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A Mojave rattlesnake (Crotalus scutulatus) sidewinding

Undulatory locomotion is the type of motion characterized by wave-like movement patterns that act to propel an animal forward. Examples of this type of gait include crawling in snakes, or swimming in the lamprey. Although this is typically the type of gait utilized by limbless animals, some creatures with limbs, such as the salamander, choose to forgo use of their legs in certain environments and exhibit undulatory locomotion. This movement strategy is important to study in order to create novel robotic devices capable of traversing a variety of environments.


Environmental Interactions

In limbless locomotion, forward locomotion is generated by propagating flexural waves along the length of the animal's body. Forces generated between the animal and surrounding environment lead to a generation of alternating sideways forces that act to move the animal forward[1]. These forces generate thrust and drag. (add picture)



Simulation predicts that thrust and drag are dominated by viscous forces at low Reynolds numbers and inertial forces at higher Reynolds numbers.[2]. When swimming in a fluid two main forces are thought to play a role:

  • Skin Friction: Generated due to the resistance of a fluid to shearing and is proportional to speed of the flow. This dominates undulatory swimming in spermatozoa[3] and the nematode [4]
  • Form Force: Generated by the differences in pressure on the surface of the body and it varies with the square of flow speed.

At low Reynolds number (Re~100), skin friction accounts for nearly all of the thrust and drag. For those animals which undulate at intermediate Reynolds number (Re~101), such as the Ascidian larvae, both skin friction and form force account for the production of drag and thrust. At high Reynolds number (Re~102), both skin friction and form force act to generate drag, but only form force produces thrust.[2]


In animals that move without use of limbs, the most common feature of the locomotion is a rostral to caudal wave that travels down their body. However, this pattern can change based on the particular undulating animal, the environment, and the metric in which the animal is optimizing (ie. speed, energy, etc.). The most common mode of motion is simple undulations in which lateral bending is propagated from head to tail.

  • Snake Locomotion

See also Snakes

Snakes can exhibit 5 different modes of terrestrial locomotion: (1) lateral undulation, (2) sidewinding, (3)concertina, (4)rectilinear, and (5) slide-pushing. Lateral undulation closely resembles the simple undulatory motion observed in many other animals such as in lizards, eels and fish, in which waves of lateral bending propagate down the snakes body.

  • Eel Locomotion

While the American Eel typically moves in an aquatic environment it can also move on land for short periods of time. It is able to successfully move about in both environments by producing traveling waves of lateral undulations. However, differences and terrestrial and aquatic locomotor strategy suggest that the axial musculature is being activated differently [5],[6],[7] (see muscle activation patterns below). In terrestrial locomotion, all points along the body move in the on approximately the same path and, therefore, the lateral displacements along the length of the eel's body is approximately the same. However, in aquatic locomotion, different points along the body follow different paths with increasing lateral amplitude more posteriorly. In general, the amplitude of the lateral undulation and angle of intervertebral flexion is much greater during terrestrial locomotion than that of aquatic.(insert picture?)

Musculoskeletal System

Perch filets showing myomere structure

Muscle Architecture

A typical characteristic of many animals that utilize undulatory locomotion is that they have segmented muscles, or blocks of myomeres, running from their head to tails which are separated by connective tissue called myosepta. In addition, some segmented muscle groups, such as the of the lateral hypaxial musculature in the salamander are oriented at an angle to the longitudinal direction. For these obliquely oriented fiber the strain in the longitudinal direction is greater than the strain in the muscle fiber direction leading to an architectural gear ratio greater than 1. A higher initial angle of orientation and more dorsoventral bulging produces a faster muscle contraction but results in a lower amount of force production[8]. It is hypothesized that animals employ a variable gearing mechanism that allows self-regulation of force and velocity to meet the mechanical demands of the contraction[9] . When a pennate muscle is subjected to a low force, resistance to width changes in the muscle cause it to rotate which consequently produce a higher architectural gear ratio (AGR) (high velocity). However, when subject to a high force, the perpendicular fiber force component overcomes the resistance to width changes and the muscle compresses producing a lower AGR (capable of maintaining a higher force output).

