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Vertebrate Locomotion

Carl Gans, Abbot S. Gaunt, Paul W. Webb

10.1002/cphy.cp130103

Source: Supplement 30: Handbook of Physiology, Comparative Physiology

Originally published: 1997

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Techniques in the Study of Locomotion
1.1 History
1.2 Diversity and Natural History
1.3 Kinematic Techniques
1.4 Dynamics
1.5 Muscle Activities
2 The Physics of Movement
2.1 Motions and Performance
2.2 Forces
2.3 Proportions: The Physics of Size
3 Evolutionary Transitions in Locomotor Patterns
3.1 History and Locomotion of Extinct Animals
3.2 Development of Chordate Locomotion
3.3 The Swimming Radiation
3.4 The Terrestrial Invasion
3.5 Tetrapod Elongation, Limb Loss, and Burrowing
3.6 Lateral to Vertical Undulation
3.7 Origins of Flight
4 Exemplary Studies on Locomotion in Life form Groups
4.1 Phylogeny and Modes of Locomotion
4.2 Overviews of Phenotypes
4.3 Fishes
4.4 Amphibians and Reptiles: Ectothermal Tetrapods
4.5 Mammals
4.6 Birds and Bats
5 Conclusion
Figure 1. Figure 1.

Phylogenetic scheme for the vertebrates giving estimated number of species in parentheses.

after ref. 1633
Figure 2. Figure 2.

Movement of the body about the three possible axes. Rolling is rotation about the longitudinal axis of the body, pitching is rotation about the frontal axis, and yawing is rotation about the medial axis.
Figure 3. Figure 3.

Summary of the forces that animals use to generate thrust during locomotion. Drag, lift, and acceleration reaction, together with body inertia, may also contribute to resistance. Drag force (FD) is a function of propulsor surface area (S), speed (u2), and the drag coefficient (CD). Acceleration reaction (FA) of a moving appendage depends on the appendage's acceleration (du/dt) and an added mass of water (Ma) proportional to the span of the appendage (B2). Some fish may also use jet propulsion. Lift force (FL) is a function of appendage surface area, speed, and the lift coefficient (CL), which is typically much larger than CD. Ground reaction (FG) has two components. In the Y‐plane, the component FY accelerates body mass (M) vertically at a rate a. Most energy is dissipated for pedestrians in resulting vertical recoil motions of the body relative to the ground. In the X‐plane, friction, proportional to the friction coefficient μ and weight (W) resists back‐sliding of the appendage.
Figure 4. Figure 4.

Theoretic curve for power required to fly vs. forward speed. Total power required is calculated by summing induced power, which decreases with increasing velocity, with parasite power, which increases with velocity. Curves are for aerial flight, but similar curves, adjusted for greater density and viscosity of the medium, apply to aquatic situations. Phov, power required to hover (usually aerial but applicable wherever an animal's density is greater than that of the supporting medium); Pmc, power usage at a velocity (Vmc) that permits maximal range; Vmin, velocity that requires minimal power (Pmin); Po, profile power. (See also Fig. 38.)

from ref. 1583
Figure 5. Figure 5.

The three major kinds of frictional coefficient characterizing foot contact in the terrestrial locomotion of vertebrates.

from ref. 731
Figure 6. Figure 6.

Categorization of the swimming motions and propulsors of fishes, primarily by body and caudal fin (BCF) and median and paired fin (MPF) propulsors in undulatory or oscillatory motions. The major force(s) involved in thrust production varies with the nature of the motions and has been most extensively studied for BCF propulsors. Further explanation of propulsor mechanisms is included in Table 5. The moving portion of the propulsor is shaded.
Figure 7. Figure 7.

Morphological convergence in swimming mechanisms of teleostean and selachian fishes. In both groups, specialists have appeared for high‐speed sustained swimming using periodical tailbeats (Thunnus, Lamna, and Carcharhinus). Lower speeds are seen in generalist swimmers, specialized for no particular type of activity (Salmo, Scyliorhinus, and Centroscyllium). Teleosts show some well‐developed morphs for transient high‐acceleration swimming (Cottus and Psettodes), and although there are some trends among selachians toward deep bodies and fins to maximize acceleration rates, development in this direction is relatively small (Heterodontus and Ginglymostoma). Maneuvering forms (Chaetodon) occur among teleostean fishes but not selachians. In contrast, benthic forms (Pristis, Rhinobatos, and Squatina), although found among teleosts, are common among selachians and dominant in the second major batoidimorph group of elasmobranchs.
Figure 8. Figure 8.

Summary of major muscle and skeletal elements used by various bony fish propulsors. A: Myotomal FG muscle fiber trajectories; B: Dorsal fin; C: Pectoral fin; D: Caudal fin. Further explanation is given in the text.

from ref. 2240
Figure 9. Figure 9.

