Limb Swinging in Elephants and Giraffes and Implications for the Reconstruction of Limb Movements and Speed Estimates in Large Dinosaurs

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1 Mitt Mu Natkd Berl, Geowi Reihe 2 (1999) Limb Swinging in Elephant and Giraffe and Implication for the Recontruction of Limb Movement and Speed Etimate in Large Dinoaur Andrea Chritian', Reinert H G Müller z, Gundula Chritian' & Holger Preuchoft 3 With 4 figure and 3 table Abtract Speed of walking dinoaur that left foil trackway have been etimated uing the tride length time natural pendulum frequency of the limb In a detailed analyi of limb movement in walking Aian elephant and giraffe, however, ditinct difference between actual limb movement and the predicted limb movement uing only gravity a driving force were oberved Additionally, tride frequency wa highly variable Swing time wa fairly contant, but epecially at high walking peed, much horter than half the natural pendulum period An analyi of hip and houlder movement during walking howed that limb winging wa influenced by acceleration of hip and houlder joint epecially at high walking peed Thee reult ugget an economical fat walking mechanim that could have been utilied by large dinoaur to increae maximum peed of locomotion Thee finding throw new light on the dynamic of large vertebrate and can be ued to improve peed etimate in large dinoaur Key word: Dinoaur, auropod, peed, locomotion, biomechanic, functional morphology Zuammenfaung Gechwindigkeiten gehender Dinoaurier, die foile Fährten hinterlaen haben, wurden al Produkt au Schrittlänge und natürlicher Pendelfrequenz der Beine abgechätzt Eine detaillierte Analye der Beinbewegungen von gehenden Aiatichen Elefanten und Giraffen offenbarte allerding klare Unterchiede zwichen den tatächlichen Extremitätenbewegungen und den Bewegungen, die zu erwarten wären, wenn die Gravitation die einzige treibende Kraft dartellte Zudem erwie ich die Schrittfrequenz al hochgradig variabel Die Schwingzeit der Gliedmaßen war recht kontant, aber beonder bei hohen Gehgechwindigkeiten viel kürzer al die halbe natürliche Pendelperiode der Extremitäten Eine Analye der Bewegungen der Hüft- und Schultergelenke während de Gehen zeigte, daß da Schwingen der Gliedmaßen durch Bechleunigungen dieer Gelenke beeinflußt wurde, inbeondere bei hohen Gehgechwindigkeiten Die Reultate legen einen ökonomichen Mechanimu für chnelle Gehen nahe, der von großen Dinoauriern zur Erhöhung der Höchtgechwindigkeiten eingeetzt worden ein könnte Die Ergebnie werfen neue Licht auf die Dynamik großer Wirbeltiere Sie können zu Verbeerungen in den Schätzungen der Fortbewegunggechwindigkeiten großer Dinoaurier eingeetzt werden Schlüelwörter- Dinoaurier, Sauropoden, Gechwindigkeit, Fortbewegung, Biomechanik, Funktionelle Morphologie Introduction Speed of locomotion of dinoaur can be etimated from comparative tudie among recent vertebrate and from the law of mechanic Maximum peed can be etimated roughly from morphological trait like limb proportion and modelled trength of keletal element (Coomb 1978, Alexander 1985a, 1989a, Farlow et al 1995 ; but ee alo Alexander 1996) Speed can alo be etimated from foil trackway (Alexander 1976, 1985a, 1989a, Thulborn 1990) The uually narrow trackway of dinoaur (Lockley 1991, Thulborn 1990, Lockley & Hunt 1995) indicate that limb movement were retricted to paraagittal plane like mot mammal Additionally, a mammal-like limb poture for mot dinoaur can be modelled from keletal feature (Charig 1979, Bakker 1986, Paul 1987, 1988, Weihampel et al 1990, Fatovky & Weihampel 1996 ; but ee alo Johnon & Otrom 1995) Given a et of track and auming mammal like limb movement, relationhip among tride length, hip height, and peed can be applied to ' Mueum für Naturkunde, Intitut für Paldontologie, Invalidentr 43, Berlin, Germany 2 FIBUS, Arnheimer Str 120, Düeldorf, Germany 3 Ruhr-Univerität Bochum, Fakultät für Medizin, Anatomiche Intitut, Univeritättr 150, Bochum, Germany Received January 1999, accepted June 1999

2 82 Chritian, A, R H G Müller, G Chritian & H Preuchoft, Limb Movement in Large Dinoaur predict the approximate peed of the track-maker (Alexander 1976) Mot foil trackway of large dinoaur indicate a walking gait (Thulborn 1990) In thi paper "walking" i ued for any gait with a duty factor (fraction of time a foot i placed on the ground during a tride) above 0 5 in all limb (in accordance with Hildebrand (1985)) It ha been uggeted that walking peed from foil trackway can be etimated by multiplying tride length with tride frequency (Demathieu 1986) Becaue of the relatively low mucle force compared with body weight in large vertebrate (Alexander 1985b, Denie & Giinther 1989 ; Preuchoft et al 1994), minimal mucle force to accelerate the limb can be expected During walking, paive limb winging driven by gravity would minimie force and energy expenditure (Hildebrand 1985) Therefore, in a imple model of a tiff limb winging about a fixed