run walk distinctions

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Correlation of Symmetrical Gaits

and Whole Body Mechanics: Debunking Mythsin Locomotor BiodynamicsAUDRONE R. BIKNEVICIUS1 AND STEPHEN M. REILLY21Department of Biomedical Sciences, Ohio University College of OsteopathicMedicine, Athens, Ohio 457012Department of Biological Sciences, Ohio University, Athens, Ohio 45701

ABSTRACT Independent maturation of gait (Hildebrand) and whole body mechanics (Cavagnaet al.) traditions in locomotor analyses has led to conflicting terminology. Re-evaluation of thesetraditions yields three primary insights. First, walking and running should be recognized by theirfundamentally different mechanics. Because duty factor fails to consistently distinguish these

mechanics, its use in discriminating walks from runs should be abandoned in preference toparameters that more accurately reflect the movements of the center of mass (COM; phase differencein external mechanical energy or Froude number). Second, trot should be reserved as a descriptorof a particular footfall pattern. This and all gait terms lack explicit information about limb com-pliance and thus COM movements. Third, symmetrical gait definitions should be broadened toreflect the four primary footfall patterns: the lateral-couplet dominated pattern of the pace, thediagonal-couplet dominated pattern of the trot and the more independent sequencing of footfallsof the two singlefoots. Intermediate gaits (perennially confusing and a mouthful to pronounce) arethereby subsumed by these four discrete gaits. Confusion between gait terminologies would be avoidedif limb phase were consistently reported. J. Exp. Zool. 305A:923934, 2006. r 2006 Wiley-Liss, Inc.

How to cite this article: Biknevicius AR, Reilly SM. 2006. Correlation of symmetricalgaits and whole body mechanics: debunking myths in locomotor biodynamics. J. Exp.Zool. 305A:923934.

Scientific discovery is disseminated throughpublished reports or professional presentations.The common feature of both venues is the relianceon wordswords that link the thoughts of theauthor with the imagination of the audience.While science prides itself in its precision, some-times the same words are applied to differentphysical entities. For example, a navicular boneis one of the tarsal bones in humans but it is alsothe distal sesmoid bone in the feet of ungulates

(Riegel and Hakola, 99). Adoption of commonwords to reflect discrete physical entities inscience is perhaps even more likely to yieldconfusion. Hence, reference to a knee conjuresup the image of the femurtibia articulationunless, of course, the audience is composed ofequine researchers for whom knee implies thecarpus (Riegel and Hakola, 99). Independentdevelopment of terminology can occur because ofdisciplinary isolation or methodological differ-ences between avenues of research (Reilly and

Biknevicius, 2003). One consequence of autono-mously maturing research fields is that walksand runs have been defined using differentparameters that signify overlapping, but notequivalent, physical realities.

Walking and running footfall patternsHildebrand gait model

The first method to distinguish walks from runsis based exclusively on duty factor (the ratio ofsupport duration to stride duration), a parameter

Published online 6 October 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/jez.a.332.

Received 12 February 2005; Accepted 28 June 2006

Grant sponsor: National Science Foundation; Grant number: IBN0080158.

Correspondence to: A.R. Biknevicius, Department of BiomedicalSciences, 125 Life Sciences Building, Ohio University Collegeof Osteopathic Medicine, Athens, OH 45701.E-mail: [email protected]

2006 WILEY-LISS, INC.

JOURNAL OF EXPERIMENTAL ZOOLOGY 305A:923934 (2006)


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that is frequently used as a proxy for locomotorspeed (duty factor most commonly scales inverselywith speed; Demes et al., 94). As codifiedby Hildebrand (65), with inspiration from earlierworkers (e.g., Howell, 44), running occurs when

duty factor falls below 0.5; conversely, duty factorsZ0.5 are considered to be walks.Walks and runs are further categorized into

gaits (timing of footfalls), a tradition that stemsfrom at least the time of Goiffon and Vincent(1779). About 200 years later, Hildebrand(65, 76) systematized symmetrical gaits accord-ing to limb phase, defined as the phase differencebetween the touchdowns of ipsilateral hind- andforelimbs as a ratio of stride duration (Fig. 1A).A forelimb lands progressively later in the strideduration relative to its ipsilateral hindlimb as limbphase increases, i.e., ipsilateral fore- and hind-

limbs land synchronously at a limb phase of 0whereas forelimb touchdown is half a strideduration after the ipsilateral hindlimb when limbphase is 0.5. The discrete symmetrical gaits arepace (limb phase50), trot (0.5) and the twosinglefoots (0.25 and 0.75), allowing approximately70.06 limb phase about these values. The re-mainder of the limb phase range can either beconsidered to represent intermediate gaits or lesssynchronized versions of the discrete gaits (e.g.,a 0.41 limb phase is either deemed a lateral-sequence diagonal couplets or a 4-beat trot,

respectively). [We refer the readers to Reilly andBiknevicius (2003) or Stevens (this volume) fora more detailed explanation of how symmetricalgaits are identified.] The classic Hildebrandsymmetrical gait plot (Fig. 1A) charts limb phase(gait) against duty factor (speed); the footprint-shaped area on the plot circumscribes symmetricalgaits in walks and runs (as per Hildebrand, 76).By this method, some gaits are theoreticallypossible as both walks and runs (trots, singlefoots)whereas other gaits occur primarily as runs (pace)or as walks (all other symmetrical gaits).