Combination of several analytical schemes for analysis of symmetrical gaits. In gait formula analysis (upper left, after refs. 1024,1029), contact duration of a hindfoot is mapped vs. the lag between its contact and that of the ipsilateral forefoot; both are standardized by stride length. The plot using the two percentages as coordinates characterizes many species and motor patterns by documenting that they fall on a particular site of the graph; however, what is even more important, the plot shows regions for which no locomotor patterns exist. Note that the classical gaits are actually regions of support positions with numerous intermediates. The terms “lateral sequence” and “diagonal sequence” have been transposed to match the more classical terms (right side of figure; after Gans and Zug, unpublished data). In walk pattern analysis (bottom right side of figure; after refs. 477,478,2361), the pattern of each foot is indicated by a bold line along the time axis while the foot is in contact with the ground (and sometimes a thin line while the foot is lifted). Sections at right angles to the lines representing the position of the four feet indicate the sequence of support postures, ranging from quadrupedal to apodal (during rapid jumps). The method has the merit that one can easily quantify the numbers of, and the durations occupied by, particular support positions; this permits their characterization by standard statistical methods.
Figure 10. Figure 10.

Gait formula analysis for asymmetrical gaits 1029. The ordinate represents the percentage of the stride interval that the forefoot midtime follows the midtime of the hindfoot. The abscissa represents the percentage of the stride interval that the body is supported by a single or both hindfeet. The diagrams show major locomotor patterns but also note some cases in which particular species can propel themselves by various distinct locomotor sequences.
Figure 11. Figure 11.

Stages of a pacing dromedary (after ref. 814).
Figure 12. Figure 12.

Normal sequence of limb movements of the newt Triturus cristatus; the numerals in circles indicate the sequence of flexion. Right fore 1, right fore 2, left hind 3, left fore 4, right hind. The twenty‐eight phases of single step derive from photographs taken at intervals of 1/12 sec. Four drawings are marked to indicate the foot that is being lifted from the ground.

From original photographs of Gray [883,889]
Figure 13. Figure 13.

Series of diagrams showing the position, relative to the ground, assumed by the limbs during locomotion in the newt Cynops pyrrhogaster. The positions are copied from cinematic records (after ref. 1852).
Figure 14. Figure 14.

A: Forces exerted by the undulating animal against a resistance site (peg, point d'appui) placed laterally (see also camfollower analysis in Fig. 15). The moving curves exert forces against resistance sites and their reaction propels the animal. The sliding trunk not only induces reaction, but generates frictional components acting in opposition to the propulsive effect. B: Grass snake (Natrix natrix) traveling over a plane surface by lateral undulation, showing the direction and magnitude (in g) of the forces exerted by letting the snake act against a series of pendulums. Whenever there is only a single peg, the animal must propel itself by the concertina effect. In each case, the animal was permitted to select certain pegs and only those deflected are illustrated here (after refs. 723,724,892).
Figure 15. Figure 15.

Pattern of a cam‐follower deriving from the principle that if tension is exerted on a peg (A, at right angles to its length) by a curved hook, the hook will slide along its internal curve. B: The hook will come to rest at the site at which the imposed force will be at a right angle to the surface. If the internal curve against which force is exerted is irregular, the rest position of the system will be that of least internal radius. C: If the hook can deform, it will then move (internal arrow) along the peg from the side of lesser to that of greater curvature.
Figure 16. Figure 16.

Positions occupied by a completely limbless lizard, the scheltopusik Ophisaurus apodus, undulating simply through a field of pegs, with contact points indicated by circles. Although the animal undulates its entire trunk and tail, it maintains its trunk in regular curves; hence it is not using lateral undulation. The lizard's successive centers of gravity are shown by dots; the centers of gravity of the positions indicated by computer traces are shown by crosses. The top of the illustrated area was occupied by nails spaced 8 cm apart, and the bottom by nails spaced 4 cm apart. Note that despite relatively extensive excursions of the body, the center of gravity travels along a close‐to‐rectilinear path (after ref. 754).
Figure 17. Figure 17.

Sketch of snake engaging in concertina locomotion within a tunnel. The shaded areas of the animal indicate zones in static contact 731.
Figure 18. Figure 18.

Locomotion of completely limbless lizard, the scheltopusik Ophisaurus apodus, engaging in slide‐pushing. The center of gravity in every fifth frame in the sequence is shown by a dot. In this species, the musculature of the tail provides a continuation of that of the trunk. The center line of the animal is shown for four positions in the middle of a sequence; a cross represents the center of gravity in each. The scale bar equals 100 mm and total length of the specimen is 756 mm. A: The tail is thrown away from the center of gravity. B: The tail approaches the center of gravity (after ref. 754).
Figure 19. Figure 19.