pivot, tride frequency hould be imilar to the natural pendulum frequency of the limb Moderate deviation of the pendulum frequency up to ome ten percent are uggeted by more ophiticated model of limb winging during walking taking movement of the proximal joint and elatic propertie of the limb into account (Mochon & McMahon 1980a, b, McGreer 1990, 1992, Witte et al 1991, 1995, Alexander 1995) Stride frequency ha indeed been hown to be imilar to the natural pendulum frequency of the limb in everal walking vertebrate (Hildebrand 1985) However, coniderable variation in tride frequency of walking animal doe occur For peed etimate baed on etimated tride frequencie, a deeper undertanding of the mechanim of limb winging i needed to increae the accuracy Like mot large dinoaur, elephant have maive and pillar-like limb Limb winging in elephant i retricted to paraagittal plane Addi- tionally, like large dinoaur, elephant do not gallop Therefore, elephant are uitable for modelling the limb mechanic of large dinoaur (Chritianen 1997) In thi tudy, the winging behaviour of the limb of Aian elephant wa analyed during walking at different peed Stride frequency wa compared to the natural pendulum frequency of the limb at different peed The role that acceleration of hip and houlder joint play in accelerating the winging limb wa examined, a well Movement of hip and houlder joint were alo tudied in walking giraffe to examine the applicability of a model derived from elephant to other taxa The reult are dicued with repect to the mechanic of limb movement and peed etimate in large dinoaur Method Four adult Aian elephant (Elepha) of imilar ize were tudied at the Zoo Krefeld, Germany The animal were guided by their trainer who walked or ran in front of them along a traight line ("race track") of about 30 m length The walking peed of the elephant ranged between 0 5 m/ and 2 8 m/ Sequence were recorded with the help of the piccolor image analyi ytem (ee below) Additional equence were recorded from the elephant walking freely around in the encloure Stride period, duration of the wing phae (wing time), and duration of the upport phae (upport time) of ingle limb were determined in all equence Speed of locomotion could only be determined from the video for elephant moving along the race track In order to analye the limb movement in more detail, in one individual white marker were glued on the kin at everal poition on the limb, epecially at the location of the major joint (Fig 1) In the analyi of limb winging, angle Fig 1 Excurion angle a of the right hindlimb of an elephant relative to the vertical during a walking tride at a peed of about 1 6 m/ (olid line) compared to a ine-function (dotted line) t, time ; a, cp, contant ued to make the ine-function fit to the excurion angle during the wing phae

3 Mitt Mu Natkd Berl, Geowi Reihe 2 (1999) 83 the hindlimb wa repreented by the line that connected the marker fixed at the hip joint and a marker poitioned cloely above the ankle joint In ide-view, the centre of ma of the limb (CM) wa located cloe to thi line during the whole tride Skin diplacement relative to underlying bone were large at knee, elbow, and houlder, but mall enough at hip, at the dital part of the lower hindlimb, and at the hindfeet to conduct a quantitative analyi of angular diplacement of the hindlimb about the hip joint and to analye the movement of the hip joint during a tride Due to the large diplacement of the kin relative to the underlying bone in the forelimb, epecially at the houlder joint, angular diplacement of the forelimb and movement of the houlder joint were not quantified Additionally, hip and houlder movement of two adult giraffe were tudied at the Allwetterzoo Munter, Germany The animal walked along a traight wall in their paciou encloure without being influenced by any human The mean walking peed of the two animal wa cloe to 1 1 m/ and 1 3 m/, repectively, with little variation Reference point (marker) on the animal were identified with the help of the kin pattern The "piccolor" image analyi ytem, developed at ELBUS reearch intitute (Forchung-Intitut fur Bildverarbeitung, Umwelttechnik & Strbmungtechnik), ha been ued for all video equence acquiition and pot proceing "piccolor" i a PC-compatible computer ytem incorporating a powerful frame grabber, an imaging proceor board, and a modular interactive imaging oftware A black/white Hitachi KPMlek CCD camera wa ued at a geometrical image reolution of 768x512 picture element (pixel) 64 MByte of imaging memory allowed the acquiition of 7 econd real time equence at 25 Hz Every half-frame wa ued in the analyi in order to achieve a image rate of 50 Hz Thi procedure yielded only half the patial reolution in y-direction (the vertical) a in uing full frame The camera wa intalled at a ditance of 20 m from the elephant and 30 m from the giraffe perpendicular to the direction of locomotion Several image equence were tored on hard dik for later proceing In ome