The popularity of this footfall-kinematics ap-proach to defining walks and runs (as well as gaits)is its ease of data capture: all that is required is acamera, preferably high-speed. As early as 1976, arich database already existed on the gaits of at

least 143 non-avian tetrapod genera (sevenamphibians, four lizards, two crocodilians and130 mammals) plus 37 dog breeds and 13 horsebreeds (Hildebrand, 65, 67, 68, 76). Hildeb-rands work recorded gaits across a wide array oflocomotor behaviors, including linear and turningtrials as well as steady and non-steady speed.Although subsequent studies largely focused onsteady speed and level terrestrial locomotion (e.g.,White and Anderson, 94; Parchman et al., 2003),some have branched out to other substrates (e.g.,arboreal locomotion: Lammers and Biknevicius,2004; Stevens, 2006). The underlying importance

of understanding footfall gaits is that they are oneway to quantify the output of the neuromotorsystem to move the body in response to environ-mental demands.

Walking and running center of mass(COM) mechanicsCavagna et al. model

Another method for distinguishing walks fromruns involves the movements of the COM of theentire body (Fig. 1B) and is referred to here asthe whole body mechanics approach (Cavagnaet al., 77). Because slow moving tetrapods travel

with limbs that have a high level of stiffness, theirCOM is at its highest position near midstancewhen the forward velocity of the COM is low.Consequently, gravitational potential energy (Ep)cycles out of phase with total kinetic energy (Ek)and the phase difference between minima of Epand Ek (phase shift) is near 1801. This pendu-lum-like exchange of energies provides an oppor-tunity to recover external mechanical energy withevery step, thereby reducing muscular effort andthe metabolic cost of locomotion at slow speeds. Atfaster speeds, the limbs of tetrapods function with

Fig. 1. Synthesis of symmetrical gaits and whole body mechanics. (A) Kinematic (footfall) approach to terrestriallocomotion. Shaded area represents symmetrical gaits. Gaits are determined by limb phase; duty factor distinguishes walking(Z0.5) from running (o0.5) gaits. Modified from Hildebrand (76). (B) Whole body mechanics approach to terrestriallocomotion. Total kinetic and gravitational potential energies fluctuate out of phase with one another during walking(pendulum-like or vaulting mechanics; left). In-phase fluctuations of these external mechanical energies occur during running(spring-mass or bouncing mechanics; right). Modified from Farley and Ko (97). (C) If the two definitions of walking and runningin (A) and (B) were completely congruent, then vaulting mechanics would be found only on the high duty factor (walking) side ofthe gait plot and bouncing mechanics only on the low duty factor (running) side of the gait plot. ( D). Empirical evidence refutesthe idealistic synthesis (i.e., complete congruence between footfall and whole body mechanics definitions) primarily by thecommon finding of bouncing mechanics used at high duty factors. Gait space occupied by quadrupeds indicated by the ellipses(Sources: lizards and salamander, E.J. McElroy, unpublished data; all others, see Table 1). (E) Symmetrical gaits redefined asfour primary gaits (pace, lateral-sequence singlefoot, trot, diagonal-sequence singlefoot), each occupying a range of 0.25 limbphase. Intermediate gaits are subsumed into the primary gaits.

A.R. BIKNEVICIUS AND S.M. REILLY924

J. Exp. Zool. DOI 10.1002/jez.a


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UNIFYING LOCOMOTOR PERSPECTIVES 925



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greater compliance so that the COM no longerrises during the first half of stance but ratherdrops to its lowest position near midstance. Theresulting in-phase fluctuations in Ep and Ekare inconsistent with pendulum-like mechanics

(phase shift near 01

) but some recovery ofmechanical energy is still, at least theoretically,possible via the storage and release of elasticstrain energy (another form of potential energy) inthe ligaments, tendons and muscles of the limbsand back. Therefore, from the perspective of wholebody mechanics, walks and runs are synonymouswith inverted pendulum (vaulting) and spring-mass (bouncing) mechanics, respectively.