Another computer‐corrected sequence of locomotion of the completely limbless lizard, the scheltopusik Ophisaurus apodus, engaging in slide‐pushing, with the contact zones in the middle of the body and the animal traveling slightly diagonally from top to bottom of the figure. The dots indicate the center of gravity for all points plotted; the crosses, for the eleven positions shown here. Every fifth line is plotted and the scale bar equals 100 mm; total length of the specimen is 910 mm (after ref. 754).
Figure 20. Figure 20.

Aspis cerastes moving by sidewinding from right to left. A: The center of gravity in each outline is indicated by a cross. Intervals between positions equal 1/32 sec. Note the position of the tracks, the intertrack zones, and the generally smooth and constant line of progress for the center of gravity. The line measures 10 cm to scale; average wave velocity is 33 cm/sec. B: Same sequence as A, showing the position of the specimen traced for four sample frames, with the path of the center of gravity (dots) that of the midbody position (point 25 of 50) (after ref. 758).
Figure 21. Figure 21.

Sketches of sidewinding locomotion after a film of Crotalus cerastes, showing successive positions and the tracks formed in the sand. The shadows indicate the portion of the body lifted off the ground and the intertrack position at which the orientation of the trunk occupies its greatest angle to the trackline (after ref. 731).
Figure 22. Figure 22.

Illustration of muscular activity during propulsion of Python regius by pushing against a single peg. A: Contractions of the LLD, left longissimus dorsi; RLD, right longissimus dorsi; and RSC, right supracostalis lateralis ventralis, are shown. The diagrams are based on electromyograms but neglect the fact that a single EMG may reflect action in three or more adjacent muscular bundles. B: Anatomical correspondence of the site of contraction. The vertebrae connected by the same bundle are marked by symbol and the large arrow indicates the direction in which the snake is moving (after ref. 790).
Figure 23. Figure 23.

Reaction force patterns in burrowers in which a variously conical head penetrates a more or less homogeneous soil. The forces are assumed to be distributed uniformly and to act normally to the surface of the shield. The greater the friction along the contact zone, the less the penetration 731.
Figure 24. Figure 24.

Trogonophids or amphisbaenians use torsional oscillation to scrape sandy soils off the end of the tunnel 731.
Figure 25. Figure 25.

Spade‐snouted amphisbaenians (1) extend their tunnel by two‐cycle movements. The snout first drives a penetrating divot, which normally starts near the bottom level of the tunnel. Once the snout has penetrated to a maximum (1a–b), the nuchal muscles rotate the skull around the head joint. The dorsal surface of the head then compresses the overburden and widens the tunnel (1b–1c) for the beginning of the next penetrating stroke. In keel‐headed amphisbaenians (2), the head first drives forward (2a–2b) and the snout is then shifted alternately to the right (2c) and then to the left. Bipedid amphisbaenians (3) extend their tunnels by scraping movements analogous to those of moles. The short forearm and clawed hand are extended to the front and swung straight past the tunnel end (3a). During each movement they tunnel. The freed material is then pressed into the sides (3b). 731.
Figure 26. Figure 26.

General morphology of a tetrapod caudate. Note the general tetrapod pattern with neck, trunk, caudal vertebrae, and two distinct girdle segments to which pectoral and pelvic appendages attach, as well as the heavily muscularized trunk and tail. Note that the body tends to twist in opposite directions at the two foot contact levels (after ref. 385).
Figure 27. Figure 27.

A: Track of an adult male urodele Hydromantes platycephalus walking over a surface sloped 30 degrees laterally. Six images were generated by allowing the animal to wallow in black ink before walking across drawing paper. Diagrams 1 through 6 show successive stages of a single tail movement. The tail is used to prop the lower left side of the animal. B: Trackway over five steps. C: Frontal aspect of body and tail in typical walking pose on an inclined surface. D: Lateral (top) and dorsal (below) views of the blunt caudal tip.
Figure 28. Figure 28.

Synchronous dorsal and lateral views of the normal walking of a toad (Bufo vulgaris). The numerals indicate the phases of the stride employed as a relative time scale. Phases 0–6 constitute a complete stride and phases 0, 3, 6, and 9 are corresponding stages of different steps (the drawing for phase 0 is a little early because the right hind foot is not yet off the ground). The symbols represent the relation of the left limbs to the recording platform, indicated in the side views by black bars. The limbs shown in the symbols by a solid line are on the platform; limbs indicated by a broken line are off the platform. Because the side view was obtained using a mirror, the near limbs are those of the left side. The left forefoot first carries the weight about midway between phases 0 and 1; the left hind limb is lifted off the ground between phases 8 and 9. The limbs of the right side do not touch the recording platform, which is on the left of the stage (after refs. 166,889).
Figure 29. Figure 29.

Simple series of a frog's jump. Note the change in orientation of the trunk during flight (after ref. 889).
Figure 30. Figure 30.