Muscle Activity

In addition to a rostral to caudal kinematic wave that travels down the animals body during undulatory locomotion, there is also a corresponding wave of muscle activation that travels in the rostro-caudal direction. However, while this pattern is characteristic of undulatory locomotion, it too can vary with environment.

American Eel

Aquatic Locomotion: Electromyogram (EMG) recordings reveal a similar pattern of muscle activation during aquatic movement as that of fish. At slow speeds only the most posterior end of the eels muscles are activated with more anterior muscle recruited at higher speeds [5][7]. As in many other animals, the muscles activate late in the lengthening phase of the muscle strain cycle, just prior to muscle shortening which is a pattern believed to maximize work output from the muscle.

Terrestrial Locomotion: EMG recording show a longer absolute duration and duty cycle of muscle activity during locomotion of land[5]. Also, the absolute intensity is much higher while on land which is expect from the increase in gravitational forces acting on the animal. However, the intensity level decreases more posteriorly along the length of the eel's body. Also, the timing of muscle activation shifts to later in the strain cycle of muscle shortening.


Animals with elongated bodies and reduced or no legs have evolved differently from their limbed relatives [10]. In the past, some have speculated that this evolution was due to a lower energetic cost associated with limbless locomotion. The biomechanical arguments used to support this rational include that (1) there is no cost associatied with the vertical displacement of the center of mass typically found with limbed animals[10][11], (2) there is no cost associated with accelerating or decelerating limbs[11], and (3) there is a lower cost for supporting the body[10]. This hypothesis has been studied further by examining the oxygen consumption rates in the snake during different modes of locomotion: lateral undulation, concertina[12] and sidewinding[13]. The net cost of transport (NCT), which indicates the amount of energy required to move a unit of mass a given distance, for a snake moving with a lateral undulatory gait is identical to that of a limbed lizard with the same mass. However, a snake utilizing concertina locomotion produces a much higher net cost of transport, while sidewinding actually produces a lower net cost of transport. Therefore, the different modes of locomotion are of primary importance when determining energetic cost. The reason that lateral undulation has the same energetic efficiency as limbed animals and not less, as hypothesized earlier, might be due to the additional biomechanical cost associated with this type of movement due to the force needed to bend the body laterally, push its sides against a vertical surface, and overcome sliding friction[12].

Neuromuscular System

Intersegmental Coordination

Wavelike motor pattern typically arise from a series of coupled segmental oscillator. Each segmental oscillator is capable of producing a rhythmic motor output in the absence of sensory feedback. One such example is the half center oscillator which consist of two neurons that are mutually inhibitory and produce activity 180 degrees out of phase. The phase relationships between these oscillators are established by the emergent properties of the oscillators and the coupling between them[14]. Forward swimming can by accomplished by a series of coupled oscillators in which the anterior oscillators have a shorter endogenous frequency than the posterior oscillators. In this case, all oscillators will be driven at the same period but the anterior oscillators will lead in phase. In addition, the phase relations can be established by asymmetries in the couplings between oscillators or by sensory feedback mechanisms.

  • Leech

The leech moves by producing dorsoventral undulations. The phase lags between body segments is about 20 degrees and independent of cycle period. Thus, both hemisegments of the oscillator fire synchronously to produce a contraction. Only the ganglia rostral to the midpoint are capable of producing oscillation individually. There is U-shaped gradient in endogenous segment oscillation as well with the highest oscillations frequencies occurring near the middle of the animal[14]. Although the couplings between neurons spans six segments in both the anterior and posterior direction, there are asymmetries between the various interconnections because the oscillators are active at three different phases. Those that are active in the 0 degree phase project only in the descending direction while those projecting in the ascending direction are active at 120 degrees or 240 degrees. In addition, sensory feedback from the environment may contribute to resultant phase lag.

  • Lamprey

The lamprey moves using lateral undulation and consequently left and right motor hemisegments are active 180 degrees out of phase. Also, it has been found that the endogenous frequency of the more anterior oscillators is higher than that of the more posterior ganglia[14]. In addition, inhibitory interneurons in the lamprey project 14-20 segments caudally but have short rostral projections. Sensory feedback may be important for appropriately responding to perturbations, but seems to be less important for maintaince of appropriate phase relations.