There is a limit to how quickly tetrapods canmove and still take advantage of inverted pendu-lum mechanics while retaining constant contactwith the ground (Alexander, 76). As the COM

moves in an arc over a stiff limb, it resembles amass attached to the end of a string moving ina circle. The mass will continue to move about thecircle as long as the centripetal force required tomaintain the movement of the body mass alongthe arc (mv2/l where m is mass, v is forwardvelocity and l is length of the string or, in the caseof walking, hip height at midstance) does notexceed gravitational force (mg where g is thegravitational acceleration or 9.81 m sec1). Theratio of these forces is known as Froude number(Fr5 v2/gl). In theory, animals may continue to

move with inverted pendulum mechanics as longas Fro1 but empirical data show that animalstypically switch to bouncing mechanics at muchslower speeds (Fr$0.5 for bipeds, $0.35 forquadrupeds; Alexander, 77; Alexander and Jayes,83; Gatesy and Biewener, 91; Griffin et al.,2004), so that the trigger for a vaultbouncetransition is determined not by the limits ofcentripetal force but rather by some metabolic,mechanical and/or perceived exertion factors(Hoyt and Taylor, 81; Farley and Taylor, 91;Raynor et al., 2002; Griffin et al., 2004). BecauseFr also reflects the ratio of Ek to Ep, this approachis actually an extension of the whole bodymechanics approach.

The dataset for whole body mechanics is lessextensive than that for gaits. Nearly 30 years laterafter Cavagna et al.s (77) study, whole bodymechanics have been recorded for only 18 non-avian genera (one amphibian, three lizards, onecrocodilian and 13 mammals; Table 1). The countrises to 29 genera when birds (eight genera) andinvertebrates (three) are included, still a far cryfrom the sampling of gaits in tetrapods. Further-

more, whole body mechanics studies tend toexplore a small subset of terrestrial locomotorbehavior, namely, steady-speed locomotion onlevel substrates. When an animal moves in bursts,Ek is lost and the work required for locomotion

increases (Alexander, 89).

Integrating walking and runninggaits with vaulting and bouncing

COM mechanics

How well do the footfall and whole bodymechanics approaches to defining walks and runscoincide? The most simplistic (and optimistic)synthesis (Reilly and Biknevicius, 2003) wouldmap vaulting mechanics (out-of-phase fluctuationsof Ep and Ek) on the walking side (duty factorZ0.5) of the Hildebrand gait space and bouncing

mechanics (in-phase Ep and Ek) on the runningside (duty factor o0.5; Fig. 1C). Locomotor dataon tetrapods that include hindlimb duty factor,whole body mechanics and gait (footfall patternsof all limbs) are surprisingly limited (12 non-hopping quadrupeds: Table 1); nevertheless, aclear pattern has emerged (Fig. 1D). At first, theidealistic synthesis appears to have some support:vaulting mechanics is limited to high duty factorsand only bouncing mechanics occurs at low dutyfactors. But on closer inspection, one finds thatthe 0.5 duty factor line does not cleanly separatevaulting and bouncing strides because bouncingmechanics repeatedly breaches the 0.5 walkrunduty factor boundary (e.g., trotting opossums,singlefooting horses; Fig. 1D). In fact, the entiremechanical repertoire of some species, such asrats, occurs at duty factors greater than 0.5! Theidealistic synthesis is, therefore, soundly rejected,and one is led to the conclusion that theHildebrand (footfall kinematics) and Cavagnaet al. (whole body mechanics) definitions of walksand runs are not interchangeable.

BRIDGING THE VOCABULARY GAP

Recognizing that some terminology (walk, run,trot) is used inconsistently within the locomotorbiodynamics community is but the first and easieststep in resolving semantic conflicts. Much moredifficult is implementing a change in the culture sothat these inconsistencies and misunderstandingsare minimized. In the subsequent sections, weoffer several compromises that are supported byempirical evidence from both the Hildebrand andCavagna et al. traditions. These are organized as




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mythspopular beliefs that are unsupported byfacts and that result in distorted truths. The firstinvolves the belief, held by some kinematicallyoriented biomechanists, that runs necessarilyinclude a flight phase. The second myth exploresthe assumption, held by some biomechanists ofthe whole body mechanics tradition, that trots arealways runs.

Myth 1: Runs contain an aerial phase

We propose that walk and run be used toexplicitly describe vaulting and bouncing COMmechanics, respectively (a convention that will beused hereafter in this paper). There is no simpleequivalence between the Hildebrand (footfall) andCavagna et al. (whole body mechanics) definitions

TABLE 1. Gaits used during whole body mechanics studies

Gaits1

Common name Genus species Vaulting Bouncing Source

Quadrupeds

Anuran Frog Kassina maculata LSDC LSDC, T Ahn et al. (2004)

Lizards Skink Eumeces skiltonianus T T Farley and Ko (97)

Gecko Coleonyx variegatus T T Farley and Ko (97)

Lizard Sceloporus magister T Our dataunpubl.

Crocodilian Alligator Alligator

mississippiensis

LSDC, T Willey et al. (2004)

Mammalian Opossum Monodelphis domestica LSDC, T Parchman et al. (2003)

Rat Rattus norvegicus T Our dataunpubl.