Locomotion in turtles. Top: Terrestrial walking in Gopherus polyphemus. Lateral view of a single stride of the left hind limb. A–D, retractive or propulsive phase; E–H, protractive or recovery phase; A, footfall; E, beginning of protraction (after ref. 2357). Bottom left: Swimming in Trionyx spinifer. Lateral view of a single‐stride swimming stride of the left hindlimb. A–D, retractive phase; E–H, protractive phase. Note folding of the foot. Bottom right: Sequence of walking tortoise showing the footfall in very slow and unstable locomotion. LF, left front; LH, left hind; RF, right front; RH, right hind (after ref. 1128).
Figure 31. Figure 31.

Rapid tetrapod locomotion in the collared lizard Crotaphytus c. collaris. Lateral view of the locomotor cycle is shown in sequence A–G. Details of the position of distal digits are partially obscured by substrate. Note the long, substantially greater leg and stride length of the hindlimb over the forelimb and the consequent bipedal portions of the stride sequence (after ref. 1927).
Figure 32. Figure 32.

Bipedal locomotion of juvenile Basiliscus basiliscus.

Made from motion picture by projection, with the camera 1 foot above the substrate. Top: Lateral views (A–J). Bottom; Posterior aspects (A–E) (after refs. 1928,1930)
Figure 33. Figure 33.

Tunnel penetration in advanced uropeltids (and in some caecilians) involves a two‐stroke system. Top: First, the snout drives forward (A). Next, concertina expansion of the neck effectively widens the body and hence the tunnel (B). It also provides a fixed site from which the head may be pushed forward, developing a new divot. The straightened column is then brought into a new concertina curvature starting at the back of the skull (C). Bottom: The tunnels formed meander because the animal's path is deflected by various resistance sites, such as roots and pebbles.
Figure 34. Figure 34.

Foot diversity of small mammalian species. Hoofed forms and carnivores have been omitted. A: Giant armadillo (Priodontes maximus); B: Two‐toed sloth (Choloepis hoffmanni); C: mole (Talpa); D, E: tarsier; F: prehensile‐tailed porcupine (Coendou); G: tree squirrel; H: spider monkey (Ateles); I–K: diversity within gibbon (Hylobates agilis); L: Eumetopias; M: potto (Perodicticus potto); N: beaver (Castor); O: koala (Phascolarctos cinereus); P: cuscus (Phalanger s.l., but this has now been broken up into four genera); Q: silky anteater (Cyclopes didactylus); R: platypus (Ornithorbynchus anatinus); S: Lutra maculicollis; T, U: Aonyx capensis; V, W: Amblyonyx cinerus; X, Y: Hydromys chrysogaster.

modified from ref. 1218
Figure 35. Figure 35.

Mammalian diversity. Whereas the basic body plan is tetrapodal, the diagram documents structural and clearly locomotor diversity (after ref. 2049).
Figure 36. Figure 36.

Support of membranous wings. A: Force diagram of a cross‐section of a bat‐type wing. Many force vectors cancel. A‐1: Forces acting on the digits of a bat's wing. B: Force diagram of a cross‐section of a pterosaur‐type wing. B‐1: Forces acting on supporting digit of a pterosaur wing. No vectors cancel, and the single digit must withstand bending forces transmitted from the entire wing membrane. Arrows in B‐1 indicate assumed tensile vectors in pterosaur wing; lines indicate directions of elastic fibers, which may also occur along trailing edge.

from ref. 1513
Figure 37. Figure 37.

Birds engaged in nonsteady flight. A: Tracings from photographs taken at intervals of 0.01 s of a pigeon in slow flight. Top series are of downstrike (primarily lift), bottom series of upstroke (primarily propulsion) (after ref. 339). B: Vortex patterns generated by a hummingbird engaged in symmetrical hovering. C: A small passerine in asymmetrical hovering (C) (after ref. 1510).
Figure 38. Figure 38.

Power curves. A: Theoretical total mass‐specific power vs. speed for a 333 g pigeon, according to the models of Pennycuick (P) and Rayner (R), and for a 9 g bat, according to Norberg (N). B: Measured mass‐specific power vs. speed from experiments with animals in wind tunnels.

modified from refs. 600,1513. modified from ref. 600
Figure 39. Figure 39.

A: Positive dihedral of wings promotes stability in roll. A roll to the left (left wing down) increases lift (L) on the left wing and decreases lift on the right wing. B: Partial retraction of left wing decreases left wing area and lift, adjusting for roll. Wing position is middle of downstroke. L and L′, lift forces; Lv and Lv′, vertical lift forces on the two wings.

modified from ref. 1513
Figure 40. Figure 40.