equence, the background wa graphically removed by mathematically ubtracting a reference image For the mall number of imple marker on the kin of an elephant the object tracking method wa ued Depending on the viibility and contrat of the marker, object tracking wa performed either automatically or by manually clicking on the marker with the moue pointer The poition of a marker wa determined with ubpixel accuracy by calculating the centre of gravity of it pixel area Thi proce revealed the path of elected pot of the animal in vectorized form For the net giraffe pattern, a cro correlation algorithm wa ued to determine diplacement of pot on the kin between two image The excurion angle of the hindlimb of the elephant relative to the vertical wa determined by repreenting the limb by a traight line connecting the marker at the hip joint with a marker that wa fixed cloely above the ankle joint In ide-view, the centre of ma of the limb wa located cloe to thi line during the whole tride In the elephant, the giraffe, and the Tendaguru-auropod dicued here, the location of the centre of ma and the natural pendulum period of the limb were etimated from limb proportion For thi purpoe, caled rubber model of the limb were cut In the giraffe, the diameter of the lower limb were increaed in order to compenate for the high fraction of bone Otherwie, contant denity wa aumed With a caled model, the location of the centre of ma of a limb can be directly determined uing the method decribed by Alexander (1989a) The natural pendulum period of the model were meaured by letting them wing friction-free around tranveral axe through the poition of hip and houlder joint, repectively To obtain the pendulum period of the full ized limb, the pendulum period of the model ha to be multiplied by the quare root of the caling factor The etimated natural pendulum period and frequencie were in accordance to reult of Hildebrand (1985) on large recent vertebrate and Demathieu (1986) on dinoaur Although the flexion of a limb changed during a tride and wa lightly different at different peed, the pendulum period wa little affected by thee change and nearly independent of walking peed Reult In the elephant, tride frequency varied coniderably, panning more than a factor of 3 in all pecimen It ranged from 0 34/ to 1 19/ in the individual with the highet variation All elephant frequently utilied tride frequencie far

4 84 Chritian, A, R H G Müller, G Chritian & H Preuchoft, Limb Movement in Large Dinoaur above the natural pendulum frequency of the limb, which wa 055 ± 0 05/ for all examined limb Support time wa variable, panning a factor of 4 or more in all individual in the hindlimb a well a in the forelimb Swing time, however, wa much le variable, ranging from 036 to 06 in the forelimb and from 038 to 064 in the hindlimb in the individual howing the widet range Shorter period were generally utilied at lower peed and were aociated with hort tride length, a typical for terretrial locomotion (Alexander 1976, McMahon & Bonner 1983) Table 1 preent the data collected from the hindlimb of two equally ized elephant Thee data were ued to compare the actual peed of locomotion with peed etimate from the literature (ee dicuion) During the wing phae, angular diplacement of the hindlimb approximately fitted inefunction (Fig 1), a expected for limb that move like pendula driven by gravity The wing time, however, wa coniderably horter than half the natural pendulum period (T = 1 75 ± 010, T/2 = 088 ± 005 ) of the limb, epecially during fat walking (Table 1) A expected (ee dicuion), during the upport phae, variability of upport time, angular diplacement of the limb, and vertical hip diplacement were very different from a gravitydriven pendulum model of limb motion The hip joint experienced coniderable acceleration during a tride During the firt 30%-40% of the wing phae, the hip joint of the winging hindlimb wa accelerated upward (Fig 2) Afterward, at the middle of the wing phae, it wa accelerated downward Thee hip acceleration increaed with tride frequency, but were difficult to quantify at low peed At high walking peed upward hip acceleration were nearly 10 m/2, cloe to the acceleration due to gravity _g = 9 81 m/ 2 Forward and backward acceleration of the hip joint were much lower and difficult to quantify becaue of error in locating the poition of the joint Although the poition of the houlder joint could not be recontructed in walking elephant, the reduction of wing time at high walking peed and the houlder movement in giraffe (ee below) upport the idea of a imilar acceleration mechanim in the forelimb Different from elephant, in giraffe, peed and tride frequency howed little variation, probably becaue the giraffe were not guided or chaed Mean value and tandard deviation are preented in Table 2 Speed ranged from 1 12 m/ to 184 m/ in the adult and from 093 m/ to 168 m/ in the emi-adult individual Stride period ranged from 1 58 to 226 in the adult and from 158 to 