Chipmunk Tamias striatus G Heglund et al. (82)

Ground squirrel Spermophilus

tridecemlineatus

G Heglund et al. (82)

Macaque Macaca speciosa W T Cavagna et al. (77)

Dog (domestic) Canis familiaris W T Cavagna et al. (77)

Dog (domestic) Canis familiaris LSLC Griffin et al. (2004)

Horse (domestic) Equus caballus LSSF T, G Minetti et al. (99)Ram (domestic) Ovis musimon W T Cavagna et al. (77)

Bipeds

Mammalian Kangaroo Megaleia rufa H Cavagna et al. (77)

Kangaroo rat Dipodomys merriami H Heglund et al. (82)

Kangaroo rat Dipodomys spectabilis H Heglund et al. (82)

Springhare Pedetes cafer H Cavagna et al. (77)

Human

(normal loco)

Homo sapiens W R Cavagna et al. (77)

Human (Groucho) Homo sapiens GW GR McMahon et al. (87);

Bertram et al. (2002)

Avian Tinamous Eudromia elegans W GR, R Hancock et al. (2004)

Rhea Rhea americana W R Cavagna et al. (77)

Ostrich Struthio camelus W GR, R Rubenson et al. (2004)

Quail Excalfactoria chinensis W R Heglund et al. (82)Quail Colinus virginianus W R Heglund et al. (82)

Chicken Gallus gallus W GR, R Muir et al. (96)

Turkey Meleagris gallopavo W R Cavagna et al. (77)

Penguin Aptenodytes forsteri W Griffin and Kram (2000)

Polypeds

Invertebrate Cockroaches Blaberus discoidalis ATr Full and Tu (90)

Cockroaches Periplaneta americana ATr Full and Tu (91)

Crab Ocypode quadrata ATe ATe Blickhan and Full (87)

Blank cells in the Vaulting and Bouncing columns indicate that either vaulting or bouncing mechanics have not been recorded (human

studies listed are representative only).1Abbreviations for gaits: ATe, alternating tetrapod gait (Barnes, 75); ATr, alternating tripod (polypedal version of the trot); G, gallop; GR,

bipedal grounded run (signifies Groucho run in humans); GW, groucho walk (humans only); H, bipedal hop; LSDC, lateral-sequence

diagonal couplets (4-beat trot); LSLC, lateral-sequence lateral couplets (4-beat pace); LSSF, lateral-sequence singlefoot; R, bipedal run; T, trot;

W, bipedal walk; W, unspecified walking gait.




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of walks and runs, and in this section we presentsupportive evidence that duty factor fails toprovide consistent and meaningful mechanicaldistinctions between locomotor behaviors.

At the core of the first myth (runs contain an

aerial phase) is the 0.5 duty factor boundarybetween walks and runs sensu Hildebrand (65).The concept that running requires a period ofsuspension between steps is virtually dogma incommon parlance. It is fostered by Muybridges(1887) sensational serial snapshot photographsthat revealed aerial phases in trotting horses orthe fact that human racewalkers fault when anaerial phase is detected (Rogers, 2000). Yet, datafrom both the Cavagna et al. and Hildebrandtraditions have repeatedly shown that a flightphase is not a prerequisite for running.

Bipeds provide the simplest case in point.

Although the natural vaultbounce transition inhumans is coincident with an abrupt drop in dutyfactor and an incorporation of an aerial phase(Gatesy and Biewener, 91; Kram et al., 97),humans can modify hindlimb dynamics to runwithout an aerial phase. This was first demon-strated with Groucho running, an unnaturalgait in humans characterized by a high degreeof limb compliance, elongated step lengths andno period of suspension (McMahon et al., 87).Vertical oscillations of the COM are reducedduring Groucho running but still include a small

drop near midstance (relative to its verticalposition at touchdown and liftoff) that is consis-tent with bouncing mechanics. Increased sub-strate compliance may work together with limbcompliance to produce similar results (McMahonand Greene, 79).

While Groucho running is a contrived gait inhumans, terrestrial locomotion with bouncingmechanics in the absence of an aerial phase occursnaturally within another group of striding bipeds,namely birds. Ground-dwelling birds smoothlypass across the 0.40.6 Fr boundary traditionallyset for walkrun transitions without incorporatinga period of suspension between steps (Gatesy andBiewener, 91). Nor do these birds display discretechanges in limb kinematics as they cross thisboundary. Although the birds traveling at theseintermediate speeds move with high stride fre-quencies typical of running, the lack of an aerialphase has led many researchers to label thislocomotor behavior as a walk (e.g., Reilly,2000). However, recent whole body mechanicsstudies verified that Ep and Ek of the COMfluctuate in phase with one another (a hallmark

of bouncing mechanics) when Fr is greater than$0.6 even if the birds have not crossed the 0.5duty factor boundary to an aerial run (ostrichesStruthio camelus, Rubenson et al., 2004; tinamousEudromia elegans, Hancock et al., 2004). Thus,

Fr is more accurate than duty factor in predictingthe transition from vaulting mechanics to boun-cing mechanics in striding birds that employgrounded running.

