8) FGMTX= (FG) (MTx%), where x is the number of the metatarsal and MTxOlb is me relative area. Figure 4.1 diagrams the resulting axial forces on each metatarsal: FGmi=(37873 N)(0.3)=11362 N Fcmi~(37873 N)(0.4)=15149 N F~~nv=(37873 N)(0.3)=11362 N.
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THE UNIVERSITY OF CALGARY Functiona
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Many figures in this thesis use col
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ACKNOWLEûGEM ENTS Many friends and
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Approval page Acknowledgements Tabi
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CONCLUDING COMMENTS Figures for Cha
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CHAPTER 5: Mechanical and phylogene
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LIST OF FIGURES Figure 1 .l. Phylog
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Figure 3.6. Osteological correlates
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AMNH GI HMN IVPP MOR NMC OMNH PIN P
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and constructional morphology revea
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1985, Bryant and Seymour 1990). If
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surfaces of a Tyrannosaurus rex spe
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3. Troodontidae (Figure 1.2): Trwdo
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Hypothesized functions of the tyran
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1. Atomization (Chapters 2 and 3).
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Figure 1.1. P hylogenetic diagram o
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Figure 1.2. Phylogenetic diagram of
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Figure 1 .S. Skeletal restorations
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did not quantify the degree of prox
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qualitative debate over arctometata
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This hypothesis focuses on tyrannos
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Table 2.1. Theropod and Plafeosauru
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specimens in the figures reflects a
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were not attempted. While this limi
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Chapter 3). 1 now address variation
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- Ç6'P 1 68'€tr 1 L'OC 99'66 L'9
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Table 2.3: Log-transformed values f
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experiences a sharp laterally indin
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ecause it can be cursorily dassifie
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arctometatarsalian specimens, the l
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) Shaf€ and region of proximal ar
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a) Ginglymus. Figure 2.14 shows the
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) Shaft and region of proximal arti
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measurements of width pV2S%TU-DE an
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Table 2.4b Variancelmeasurement eac
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the largest sum of linear measureme
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Table 2.5: Specimen statistics Herr
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and Sinraptor dongi specimens. With
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In addition, a hook like proximal a
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oth physical narrowing and elongati
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1s the MT 111 shape segregation fun
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tyrannosaurids, ornithomimid, and t
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proximal constriction, white EImisa
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Figure 2.2. Tyrannosaurid, trwdonti
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Figure 2.4. Dromaeosaurid and carno
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- Anterior (flexor) surface medial
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Figure 2.7. Left MT III of Tyrannos
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Figure 2.8. Left MT III of Gorgosau
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Figure 2.9. Left MT III of an omith
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Figure 2.10. Left metatarsus of Tmd
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Figure 2.1 1. Left MT III of Elmisa
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Figure 2.12. Right MT III of Deinon
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Figure 2.13. Left MT III of Allosau
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Figure 2.14. Left metatarsus of Sin
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Figure 2.15. Plots of MT Ill specir
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Figure 2.16. Plot of third metatars
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tv . ... . Ri. . . .
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Figure 2.19. Plot of third metatars
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CHAPTER 3: Tensile keystone model o
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dynamically transmitted Iommotor fo
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Table 3.1 . Metatarsi examined in t
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interrnetatarsal dynamics in these
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compelled analysis of movement evid
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Once prepared, TMP 94.1 2.602 and i
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Daspletosaurus tomsus (MOR 590), an
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2. Freedom of movement inferred fro
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Table 3.2. Surface areas of intemet
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phylogenetic bracketing Wtmer 1995)
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4) Forces from anterior displacerne
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Page 155 and 156: The preceding discussion derives fr
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Page 159: Figure 3.1. Schematic representatio
Page 163: Figure 3.3. CT reconstruction of ri
Page 167: Figure 3.5. MT II (left element) an
Page 171: Figure 3.7. Osteological correlates
Page 175: Figure 3.9. Osteological correlates
Page 179: Figure 3.1 1 ae. The metatarsal rec
Page 187: Figure 3.13. Ligament contribution
Page 191 and 192: Figure 3.15. Anatorny of the equid
Page 193: Figure 3.16. Cornparison of loading
Page 196 and 197: (nodes), and solving stresslstrain
Page 198 and 199: The practicality of the finite elem
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Page 202 and 203: A FORCE INPUTS AND MATERIAL PROPERT
Page 206 and 207: The preceding loading regime entait
Page 208 and 209: detemined by using the photographic
Page 210 and 211: 2. Preparation of data for contour
Page 212 and 213: . - Elastic modulus (GP4 Ex EY Ez P
Page 214 and 215: conversion. Volume-to-nuages facili
Page 216 and 217: maintained. An angle of 2 degrees p
Page 218 and 219: of MT III (Figure 4.4, pinpointed b
Page 220 and 221: anterodorsal rotation of the distal
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Page 224: Figure 4.1. Initial loads and bound
Page 228: Figure 4.3. Finite element mesh of
Page 232: Figure 4.5. Strain distribution in
Page 236 and 237: CHAPTER 5: Mechanical and evolution
Page 238 and 239: y distal intermetatarsal ligaments,
Page 240 and 241: Probable fundion of the tyrannosaur
Page 242 and 243: Ornitholestes, and camosaurs) incre
Page 244 and 245: morphology matches in degree the co
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Page 248 and 249: face of the skull met part of the m
Page 250 and 251: Alternately, a morphological novelt
Page 252 and 253: outgroup to ail theropods, and the
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convincingly evident in figures of
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parsimonious scenarios are outlined
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dromaeosaurids], and a dade compris
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arctometatarsalian forrns. The conv
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Proximal intermetatarsal ligaments
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witti a surfeit of potentially supp
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Figure 5.2. Phylogeny of the Therop
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Bock W.J. and von Wahlert G. Evolut
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Cume P.J. 1997. Theropoda. In: Fari
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Grenard S. 1991. Handbook of Alliga
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Liem K.F. and Osse J.W.M. 1975. Bio
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Richtsmeier J.T. and Cheverud J.M.
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Woo S., Maynard J., Butler O. 1987.
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Different variables in a PCA will h
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