204 in the emi-adult giraffe Like elephant, wing time wa more contant than upport time and coniderably horter than half the natural pendulum period of the limb In the adult pecimen upport time ranged from 090 to 136 and wing time from 068 to 074 In the emi-adult pecimen upport time ranged from 1 02 to 1 56 and wing time from 056 to 064 The natural pendulum period wa T = 1 83 ± 0 10 in the adult giraffe (hip height h = 204 m) and T = 1 66 f 010 in the emi-adult giraffe (h = 164 m) In giraffe, hip moved in a imilar manner a in elephant Different from elephant, movement of the houlder joint could be determined Like the hip joint, the houlder joint accelerated upward during the firt part of the wing phae The range of error in determining the location of the houlder joint, however, wa till too large to quantify the magnitude of houlder joint acceleration Dicuion The variation of tride frequency Theoretical conideration concerning the energetic of locomotion and imple model of limb movement in biped a well a in quadruped ugget tride frequencie not far away from the natural pendulum frequency of the limb during walking (Mochon & McMahon 1980a, b, Hoyt & Taylor 1981, Alexander 1989b, 1995, McGreer 1990, 1992, Witte et al 1991, 1995, Preuchoft & Günther 1994, Preuchoft et al 1994) Although the range of tride frequencie in walking elephant wa found to overlap with the natural pendulum frequency of the limb, in accordance to finding in other vertebrate (Hildebrand 1985), the variation of tride frequency wa high At low peed, tride frequency wa coniderably below the natural pendulum frequency wherea it wa much higher at high walking peed (Table 1) The high variation of tride frequencie among elephant wa upported by data collected from video howing elephant in their natural habitat The more contant tride frequencie oberved in giraffe were cloe to the natural pendulum frequencie of the limb (Table 2) However, there wa little variation of peed in the giraffe Video howing giraffe in

5 Mitt Mu Natkd Berl, Geowi Reihe 2 (1999) 85 Table 1 The walking peed v of two ame ized elephant (pecimen 1 and pecimen 2) compared to peed etimate after the method of Demathieu (1986) : v', and Alexander (1976) : v", repectively T, tride period ; Tu, upport time ; T,, wing time ;, tride length; h, hip height ; /h = tride length/hip height (relative tride length) Bold letter : the actual peed deviate le than 50% from the etimated peed pecimen T Tu Tw 1 084± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± m /h v m/ v' m/ v" m/ their natural habitat alo prove coniderable variation of tride frequency during walking Therefore, etimating the tride frequency of a foil track-maker by etimating the natural pendulum frequency of it limb cannot be expected to give precie reult A poible error of a factor of 2 in each direction hould be taken into account Elephant a well a giraffe tended to prefer tride frequencie cloe to or a little bit below the etimated natural pendulum frequencie of the hindlimb, if they walked unditurbed over a long ditance However, from a hort preerved trackway it can be difficult or even impoible to derive whether an animal wa walking in a comfortable way or relatively low or fat Wherea tride frequencie cloe to the natural pendulum frequencie of the limb eem to be preferred by animal that walk unditurbed over a long ditance, coniderably higher frequencie can be expected at high walking peed and coniderably lower frequencie at low walking peed If ufficient information i available to decide whether an animal wa walking at a relatively low or high peed, the increae of tride frequency with peed hould be taken into account for etimating the tride frequency more preciely Very long trackway, however, might indicate comfortable walking peed with tride frequencie not too far away from the natural pendulum frequency of the limb Speed etimate baed on etimate of tride frequencie are a good or bad a the etimated tride frequencie In the elephant and giraffe tudied, peed etimate baed on etimate of the natural pendulum frequency of the hindlimb are preented in Table 1 and Table 2 Thi method give good reult at mean walking peed but poor reult at extreme peed, epecially at high peed In contrat, the equation propoed by Alexander (1976) v = ~ h11~ (v : etimated peed ; g = 981 m/2, acceleration due to gravity ; : tride length; h : height of hip from the ground) yielded bet reult at high walking peed The actual peed of locomotion wa uually within ±50% of the peed etimate Table 2 Locomotion parameter of two giraffe with hip height of 204 m (pecimen 1) and 164 m (pecimen 2), mean value ± tandard deviation Speed were calculated from mean value of tride period and tride length Symbol a in Table 1 pecimen 1 200± ± ± ± ± ± 003 /h m m/ m/ m/ 260 ± ± ± ±