Grounded running has also been observed acrossquadrupedal tetrapods: primitive mammals (opos-sum Monodelphis domestica, Parchman et al.,2003; rat Rattus norvegicus, pers. obs.), amphi-bians (frog Kassina maculata, Ahn et al., 2004)and lizards (Sceloporus magister, pers. obs.).Moreover, it is a natural component of locomotionin invertebrate polypeds (cockroaches Blaberusdiscoidalis and Periplaneta americana and ghost

crab Ocypode quadrata; Blickhan and Full, 87;Full and Tu, 90, 91). In other words, groundedrunning is a common feature of terrestriallocomotion at intermediate to fast speeds.

What predisposes some tetrapods to usegrounded running? Once again, a comparison withthe artificial running gait of humans is instructive.Two key parameters in Groucho running are ahigh degree of limb compliance (bent kneerunning) and prolonged support durations(McMahon et al., 87; Bertram et al., 2002). Thesprawled and crouched postures of small tetrapods

may provide multiple links along the limb toenhance limb compliance. For example, birds thatmove with a more crouched posture (kiwi, guineafowl, quail) rarely demonstrate an aerial phasewhen running after crossing the vaultbounceFr boundary, rather they preferentially stay witha grounded run (Gatesy and Biewener, 91; Reilly,2000). By comparison, the stretched limb cursor-ial birds (tinamous, rhea, ostrich), that presum-ably have greater limb stiffness, transition to anaerial run following a period of grounded running(Abourichid and Renous, 2000; Abourichid, 2001;Hancock et al., 2004). Foot length may be anotherfactor determining grounded running: the rela-tively long feet of birds (Gatesy and Biewener, 91)as well as the plantigrade feet of many non-aviantetrapods may predispose these animals togrounded running by incurring relatively highsupport durations. This may explain why, forexample, the desert spiny lizard Sceloporus mag-ister, which has especially long hindfeet and toes,transitions from an aerial trot to a grounded trotwith slower speeds (all the while using bouncingmechanics; A.R.B and S.M.R., pers. obs.).




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Gait choice is also a potent factor in determiningwhether or not a tetrapod uses grounded running.For example, while a crouched posture (andpresumably higher limb compliance) may contri-bute to grounded trots in the short-tailed grayopossum M. domestica, a speed-related shift inlimb phase may be equally important in explainingits other grounded runs (Fig. 2). Monodelphistends to shift from a trot to a lateral-sequencediagonal couplets (4-beat trot) as speed decreases(Parchman et al., 2003). Support durations of each

limb are more evenly distributed over the strideduring a 4-beat gait than they are in a trot.Consequently, there is a range of duty factors atwhich the lateral-sequence diagonal couplets lackperiods of suspension whereas the trots at theseduty factors are already aerial. Finally, slightshifts in the timing of touchdown or liftoff canresult in the inclusion or exclusion of an aerialphase during the stride (illustrated by in Fig. 2).

Any discussion on grounded running would notbe complete without highlighting the observationthat some symmetrical gaits virtually never dis-play periods of suspension even at their highestspeeds and lowest duty factors. These are thesinglefoot gaits, in which feet land sequentiallyapproximately 0.25 limb phase after one another.Animals that use the lateral-sequence singlefootacross a large range of speeds (walking throughrunning) include elephants (Hutchinson et al.,2003) and breeds of gaited horses (Hildebrand,65). For example, the tolt, the lateral-sequencesinglefoot gait characteristic of Icelandic horses, isused at speeds and duty factors that overlap withfast walking to cantering (albeit leaning towards

the lateral-sequence lateral couplets gait space, or4-beat pace, at higher speeds; Zips et al., 2001).Although tolting Icelandic horses rarely obtaina suspension phase, all tolts for which whole bodymechanics were recorded displayed in-phase fluc-tuations Ep and Ek (Biknevicius et al., 2006), thustolts are grounded runs. The lack of a period ofsuspension in lateral-sequence singlefoot gaits ineither elephants or gaited horses is related neitherto posture nor foot length because these areextremely erect and/or cursorial animals. Rather,

an aerial phase in a pure lateral-sequence single-foot gait is simply impossible unless duty factorso0.25, i.e., speeds at which singlefoot gaits havenever been recorded.