Skeletal elements of forelimb in five species of modern bird plus Archaeopteryx (A) scaled so that the carpometacarpi (hand or propeller elements) are of equal length. Birds capable of hovering and/or steep ascent [hummingbird (B), dove (C), and grouse (D)] using nonsteady flight (variants of slow, forward flight) possess robust skeletal elements, with the ulna and radius bowed away from each other, indicating significant muscle mass associated with the antibrachium. Gliders, such as the albatross (F), have little forelimb musculature. Most passerines, such as the starling (E), show intermediate conditions.

modified from ref. 525
Figure 41. Figure 41.

Comparison of regions in principal components space of flight morphology for birds and bats. A: First (body mass) and second (wing‐loading) components. B: Second and third (aspect) components. Components are normalized to zero mean and unit standard deviation so distribution appears circular; ticks on axes = 1 SD. Zones occupied by hummingbirds are stippled; zone of Microchroptera hatched ///; zone of Megachiroptera hatched WW. Positions of a few other key species of bird are indicated for reference.

modified from ref. 1699


Figure 1.

Phylogenetic scheme for the vertebrates giving estimated number of species in parentheses.

after ref. 1633


Figure 2.

Movement of the body about the three possible axes. Rolling is rotation about the longitudinal axis of the body, pitching is rotation about the frontal axis, and yawing is rotation about the medial axis.



Figure 3.

Summary of the forces that animals use to generate thrust during locomotion. Drag, lift, and acceleration reaction, together with body inertia, may also contribute to resistance. Drag force (FD) is a function of propulsor surface area (S), speed (u2), and the drag coefficient (CD). Acceleration reaction (FA) of a moving appendage depends on the appendage's acceleration (du/dt) and an added mass of water (Ma) proportional to the span of the appendage (B2). Some fish may also use jet propulsion. Lift force (FL) is a function of appendage surface area, speed, and the lift coefficient (CL), which is typically much larger than CD. Ground reaction (FG) has two components. In the Y‐plane, the component FY accelerates body mass (M) vertically at a rate a. Most energy is dissipated for pedestrians in resulting vertical recoil motions of the body relative to the ground. In the X‐plane, friction, proportional to the friction coefficient μ and weight (W) resists back‐sliding of the appendage.



Figure 4.

Theoretic curve for power required to fly vs. forward speed. Total power required is calculated by summing induced power, which decreases with increasing velocity, with parasite power, which increases with velocity. Curves are for aerial flight, but similar curves, adjusted for greater density and viscosity of the medium, apply to aquatic situations. Phov, power required to hover (usually aerial but applicable wherever an animal's density is greater than that of the supporting medium); Pmc, power usage at a velocity (Vmc) that permits maximal range; Vmin, velocity that requires minimal power (Pmin); Po, profile power. (See also Fig. 38.)

from ref. 1583


Figure 5.

The three major kinds of frictional coefficient characterizing foot contact in the terrestrial locomotion of vertebrates.

from ref. 731


Figure 6.

Categorization of the swimming motions and propulsors of fishes, primarily by body and caudal fin (BCF) and median and paired fin (MPF) propulsors in undulatory or oscillatory motions. The major force(s) involved in thrust production varies with the nature of the motions and has been most extensively studied for BCF propulsors. Further explanation of propulsor mechanisms is included in Table 5. The moving portion of the propulsor is shaded.



Figure 7.

Morphological convergence in swimming mechanisms of teleostean and selachian fishes. In both groups, specialists have appeared for high‐speed sustained swimming using periodical tailbeats (Thunnus, Lamna, and Carcharhinus). Lower speeds are seen in generalist swimmers, specialized for no particular type of activity (Salmo, Scyliorhinus, and Centroscyllium). Teleosts show some well‐developed morphs for transient high‐acceleration swimming (Cottus and Psettodes), and although there are some trends among selachians toward deep bodies and fins to maximize acceleration rates, development in this direction is relatively small (Heterodontus and Ginglymostoma). Maneuvering forms (Chaetodon) occur among teleostean fishes but not selachians. In contrast, benthic forms (Pristis, Rhinobatos, and Squatina), although found among teleosts, are common among selachians and dominant in the second major batoidimorph group of elasmobranchs.



Figure 8.

Summary of major muscle and skeletal elements used by various bony fish propulsors. A: Myotomal FG muscle fiber trajectories; B: Dorsal fin; C: Pectoral fin; D: Caudal fin. Further explanation is given in the text.

from ref. 2240


Figure 9.

Combination of several analytical schemes for analysis of symmetrical gaits. In gait formula analysis (upper left, after refs. 1024,1029), contact duration of a hindfoot is mapped vs. the lag between its contact and that of the ipsilateral forefoot; both are standardized by stride length. The plot using the two percentages as coordinates characterizes many species and motor patterns by documenting that they fall on a particular site of the graph; however, what is even more important, the plot shows regions for which no locomotor patterns exist. Note that the classical gaits are actually regions of support positions with numerous intermediates. The terms “lateral sequence” and “diagonal sequence” have been transposed to match the more classical terms (right side of figure; after Gans and Zug, unpublished data). In walk pattern analysis (bottom right side of figure; after refs. 477,478,2361), the pattern of each foot is indicated by a bold line along the time axis while the foot is in contact with the ground (and sometimes a thin line while the foot is lifted). Sections at right angles to the lines representing the position of the four feet indicate the sequence of support postures, ranging from quadrupedal to apodal (during rapid jumps). The method has the merit that one can easily quantify the numbers of, and the durations occupied by, particular support positions; this permits their characterization by standard statistical methods.