6 86 Chritian, A, R H G Müller, G Chritian & H Preuchoft, Limb Movement in Large Dinoaur compared to a maximum error of about 100% if the peed wa etimated from the natural pendulum frequency of the limb Equation (1) ha been hown to give good reult for a variety of walking and running animal (Alexander 1976, 1989a) Becaue of the uncertainty in etimating the tride frequency from a trackway, thi method eem generally more reliable for peed etimate than the method baed on etimate of the natural pendulum frequency of the limb Additionally, there might be coniderable uncertainty in modelling the natural pendulum frequencie of the limb of extinct vertebrate and natural pendulum frequencie might be very different in forelimb and hindlimb raiing the quetion which pair of limb ha to be ued for peed etimate Swing time and upport time in relation to tride frequency Higher variation of upport time than wing time can be expected During the upport phae, the foot i placed on a more or le fixed poition on the ground wherea the hip joint travel forward with a rather contant peed Therefore, a more or le linear progreion of the angle between the limb and the vertical i predicted, a wa indeed oberved (Fig 1) Support time i imply determined by the total angle the limb cover during the upport phae divided by the angular velocity of the limb Thi period will not necearily be cloely related to the wing time of the oppoite limb (Fig 1) The duration of the wing phae wa much more contant than the duration of the upport phae At low peed, it wa cloe to half the natural pendulum period At high walking peed, wing time wa coniderably le than half hip height [m m1 Fig 2 Variation of hip height (olid line) during the tride preented in Fig 1 During the firt part of the wing phae, the movement of the hip joint fit to an upward acceleration of 85 m/2 (dotted line) the natural pendulum period indicating more active force input to the limb ince horter period mean higher angular acceleration of the winging limb Epecially at high walking peed, either additional force mut be exerted upon the limb by mucle and elatic tiue or the pivot of the winging limb mut be accelerated (ee below) Acceleration of the proximal limb joint The natural pendulum period T of a limb can be calculated by : T=2 JT gi m 1 g d (2) V (m, ma of the limb, 1, moment of inertia about the hip joint, g, acceleration due to gravity, d, ditance between the hip joint and the centre of ma of the limb) The natural pendulum frequency f i the invere of the natural pendulum period T: Acceleration of the pivot alter the period of a upended pendulum thereby affecting the winging behaviour of a limb (Mochon & McMahon 1980a, b, Alexander 1995, Fig 3) If the pivot i accelerated upward by an acceleration a, then the period T and frequency f of a pendulum are altered according to T=2 jt in (g + a) -d' Equation (4) and (5) are derived from equation (2) and (3) by adding the pivot acceleration a to the acceleration due to gravity g Thi increae in total acceleration mean that the oberved upward acceleration of the hip joint during the firt part of the wing phae poitively affect the angular acceleration and, therefore, the angular velocity of the hindlimb In the middle of the wing phae, the downward acceleration of the hip joint had little effect on the angular velocity becaue the centre of ma of the limb wa more or le in line with the direction of the acceleration during thi part of the wing phae In the equence in which the upward acceleration of the hip joint could be quantified, the acceleration wa ufficiently high o that, un-

7 Mitt Mu Nat kd Berl, Geowi Reihe 2 (1999) 87 ~T=2TE 9 poition C F=m (g +a) ~T= 2 tt ~~----~~`-- poition g+a Fig 3 With an upward accelerating pivot, the period T of a pendulum i reduced F, weight force ; m, ma ; g, acceleration due to gravity; a, upward acceleration of the pivot ; 1, chord length til angular velocity wa reduced during the lat third of the wing phae, the hindlimb winging could be explained a a pendulum-like movement that wa driven motly by gravity and the upward acceleration of the hip joint with little input of mucle force During the lat third of the upport phae, however, force from mucle or tendon i neceary to upport the deceleration of the limb In the example given in Fig 2, the upward acceleration of the hip joint at the firt part of the wing phae wa a = 85 m/2 An upward acceleration of thi magnitude would increae the frequency of a pendulum by a factor of about 1 37, if it wa contant during the complete wing phae There may be an additional force and energy input to the winging hindlimb by horizontal acceleration of the hip joint which could not be examined here due to the problem in quantifying horizontal hip acceleration mentioned above The additional reult on giraffe indicate that the mechanim of upporting the limb winging by acceleration of the proximal limb joint i neither retricted to elephant nor to the hindlimb It hould be mentioned here that in the forelimb the pivot i not identical with the proximal joint (houlder joint) if the houlder blade i regarded a part of the winging limb Due to movement of the capula relative to