In summary, the exploration of the first mythdraws several conclusions about locomotor bio-dynamics. First, the myth is soundly debunked:both bouncing mechanics (in-phase Ep and Ek)and Hildebrand-defined running gaits (duty factoro0.5; singlefoots) have the capacity to occurwithout a period of suspension. The widespreadrepresentation of grounded running at intermedi-ate speeds signifies that grounded running is acommon locomotor behavior in terrestrial tetra-pods. Therefore, running does not require anaerial phase. Second, the Hildebrand definitionof walks and runs based solely on hindlimb footfallpatterns (duty factors o0.5) is inadequate fordiscriminating the mechanics of the COM. Indeed,an arbitrary designation of any other duty factorwould similarly fail to distinguish vaulting andbouncing mechanics across all tetrapods (Fig. 1D).Therefore, we propose that Hildebrands walkrun definitions be abandoned and that the

Fig. 2. Symmetrical gait space used by Monodelphis domestica when moving with bouncing mechanics (open symbol,grounded run; filled symbol, aerial run). Footfall patterns are indicated by gait diagrams (LH, left hindlimb; LF, left forelimb;RF, right forelimb; RH, right hindlimb). Slight asymmetries in contralateral footfall or support durations (indicated by ) mayresult in aerial phases. Modified from Parchman et al. (2003).




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terms walk and run explicitly imply whole bodymechanics (vaulting and bouncing mechanics,respectively).

This proposal creates some practical difficultiesbecause few labs are equipped to verify whole body

mechanics, it is difficult to apply in field situationsand, thus far, it is only applicable to steady-statelocomotion. How then can students of locomotioninfer vaulting and bouncing mechanics whenwhole body mechanics data are impractical tocapture? Fortunately, Froude number (Fr) mayprovide an acceptable and accessible alternative.The same equipment that is used to determinefootfall patterns can be used to measure forwardvelocity and midstance hip height required forcalculatingFr. Currently, walkrun boundariesdetermined empirically for bipeds and quadrupedsusing Fr (Alexander and Jayes, 83) are better

indicators of vaultbounce boundaries than oftransitions between walking and running sensuHildebrand based on the few studies that reportboth Fr and COM mechanics (e.g., Farley and Ko,97; Rubenson et al., 2004). Unfortunately, theability of Fr to serve as a truly robust measure fordistinguishing vaulting (walking) and bouncing(running) mechanics across tetrapods awaits abroader survey of tetrapods.

Myth 2: A trot is always a run

Cavagna et al.s (77) seminal study figured theexternal mechanical energy fluctuations ofrun5hop5 trot trials separately from walktrials. Although run clearly refers to thebouncing mechanics of the striding bipeds (hu-mans, birds) in their study, its equivalency to thehop of ricochetal mammals or trot of quadrupedalmammals was set in the minds of many compara-tive biomechanists. The labeling shorthand hasled to the assumptions that all trots are necessa-rily runs (bouncing mechanics) and that trottinggait and vaulting mechanics are mutually exclu-sive.

At first glance, these assumptions appear rea-sonable. There is a historical bias toward studyinga subset of trotters: large, primarily cursorial andoften domesticated, mammals. These models crossthe walkrun transition by switching betweendiscrete gaits, from a non-trotting walking gait toa trot for running. Although the precise walkinggaits of the quadrupeds were not identifiedby Cavagna et al. (77), inferences are possible bysurveying studies that explicitly recorded footfallpatterns in these or similar animals. Among the

many walking gaits reported for the domestic dogCanis familiaris (including lateral-sequence lat-eral couplets, singlefoot and diagonal coupletsrepresented on the high duty factor half of theHildebrand, 68 gait plot), they choose the lateral-

sequence lateral couplets (4-beat pace) gait whenwalking at steady speed (Griffin et al., 2004).Because steady speed is a requirement for wholebody mechanics studies, it is likely that theCavagna et al.s dogs similarly moved in this gait.Gait data for the ram Ovis musimon are lessaccessible but can be expected to parallel bovidsand equids that walk using one of two lateral-sequence gaits (singlefoot or lateral-couplet;Hildebrand, 76). Finally, both lateral-sequencesinglefoots and diagonal-sequence diagonal coupletshave been reported for walking adult macaques(Hildebrand, 67). In other words, the quadrupedal

mammals in Cavagna et al. (77) typically use non-trotting gaits to walk using vaulting mechanics.

However, for many terrestrial tetrapods, a trotrepresents a viable gait for walking (vaultingmechanics) and running (bouncing mechanics).Indeed, many tetrapods use trots and 4-beat trotsacross large range of speeds and duty factors (fromless then 0.2 to greater than 0.8; Fig. 1A;Hildebrand, 76). While it is likely that trotsoccurring with duty factors o0.5 are all runs(bouncing mechanics), and it is conceivable that atleast some the trots with duty factors of 0.50.6

are also operating under bouncing mechanics(grounded runs), under which whole body mecha-nics model do the remaining trots operate? Slowtrots have been reported in frogs, turtles, lizardsand crocodilians as well as in an array of mammalsas different as hedgehogs and hippopotamus(Hildebrand, 76; White and Anderson, 94; Ahnet al., 2004; McElroy et al., 2004; Willey et al.,2004), but data on whole body mechanics of slowtrots are limited to a few amphibians and reptiles(Fig. 1D; Farley and Ko, 97; Ahn et al., 2004;McElroy et al., 2004; Willey et al., 2004). In thesetrials, phase shifts between minima of Ek and Ephover closer to 1801 than 01, so that these slowtrots are inverted pendulum (walking) gaits. Thus,vaulting mechanics can and does occur with atrotting footfall pattern.