Figure 10.

Gait formula analysis for asymmetrical gaits 1029. The ordinate represents the percentage of the stride interval that the forefoot midtime follows the midtime of the hindfoot. The abscissa represents the percentage of the stride interval that the body is supported by a single or both hindfeet. The diagrams show major locomotor patterns but also note some cases in which particular species can propel themselves by various distinct locomotor sequences.



Figure 11.

Stages of a pacing dromedary (after ref. 814).



Figure 12.

Normal sequence of limb movements of the newt Triturus cristatus; the numerals in circles indicate the sequence of flexion. Right fore 1, right fore 2, left hind 3, left fore 4, right hind. The twenty‐eight phases of single step derive from photographs taken at intervals of 1/12 sec. Four drawings are marked to indicate the foot that is being lifted from the ground.

From original photographs of Gray [883,889]


Figure 13.

Series of diagrams showing the position, relative to the ground, assumed by the limbs during locomotion in the newt Cynops pyrrhogaster. The positions are copied from cinematic records (after ref. 1852).



Figure 14.

A: Forces exerted by the undulating animal against a resistance site (peg, point d'appui) placed laterally (see also camfollower analysis in Fig. 15). The moving curves exert forces against resistance sites and their reaction propels the animal. The sliding trunk not only induces reaction, but generates frictional components acting in opposition to the propulsive effect. B: Grass snake (Natrix natrix) traveling over a plane surface by lateral undulation, showing the direction and magnitude (in g) of the forces exerted by letting the snake act against a series of pendulums. Whenever there is only a single peg, the animal must propel itself by the concertina effect. In each case, the animal was permitted to select certain pegs and only those deflected are illustrated here (after refs. 723,724,892).



Figure 15.

Pattern of a cam‐follower deriving from the principle that if tension is exerted on a peg (A, at right angles to its length) by a curved hook, the hook will slide along its internal curve. B: The hook will come to rest at the site at which the imposed force will be at a right angle to the surface. If the internal curve against which force is exerted is irregular, the rest position of the system will be that of least internal radius. C: If the hook can deform, it will then move (internal arrow) along the peg from the side of lesser to that of greater curvature.



Figure 16.

Positions occupied by a completely limbless lizard, the scheltopusik Ophisaurus apodus, undulating simply through a field of pegs, with contact points indicated by circles. Although the animal undulates its entire trunk and tail, it maintains its trunk in regular curves; hence it is not using lateral undulation. The lizard's successive centers of gravity are shown by dots; the centers of gravity of the positions indicated by computer traces are shown by crosses. The top of the illustrated area was occupied by nails spaced 8 cm apart, and the bottom by nails spaced 4 cm apart. Note that despite relatively extensive excursions of the body, the center of gravity travels along a close‐to‐rectilinear path (after ref. 754).



Figure 17.

Sketch of snake engaging in concertina locomotion within a tunnel. The shaded areas of the animal indicate zones in static contact 731.



Figure 18.

Locomotion of completely limbless lizard, the scheltopusik Ophisaurus apodus, engaging in slide‐pushing. The center of gravity in every fifth frame in the sequence is shown by a dot. In this species, the musculature of the tail provides a continuation of that of the trunk. The center line of the animal is shown for four positions in the middle of a sequence; a cross represents the center of gravity in each. The scale bar equals 100 mm and total length of the specimen is 756 mm. A: The tail is thrown away from the center of gravity. B: The tail approaches the center of gravity (after ref. 754).



Figure 19.

Another computer‐corrected sequence of locomotion of the completely limbless lizard, the scheltopusik Ophisaurus apodus, engaging in slide‐pushing, with the contact zones in the middle of the body and the animal traveling slightly diagonally from top to bottom of the figure. The dots indicate the center of gravity for all points plotted; the crosses, for the eleven positions shown here. Every fifth line is plotted and the scale bar equals 100 mm; total length of the specimen is 910 mm (after ref. 754).



Figure 20.

Aspis cerastes moving by sidewinding from right to left. A: The center of gravity in each outline is indicated by a cross. Intervals between positions equal 1/32 sec. Note the position of the tracks, the intertrack zones, and the generally smooth and constant line of progress for the center of gravity. The line measures 10 cm to scale; average wave velocity is 33 cm/sec. B: Same sequence as A, showing the position of the specimen traced for four sample frames, with the path of the center of gravity (dots) that of the midbody position (point 25 of 50) (after ref. 758).



