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

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A FORCE INPUTS AND MATERIAL PROPERTIES f . Force and toque inputs Determination of the locomotor loading regime for the metatarsus of Gorgosaurus libratus requires estimates or rneasurements of several quantities. These variables include mass, moment arms, areas across which forces are transmitted, duty factors, acceleration, and the angle of the metatarsus relative to the substrate. The rationale and methods behind these estimates are now described. a. Mass and duty factor estimates: The mass of this G. libratus individual (TMP 94.12.602) was the constant parameter that determined instantaneous forces acting upon the metatarsus. Cross scaling revealed a mugh estirnate of the animal's mass. Femoral lengths of closely related animals are a common comparative benchmark for estimating masses (Paul 1988, 1997; HoItz 1994, Christiansen 1999). Paul (1 988) volumetrically estimated the mass G. Iibratus specimen TMP 81.1 0.1 at 2000 kg. The femur length (Il) of this specimen is 88 cm, while that of TMP 94.12.602 (Iz) is 91 cm. Mass (m) is proportional to the cube of ratios of linear sire (IdIr): (5) m;! = (12/ll)~ x ml The mass of Gorgosaunrs libratus TMP 94.12.602 is therefore estimated at 221 2 kg. This estimate may be slightly low, because many of its elements appear more robust than those of TMP 81.1 0.1 (Donna Sloan, pers. cornm.1999). The femora of the two animals appear to be comparable in robustness, however, so the estimate is likely to be a reasonable starting point (Anderson et al. 1985).
Dunng Iinear progression when an animal is moving at a constant speed, forces acting on the foot during stance phase are directly proportional to body weight (mg: mass x gravitational acceleration), and inversely proportional to duty factor (p), the fraction of time the foot spends wntading the ground (Alexander 1979): (6) F=xmg/4p. Quantities for rn (2212 kg, negtecting the mass of the phalanges) and g (9.81 rneters/second2) are estimated or known. The value for duty factor (p) depends upon the gait of the animal. Because animals utilize varying gains, a specific duty factor must be estimated to detemine forces germane to the problem at hand. For exarnple, at the walk-trot transition, the minimal value for P is 0.5, because each foot is on the ground half the time. When walking, animals employ a double stance phase, and the duty factor is above 0.5. This study examines the potential effects of high stresses on the G. Iibratus metatarsus; therefore faster gaits are considered. Running gaits, such as trotting or galloping, incorporate a ballistic suspended phase in which both feet are off the ground. The duty factor during running decreases to below 0.5. As a biped, Gorgosaurus libratus could not gallop, but could trot if forces and moments did not exceed safety factors for the limb bones. Gorgosaurus libratus probably employed gaits similar to those of bipedal modem ratites, such as ostriches (although limb proportions more closely match those of cursorial mammals: Carrano 1998). For a male ostrich running at high speed,
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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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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
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Page 198 and 199: The practicality of the finite elem
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Page 204 and 205: Alexander et al. (1 979) rewrded a
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
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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
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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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THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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