the thorax, the pivot of a forelimb i located omewhat above the houlder joint and might hift it poition during a tride Neverthele, movement of the free extremity can be mechanically decribed a movement of a phyical pendulum with the houlder joint a a mobile pivot Large dinoaur : efficient walker The hip acceleration oberved in large mammal may reult from force tranmitted to the pelvi from the oppoite hindlimb in combination with hip rotation The acceleration of the houlder joint are mainly achieved by rotation of the capulae In mot large dinoaur, however, both hip joint are connected firmly and are located rather cloely together and the houlder girdle appear much more rigid than in mammal Therefore, rotation of the pelvic girdle and movement in the pectoral girdle could not have been utilied for accelerating hip and houlder joint in exactly the ame way a decribed above for large mammal However, force tranmitted by the upporting hindlimb and forelimb, repectively, mut have accelerated the houlder and hip joint of the winging oppoite limb Conequently, wing time were decreaed imilar to elephant and giraffe With ground-reaction force approximately in line with the upporting hindlimb, a in large, recent vertebrate (Biewener 1989, 1990), the hip joint of the winging hindlimb of a dinoaur wa accelerated backward and upward in the firt half of the wing phae, and forward and upward in the econd half of the wing phae Thi mut have been alo true in biped where no additional ground-reaction force were exerted on the body by the forelimb With a typical bimodal time coure of the ground reaction force (Fig 4), hip acceleration magnitude would have been large at extreme excurion angle thereby upport phae Fig 4 A walking large dinoaur With the groundreaction-force F approximately in line with the upporting limb the body experience an acceleration a = F/m (m, body ma) in the direction of the ground reaction force CM, centre of ma of the winging limb; cp, excurion angle ; t, time

8 88 Chritian, A, R H G Müller, G Chritian & H Preuchoft, Limb Movement in Large Dinoaur increaing the angular acceleration of the winging hindlimb a oberved in elephant and giraffe Additionally, the large angle between the force acting on the hip joint and the hindlimb (about twice the angle between the direction of gravity and the chord in a pendulum with a fixed pivot), further increaed the torque experienced by the winging hindlimb and thereby it angular acceleration Acceleration of hip and houlder joint have been hown to be effective in tranmitting force and energy on the moving limb in prawler, a well (Chritian 1995), indicating that thi mechanim i widepread among vertebrate and not retricted to mammal with paraagittal limb movement In large walking dinoaur wing time probably wa well below half the natural pendulum period of the limb, epecially at high walking peed, a oberved in elephant A hortening of the wing phae i advantageou not only for attaining high peed but alo for increaed economy With a given upport time, hortening of the wing time decreae the average force applied by the foot to the ground A force i reduced, mucle ma can be reduced Le mucle ma mean le total body ma With le body ma, the total energy conumption of an animal i reduced at ret, a well a during locomotion (Taylor 1977, Taylor et al 1980, 1982, Schmidt- Nielen 1984, Kram & Taylor 1990) At a given tride frequency, a horter wing time implie a longer upport time Longer upport time pread the force neceary to carry the body weight over a long period and have been hown to decreae the cot of tranport in running vertebrate (Kram & Taylor 1990) A imple relationhip between time of force application and cot for tranport, however, ha not been found for walking (Taylor 1994) Shortening the wing time of a limb by accelerating hip and houlder joint help to explain how large vertebrate manage to move cheaply even with maive limb, a ha been oberved in African elephant (Langman et al 1995) Etimated peed of ome Tendaguru-dinoaur In ome form, like auropod, a variety of preerved trackway have been found (Lockley 1991, Thulborn 1990, Lockley & Hunt 1995) Different trackway of the ame kind of trackmaker can be compared In thoe trackway with the hortet tride length, tride frequency can be aumed to have been much lower than it wa in the trackway with the longet While tride length matche the natural pendulum frequency omewhere in between Thulborn (1990) found an average relative tride length (= tride length divided by limb length which i approximately equal to tride length divided by hip height, /h, in the hindlimb) of 093 in a ample of auropod trackway Thi i coniderably le than the relative tride length of elephant and giraffe at comfortable peed (Table 1) There i ome uncertainty in etimating the relative tride length of an extinct track-maker becaue the hip height ha to be recontructed Thi could lead to minor error in the etimate of comfortable walking peed Tbulborn (1990) etimate