Figure 21.

Sketches of sidewinding locomotion after a film of Crotalus cerastes, showing successive positions and the tracks formed in the sand. The shadows indicate the portion of the body lifted off the ground and the intertrack position at which the orientation of the trunk occupies its greatest angle to the trackline (after ref. 731).



Figure 22.

Illustration of muscular activity during propulsion of Python regius by pushing against a single peg. A: Contractions of the LLD, left longissimus dorsi; RLD, right longissimus dorsi; and RSC, right supracostalis lateralis ventralis, are shown. The diagrams are based on electromyograms but neglect the fact that a single EMG may reflect action in three or more adjacent muscular bundles. B: Anatomical correspondence of the site of contraction. The vertebrae connected by the same bundle are marked by symbol and the large arrow indicates the direction in which the snake is moving (after ref. 790).



Figure 23.

Reaction force patterns in burrowers in which a variously conical head penetrates a more or less homogeneous soil. The forces are assumed to be distributed uniformly and to act normally to the surface of the shield. The greater the friction along the contact zone, the less the penetration 731.



Figure 24.

Trogonophids or amphisbaenians use torsional oscillation to scrape sandy soils off the end of the tunnel 731.



Figure 25.

Spade‐snouted amphisbaenians (1) extend their tunnel by two‐cycle movements. The snout first drives a penetrating divot, which normally starts near the bottom level of the tunnel. Once the snout has penetrated to a maximum (1a–b), the nuchal muscles rotate the skull around the head joint. The dorsal surface of the head then compresses the overburden and widens the tunnel (1b–1c) for the beginning of the next penetrating stroke. In keel‐headed amphisbaenians (2), the head first drives forward (2a–2b) and the snout is then shifted alternately to the right (2c) and then to the left. Bipedid amphisbaenians (3) extend their tunnels by scraping movements analogous to those of moles. The short forearm and clawed hand are extended to the front and swung straight past the tunnel end (3a). During each movement they tunnel. The freed material is then pressed into the sides (3b). 731.



Figure 26.

General morphology of a tetrapod caudate. Note the general tetrapod pattern with neck, trunk, caudal vertebrae, and two distinct girdle segments to which pectoral and pelvic appendages attach, as well as the heavily muscularized trunk and tail. Note that the body tends to twist in opposite directions at the two foot contact levels (after ref. 385).



Figure 27.

A: Track of an adult male urodele Hydromantes platycephalus walking over a surface sloped 30 degrees laterally. Six images were generated by allowing the animal to wallow in black ink before walking across drawing paper. Diagrams 1 through 6 show successive stages of a single tail movement. The tail is used to prop the lower left side of the animal. B: Trackway over five steps. C: Frontal aspect of body and tail in typical walking pose on an inclined surface. D: Lateral (top) and dorsal (below) views of the blunt caudal tip.



Figure 28.

Synchronous dorsal and lateral views of the normal walking of a toad (Bufo vulgaris). The numerals indicate the phases of the stride employed as a relative time scale. Phases 0–6 constitute a complete stride and phases 0, 3, 6, and 9 are corresponding stages of different steps (the drawing for phase 0 is a little early because the right hind foot is not yet off the ground). The symbols represent the relation of the left limbs to the recording platform, indicated in the side views by black bars. The limbs shown in the symbols by a solid line are on the platform; limbs indicated by a broken line are off the platform. Because the side view was obtained using a mirror, the near limbs are those of the left side. The left forefoot first carries the weight about midway between phases 0 and 1; the left hind limb is lifted off the ground between phases 8 and 9. The limbs of the right side do not touch the recording platform, which is on the left of the stage (after refs. 166,889).



Figure 29.

Simple series of a frog's jump. Note the change in orientation of the trunk during flight (after ref. 889).



Figure 30.

Locomotion in turtles. Top: Terrestrial walking in Gopherus polyphemus. Lateral view of a single stride of the left hind limb. A–D, retractive or propulsive phase; E–H, protractive or recovery phase; A, footfall; E, beginning of protraction (after ref. 2357). Bottom left: Swimming in Trionyx spinifer. Lateral view of a single‐stride swimming stride of the left hindlimb. A–D, retractive phase; E–H, protractive phase. Note folding of the foot. Bottom right: Sequence of walking tortoise showing the footfall in very slow and unstable locomotion. LF, left front; LH, left hind; RF, right front; RH, right hind (after ref. 1128).



Figure 31.

Rapid tetrapod locomotion in the collared lizard Crotaphytus c. collaris. Lateral view of the locomotor cycle is shown in sequence A–G. Details of the position of distal digits are partially obscured by substrate. Note the long, substantially greater leg and stride length of the hindlimb over the forelimb and the consequent bipedal portions of the stride sequence (after ref. 1927).



Figure 32.