Based on biologically hypothesized connections of the central pattern generator in the salamander, a robotic system has been created which exhibits the same characteristics of the actual animal[15][16]. Electrophysiology studies have shown that stimulation of the mesencephalic locomotor region(MLR) located in the brain of the salamander produce different gaits, swimming or walking, depending on intensity level. Similarly, the CPG model in the robot can exhibit walking at low levels of tonic drive and swimming at high levels of tonic drive. The model is based of the four assumptions that:

  • Tonic stimulation of the body CPG produces spontaneous traveling waves. When the limb CPG is activated it overrides the body CPG.
  • The strength of the coupling from the limb to the body CPG is stronger than that from body to limb.
  • Limb oscillators saturate and stop oscillating at higher tonic drives.
  • Limb oscillators have lower intrinsic frequencies than body CPGs at the same tonic drive.

This model encompasses the basic features of salamander locomotion.

See also


  1. ^ Guo, Z.V. and Mahadeven,L. Limbless undulatory propulsion on land. PNAS 105, 9, 3179-3184. 2008
  2. ^ a b McHenry, M.J., Azizi, E. and Strother J.A. The hydrodynamics of locomotion at intermediate Reynolds numbers: undulatory swimming in ascidian larvae(Botrylloides sp.). J. Exp. Biol. 206, 327-343. 2002
  3. ^ Gray and Hancock, 1955.
  4. ^ Gray and Lissmann, 1964.
  5. ^ a b c Biewener, A.A, and Gillis, G.B. Dynamics of Mucscle Function During Locomotion: Accommodating Variable Conditions. J. of Exp Biol. 202, 3387-3396. 1999
  6. ^ Gillis, G.B. Environmental Effects on Undulatory Locomotion in the American Eel Anguilla Rostrata: Kinematics in Water and on Land. J. Exp. Biol. 201, 949-961. 1998
  7. ^ a b Gillis, G.B. Neuromuscular Control of Anguilliform Locomotion: Patterns of Red and White Muscle Activity During Swimming in the American Eel Anguilla Rostrata
  8. ^ Brainerd, E. L. and Azizi E. (2005) “Muscle Fiber Angle, Segment Bulging and Architectural Gear Ratio in Segmented Musculature.” The Journal of Experimental Biology 208, 3249-3261.
  9. ^ Azizi, E., Brainerd, E.L., and Roberts, T.J. (2008) “Variable Gearing in Pennate Muscles.” PNAS 105(5), 1745-1750.
  10. ^ a b c Gans C. Am Zool. 15, 455. 1975.
  11. ^ a b Goldspink, G. Mechanics and Energetics of Animal Locomotion, Wiley, New York, 153-167. 1977
  12. ^ a b Walton, M. Jayne, B.C. Bennet, A. F. The energetic cost of limbless locomotion. Science, 249, 1990
  13. ^ Secor, S.M., Jayne, B.C. and Bennett, A.F. Locomotor Performance and energetic Cost of Sidewinging by the Snake Crotalus Cerastes
  14. ^ a b c IHill, A. A.V., Masino, M.A. and Calabrese, Ron (2003) “Intersegmental Coordination of Rhytmic Motor Patterns.” The Journal of Neurophysiology 90, 531-538.
  15. ^ Ijspeert, A.J. (2001) “A Connectionist Central Pattern Generator for the Aquatic and Terrestrial Gaits of a Simulated Salamander.” Biological Cybernetics 84, 331-348.
  16. ^ Ijspeert, A.J, Crespi, A., Ryczko, D. and Cabelguen, J.M. (2007) “From Swimming to Walking with a Salamander Robot Driven by a Spinal Cord Model.” Science 315, 1416-1420.

External links

Lateral undulation is the most primitive of vertebrate locomotor patterns, present even in hagfish, lampreys, and lancelets. It is used both in the water and on land, most notably by snakes in the latter setting.

One can roughly describe lateral undulation as a sequence of alternating left-right body waves propagating posteriorly along the animal. This is accomplished by unilateral, posteriorly-propagating muscle activity, which means that, at any point on the animal, only muscles on the left or right side are active, and the active region of muscle contraction moves from head to tail.

In the water, this motion causes the posterior edge of each body-wave to push water backwards, which results in a net forward force on the animal. On land, the same effect is accomplished, but by pushing on soil, rocks, plants and other irregularities in the substrate.

See also

External links


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