the hip height h of a auropod a four time footprint length leading to a hip height above 44m in Brachioauru With extended knee, the large Berlin pecimen SII, however, ha a hip height of jut about 35m The hip height etimated by Thulborn (1990) might be 10% or 20% too high However, a relative tride length of 1 0 eem a realitic etimate for a comfortable walking auropod and wa ued for the etimate of comfortable walking peed lited in Table 3 According to the finding preented here, at comfortable walking peed, tride frequency probably wa about 10% or 20% below the natural pendulum frequency of the hindlimb The etimate of comfortable walking peed of ome Tendaguru-auropod of typical ize preented in Table 3 are baed on the aumption that the tride period wa about 10% above the natural pendulum period of the hindlimb At maximum peed, the relative tride length of the hindlimb Table 3 Speed etimate for ome Tendaguru-dinoaur h, etimated hip height of an adult pecimen ; T etimated natural pendulum period ; T', etimated tride period at comfortable walking peed ; v, etimated comfortable walking peed ; v', upper peed limit For further explanation ee text pecie h m T T' v m/ v km/h Brachioauru brancai Baroauru africanultornieria robuta Dicraeoauru hanemanni Dicraeoauru attleri v' m/ v' km/h

9 Mitt Mu Nat kd Berl, Geowi Reihe 2 (1999) 8 9 probably wa not greater than 2 0 (Thulborn 1990) A demontrated above, equation (1) of Alexander (1976) eem more appropriate for etimate of maximum peed and wa ued to calculate the etimated maximum peed in Table 3 auming a relative tride length of 2 0 in the hindlimb Comfortable peed of adult Tendaguru-auropod probably were around 3 or 4 km/h a in comfortable walking human Maximum walking peed could have been much higher, comparable to comfortable running peed in human Concluion In the light of reult preented here, peed etimate baed on etimate of tride frequencie from foil trackway eem le reliable for dinoaur and other extinct terretrial vertebrate than peed etimate which are baed on relation among tride length, hip height, and peed (Alexander 1976), or etimate of maximum peed that are baed on calculation of bone trength (Alexander 1985a, Farlow et al 1995 ; but ee alo Alexander 1996) Limb movement in dinoaur may have departed coniderably from a imple pendulum-like behaviour However, taking hip acceleration and the pecial morphology of different dinoaur into account, a reanalyi of limb winging in large recent mammal may allow better etimate of peed and cot of tranport in large dinoaur If a variety of trackway from a certain kind of track-maker are available, trackway with different tride length might be attributed to different tride frequencie making peed etimate more reliable Long tride that indicate high rate of locomotion probably had a frequency between the natural pendulum frequency of the limb and twice thi frequency Short tride indicate a lower tride frequency, poibly a low a half the natural pendulum frequency of the limb Mean tride length can be attributed to comfortable walking peed with tride period 10% or 20% above the natural pendulum period of the limb The very different length of forelimb and hindlimb in ome dinoaur, however, make peed etimate more complicated Thi anatomical feature implie very different natural pendulum period of hindlimb and forelimb, repectively It may indicate longer excurion of the houlder joint compared to the hip joint during a tride, or forelimb movement that were not retricted to paraagittal plane Sauropod and probably other large dinoaur uually walked at low peed comparable to low walking peed in human However, under certain circumtance, large dinoaur might have been able to walk fat and economically uing a imilar mechanim to large terretrial mammal like elephant and giraffe to hift energy from the trunk to the limb by accelerating hip and houlder joint Acknowledgement The locomotion of elephant wa tudied in the Zoo Krefeld, Germany, with the help of Wolfgang Nehring Net giraffe were tudied in the Allwetterzoo Mtinter, Germany, with the help of K Perret Figure 2-5 are drawn by M Wichniwetzki and H Schultze We are very obliged to R McNeill Alexander for contructive and encouraging comment on a hort verion of the manucript and to J O Farlow, M B Smith, and H-P Schultze for critical and contructive review of the manucript The tudy wa upported by Deutche Forchunggemeinchaft (DFG), project SCHU 212/16-1 Reference : Alexander, R McN 1976 Etimate of peed of dinoaur - Nature 261: a Mechanic of poture and gait of ome large dinoaur - Zoological Journal of the Linnean Society 83 : b Body Support, Scaling and Allometry In Hildebrand, M, Bramble, D M, Liem, K E & Wake, D B (ed ) Functional Vertebrate Morphology : Cambridge, USA (Harvard Univerity Pre) a Dynamic of Dinoaur and Other Extinct Giant 167 pp New York (Columbia Univerity Pre) b Optimization and Gait in the Locomotion of Vertebrate - Phyiological Review 69 (4) : Simple model of human movement