Bipedal locomotion of juvenile Basiliscus basiliscus.

Made from motion picture by projection, with the camera 1 foot above the substrate. Top: Lateral views (A–J). Bottom; Posterior aspects (A–E) (after refs. 1928,1930)


Figure 33.

Tunnel penetration in advanced uropeltids (and in some caecilians) involves a two‐stroke system. Top: First, the snout drives forward (A). Next, concertina expansion of the neck effectively widens the body and hence the tunnel (B). It also provides a fixed site from which the head may be pushed forward, developing a new divot. The straightened column is then brought into a new concertina curvature starting at the back of the skull (C). Bottom: The tunnels formed meander because the animal's path is deflected by various resistance sites, such as roots and pebbles.



Figure 34.

Foot diversity of small mammalian species. Hoofed forms and carnivores have been omitted. A: Giant armadillo (Priodontes maximus); B: Two‐toed sloth (Choloepis hoffmanni); C: mole (Talpa); D, E: tarsier; F: prehensile‐tailed porcupine (Coendou); G: tree squirrel; H: spider monkey (Ateles); I–K: diversity within gibbon (Hylobates agilis); L: Eumetopias; M: potto (Perodicticus potto); N: beaver (Castor); O: koala (Phascolarctos cinereus); P: cuscus (Phalanger s.l., but this has now been broken up into four genera); Q: silky anteater (Cyclopes didactylus); R: platypus (Ornithorbynchus anatinus); S: Lutra maculicollis; T, U: Aonyx capensis; V, W: Amblyonyx cinerus; X, Y: Hydromys chrysogaster.

modified from ref. 1218


Figure 35.

Mammalian diversity. Whereas the basic body plan is tetrapodal, the diagram documents structural and clearly locomotor diversity (after ref. 2049).



Figure 36.

Support of membranous wings. A: Force diagram of a cross‐section of a bat‐type wing. Many force vectors cancel. A‐1: Forces acting on the digits of a bat's wing. B: Force diagram of a cross‐section of a pterosaur‐type wing. B‐1: Forces acting on supporting digit of a pterosaur wing. No vectors cancel, and the single digit must withstand bending forces transmitted from the entire wing membrane. Arrows in B‐1 indicate assumed tensile vectors in pterosaur wing; lines indicate directions of elastic fibers, which may also occur along trailing edge.

from ref. 1513


Figure 37.

Birds engaged in nonsteady flight. A: Tracings from photographs taken at intervals of 0.01 s of a pigeon in slow flight. Top series are of downstrike (primarily lift), bottom series of upstroke (primarily propulsion) (after ref. 339). B: Vortex patterns generated by a hummingbird engaged in symmetrical hovering. C: A small passerine in asymmetrical hovering (C) (after ref. 1510).



Figure 38.

Power curves. A: Theoretical total mass‐specific power vs. speed for a 333 g pigeon, according to the models of Pennycuick (P) and Rayner (R), and for a 9 g bat, according to Norberg (N). B: Measured mass‐specific power vs. speed from experiments with animals in wind tunnels.

modified from refs. 600,1513. modified from ref. 600


Figure 39.

A: Positive dihedral of wings promotes stability in roll. A roll to the left (left wing down) increases lift (L) on the left wing and decreases lift on the right wing. B: Partial retraction of left wing decreases left wing area and lift, adjusting for roll. Wing position is middle of downstroke. L and L′, lift forces; Lv and Lv′, vertical lift forces on the two wings.

modified from ref. 1513


Figure 40.

Skeletal elements of forelimb in five species of modern bird plus Archaeopteryx (A) scaled so that the carpometacarpi (hand or propeller elements) are of equal length. Birds capable of hovering and/or steep ascent [hummingbird (B), dove (C), and grouse (D)] using nonsteady flight (variants of slow, forward flight) possess robust skeletal elements, with the ulna and radius bowed away from each other, indicating significant muscle mass associated with the antibrachium. Gliders, such as the albatross (F), have little forelimb musculature. Most passerines, such as the starling (E), show intermediate conditions.

modified from ref. 525


Figure 41.

Comparison of regions in principal components space of flight morphology for birds and bats. A: First (body mass) and second (wing‐loading) components. B: Second and third (aspect) components. Components are normalized to zero mean and unit standard deviation so distribution appears circular; ticks on axes = 1 SD. Zones occupied by hummingbirds are stippled; zone of Microchroptera hatched ///; zone of Megachiroptera hatched WW. Positions of a few other key species of bird are indicated for reference.

modified from ref. 1699
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Article Title: Vertebrate Locomotion
 

How to Cite

Carl Gans, Abbot S. Gaunt, Paul W. Webb. Vertebrate Locomotion. Compr Physiol 2011, Supplement 30: Handbook of Physiology, Comparative Physiology: 55-213. First published in print 1997. doi: 10.1002/cphy.cp130103