That a walking trot exists (and functions as aninverted pendulum gait) should not be particularlysurprising. Indeed, the walk of humans is akin to abipedal trot, with contralateral upper and lowerlimbs swinging in unison. Both bipedal andquadrupedal trots are dynamically stable gaits inspite of their small base of support. However,




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while walking bipeds can maximally recover$7080% of their external mechanical energythrough pendulum-like exchange of Ep and Ek(Cavagna et al., 77; Griffin and Kram, 2000), themaximum energy recoveries of walking trots

range lower, from 51% in the western skinkEumeces skiltonianus (Farley and Ko, 97) to amere 32% in the American alligator Alligatormississippiensis (Willey et al., 2004). Possibledetrimental factors limiting the pendulum-likeexchange of Ek and Ep in primitive tetrapodsmay include their lumbering locomotor behaviorpaired with a more sprawling posture, a highdegree of asynchrony in the footfalls of thediagonal limbs, the use of non-optimal speedsand interference due to tail dragging via its effecton limb retraction dynamics (Willey et al., 2004;Reilly et al., 2005; Reilly et al., 2006).

In summary, a trot is a footfall pattern observedin quadrupedal tetrapods in which diagonal-couplet limbs land more-or-less synchronously.Trot alone does not specify a movement patternof the COM because trotting may occur withbouncing or vaulting mechanics. Confusion arisingfrom equating trots with runs would dissolve iftrot were reserved for describing a diagonal-couplet gait, as per its original sense for hundredsof years (Reilly and Biknevicius, 2003), withoutpresumption of how the COM is moving. Thus, wepropose that trot be reserved as a designation for

a gait (a footfall pattern) with no a prioriexpectation of whole body mechanics patterns.

REVISITING HILDEBRANDSSYMMETRICAL GAIT DEFINITIONS

Hildebrands symmetrical gait definitions,based on limb phase, remain credible descriptorsof footfall patterns over the range of observedspeeds (reflected by duty factor). Even moremodern gait syntheses use limb phase as theirfoundation (e.g., Abourichid, 2003). Hildebrandenvisioned symmetrical gaits as a continuum oflimb phases along the ordinate of the symmetricalgait plot but he somewhat arbitrarily organizedthe named gaits around the octiles of limb phases(Fig. 1A). Designation of the four primary symme-trical gaits is largely uncontested, and the pace,lateral-sequence singlefoot, trot and diagonal-sequence singlefoot are easily distinguished asthe four fast gaits represented by the fingers onthe symmetrical gait space. By contrast, the slowsymmetrical gaits represent a progressive desyn-chronization in the touchdowns of the forelimb

relative to its ipsilateral hindlimb that lacksinstantly recognizable boundaries. Thus, followingHildebrands (65) terminology, increasing limbphase shifts gaits seamlessly from the lateral-sequence lateral couplets through the lateral-

sequence singlefoot to the lateral-sequencediagonal couplets to the trot and finally to thediagonal-sequence diagonal couplets (Fig. 1A).Clearly, some of the slow gaits are the sameas those listed as fast (running) gaits (trot,lateral-sequence singlefoot). The remaining gaitsrepresent the intermediate footfall patterns: lat-eral-sequence lateral couplets, lateral-sequencediagonal couplets, diagonal-sequence diagonalcouplet. Just how real are these intermediategaits?

To answer this question, it helps to begin byexamining the discrete gaits, beginning with the

trot. How synchronously must contralateral limbsland for a gait to still qualify as a trot? Simulta-neous footfalls of diagonal couplets are rare evenamong the premier trotters (e.g., dogs; Bertramet al., 97). Hildebrand (76) allowed for somevariation in footfall timing when he defined thetrot as the middle octile on his plot, so that 0.5limb phase 76% (range: 0.440.56) are thetraditional boundaries for the true trot. Flankingthe traditional trot boundaries lay what Hildeb-rand described as non-trot walks (lateral-sequencediagonal couplets and diagonal-sequence diagonal