Applied Mechanic Review 48 (8) : Tyrannoauru on the run - Nature 379 : 121 Bakker, R 1986 The Dinoaur Hereie : New Theorie Unlocking the Mytery of the Dinoaur and Their Extinction 482 pp New York, (William Morrow) Biewener, A A 1989 Scaling body upport in mammal : limb poture and mucle mechanic - Science 245 : Biomechanic of mammalian terretrial locomotion - Science 250: Charig, A J 1979 A New Look at the Dinoaur 160 pp London, (Heinemann) Chritian, A 1995 Zur Biomechanik der Lokomotion vierfitßiger Reptilien (beonder der Squamata) - Courier Forchung-Intitut Senckenberg 180: 1-58 Chritianen, P 1997 Locomotion in auropod dinoaur - Gaia Coomb, W P, Jr 1978 Theoretical apect of curorial adaptation in dinoaur - The Quarterly Review of Biology 53: Demathieu, G 1986 Nouvelle recherche ur la vitee de vertebra, auteur de trace foile - Geobio 19 :

10 90 Chritian, A, R H G Müller, G Chritian & H Preuchoft, Limb Movement in Large Dinoaur Deme, B & Giinther, M M 1989 Biomechanic and allometric caling in primate locomotion and morphology - Folia Primatologica 53: Farlow, J O, Smith, M B & Robinon, J M 1995 Body ma, bone "trength indicator", and curorial potential in Tyrannoauru rex - Journal of Vertebrate Paleontology 15 (4) : Fatovky, D E & Weihampel, D B 1996 The Evolution and Extinction of the Dinoaur 460 pp Cambridge, USA (Cambridge Univerity Pre) Hildebrand, M 1985 Walking and running In Hildebrand, M, Bramble, D M, Liem, K E & Wake, D B (ed ) Functional Vertebrate Morphology : Cambridge, USA (Harvard Univerity Pre) Hoyt, D E & Taylor, C R 1981 Gait and the energetic of locomotion in hore - Nature 292 : Johnon, R E & Otrom, J H 1995 The forelimb of Toroauru and an analyi of the poture and gait of ceratopian dinoaur In Thomaon, J (ed ) Functional Morphology in Vertebrate Paleontology : Cambridge, United Kingdom (Cambridge Univerity Pre) Kram, R & Taylor, C R 1990 Energetic of running: a new perpective - Nature 346 : Langman, V A, Robert, T J, Black, J, Maloiy, G M O, Heglund, N C, Weber, J-M, Kram, R & Taylor, C R 1995 Moving cheaply : energetic of walking in the African Elephant - Journal of Experimental Biology 198 : Lockley, M G 1991 Tracking Dinoaur : A New Look at an Ancient World 238 pp Cambridge, United Kingdom (Cambridge Univerity Pre) Lockley, M G & Hunt, A E 1995 Dinoaur Track and Other Foil Footprint of the Wetern United State 338 pp New York (Columbia Univerity Pre) McGreer, T 1990 Paive dynamic walking - International Journal of Robotic Reearch 9 (2) : Principle of walking and running In Alexander, R McN (ed ) Mechanic of Animal Locomotion Advance in Comparative and Environmental Phyiology: Berlin (Springer) McMahon, T A & Bonner, J T 1983 On Size and Life 255 pp Scientific American Book, New York (W H Freeman) Mochon, S & McMahon, T A 1980a Ballitic walking - Journal of Biomechanic 3 : b Ballitic walking: an improved model - Mathematical Biocience 52 : Paul, G S 1987 The cience and art of retoring the life appearance of dinoaur and their relative In Czerka, S & Olen, E (ed ) Dinoaur Pat and Preent: 4-49 Lo Angele, USA (Natural Hitory Mueum of Lo Angele County) The brachioaur giant of the Morrion and Tendaguru with a decription of a new ubgenu, Giraffatitan, and a comparion of the word' larget dinoaur - Hunteria 2 (3) : 1-14 Preuchoft, H & Günther, M M 1994 Biomechanic and body hape in primate compared with hore - Zeitchrift für Morphologie und Anthropologie 80 (1) : Preuchoft, H, Witte, H Chritian, A & Recknagel, S 1994 Körpergetalt und Lokomotion bei großen Säugetieren - Verhandlungen der Deutchen Zoologichen Geellchaft 87 (2) : Schmidt-Nielen, K 1984 Scaling : Why i Animal Size o Important? 241 pp Cambridge, United Kingdom (Cambridge Univerity Pre) Taylor, C R 1977 The energetic of terretrial locomotion and body ize in vertebrate In Pedley, T J (ed) Scale Effect in Animal Locomotion : London (Academic Pre) Relating mechanic and energetic during exercie In Jone, J H (ed) Advance in Veterinary Science and Comparative Medicine, vol 38A, Comparative Vertebrate Exercie Phyiology: Unifying Phyiological Principle : San Diego (Academic Pre) Taylor, C R, Heglund, N C, McMahon, T A & Looney, T R 1980 Energetic cot of generating mucular force during running - Journal of Experimental Biology 86 : 9-18 Taylor, C R, Heglund, N C & Maloiy, G M O 1982 Energetic and mechanic of terretrial locomotion I Metabolic energy conumption a a function of peed and body ize in bird and mammal - Journal of Experimental Biology 97 : 1-21 Thulborn, R A 1990 Dinoaur Track 410 pp London (Chapman and Hall) Weihampel, D B, Dodon, P & Omölka, H (ed) 1990 The Dinoauria 733 pp Berkeley, USA (Univerity of California Pre) Witte, H, Preuchoft, H & Recknagel, S 1991 Human body proportion explained on the bai of biomechanical principle - Zeitchrift für Morphologie und Anthropologie 78 (3) : Witte, H, Lech, C, Preuchoft, H & Loitch, C 1995 Die Gangarten der Pferde : Sind Schwingungmechanimen entcheidend? - Pferdeheilkunde 11 (3) :