couplets). These are often termed the 4-beat trot,trot-like walk or even dirty trot (Zips et al.,2001; Reilly and Biknevicius, 2003; Lammers andBiknevicius, 2004). These alternative labels in-clude reference to the trot because the contral-ateral fore- and hindlimbs are landing more insync than are the ipsilateral limbs, i.e., these gaitsare essentially diagonal-couplet dominated astheir formal Hildebrand titles indicate (Fig. 1D).Similarly, the lateral-sequence lateral couplets canbe regarded as poorly synchronized version ofthe pace (4-beat pace, pace-like walk). Completeincorporation of the intermediate gaits into thetrot and pace demonstrates a bias away fromthe, admittedly less common but still legitimate,singlefoot gaits. For example, the lateral-sequencelateral couplets and lateral-sequence diagonalcouplets intermediate gaits could also be consid-ered to represent poorly coordinated variants ofthe lateral-sequence singlefoot; a similar linkagemay be drawn for the diagonal-sequence diagonalcouplets and diagonal-sequence singlefoot.

We recommend a more generous interpretationof the four primary gaits. We suggest that the limb




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phase axis of the symmetrical gait plot be sub-divided into quartiles (rather than octiles;Fig. 1E), thereby subsuming the intermediate gaitsinto the four primary gaits. The effect of thisconsolidation of gait terms is two fold. First, it

emphasizes that trotting (diagonal-couplet domi-nated behavior) is the most common gait amongtetrapods and that most of what we know aboutwhole body mechanics (both vaulting and boun-cing) actually involves trots. Secondly, it drawsour attention to the lateral-sequence singlefootas a viable alternative to the trot for walkingslowly. It becomes the gait of choice for domesticdogs moving at steady speed (0.15 limb phase)when optimizing pendulum-like recovery of ex-ternal mechanical energy (Griffin et al., 2004). It isalso the gait of choice when stability needs, andnot energy economy, are to be maximized. Of the

creeping gaits that retain at least three feet on theground at all times, the most stable is the lateral-sequence singlefoot (McGhee and Frank, 68). Notsurprisingly, therefore, studies of postnatal gaitdevelopment in placental carnivorans (cats Feliscatus, Peters, 83; Howland et al., 95; dogs Canisdomestica, Hildebrand, 68), rodents (jird Mer-iones tristrami and dormouse Eliomys meanurus;Eilam, 97) and even primates (baboon Papiocynocephalus and macaque Macaca mulatta;Shapiro and Raichlen, 2005) have reported lat-eral-sequence walking gaits in the youngest

animals. Finally, confusion in describing symme-trical gaits (using either Hildebrands seven gaitsor our proposed four gaits) can be avoided ifworkers specify limb phase rather than simplyusing previous gait terms.

In summary, there is much to be gained byintegrating the Hildebrand and Cavagna et al.perspectives on locomotion. First, walking andrunning should be recognized by their fundamen-tally different mechanics. Because duty factor failsto consistently distinguish these mechanics, itsuse in discriminating walks from runs should beabandoned in preference to phase difference inexternal mechanical energy or Froude number.Duty factor remains useful as a measure of therelative time allotted for reaccelerating andredirecting the COM (when the foot is in contactwith the substrate). Furthermore, the yielding oflimbs necessary for bouncing mechanics can occurwith or without an aerial phase. Second, trots (andall other gait terms) should be reserved asdescriptors of footfall patterns. Generalizingfindings on cursorial mammals to all tetrapods hasled to the misconception that trots are only used

with bouncing mechanics. Gait terms lack explicitinformation about limb compliance and thus COMmovements. Finally, symmetrical gait definitionsshould be broadened to reflect the four primaryfootfall patterns: the lateral-couplet dominated

pattern of the pace, the diagonal-coupletdominated pattern of the trot and the moreindependent sequencing of footfalls of the twosinglefoots. Tetrapods consciously or subcon-sciously employ gaits that balance the stabilitydemands of the terrain with acceptable levelsof energy expenditure. Neuromuscular controldetermines both gait (footfall patterns interactingwith the substrate) and limb compliance (capacityfor pendulum-like or spring-like recovery ofenergy). Knowledge of only gait or only limbcompliance inadequately summarizes locomotoreffort. Decisions to employ a particular gait

or whole body mechanics may reflect other needsthan simply energy conservation (e.g., intermit-tent locomotion associated with foraging for food;Reilly and Biknevicius, in press).

ACKNOWLEDGMENTS

We thank the International Society of Verte-brate Morphology for hosting the symposiumIntegrating approaches to the study of terrestriallocomotion at its Seventh Congress and sympo-sium co-organizer Nancy Stevens. Special thanks

go to Beth Brainerd (ICVM Program Officer andassociated editor for this issue) and the Journalof Experimental Zoology for publishing the sym-posium. Eric McElroy kindly shared his lizard andsalamander data for Fig. 1; Ohio Universityundergraduate thesis researchers Amy Back andKristin Hickey collected the Rattus and Sceloporusdata. Jennifer Hancock, Eric McElroy, NancyStevens and two anonymous reviewers providedvaluable feedback.

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