LIMBLESS LOCOMOTION Last updated:  June 2, 2009

All images and videos copyright of Grace Pryor, Mike Shelley and David Hu, Applied Mathematics Laboratory at New York University and Dept. of Mechanical Engineering, Georgia Tech.

Figure 1.
How do land animals move without legs?   Limbless animals tend to be long and slender, such as the corn snake shown above.  One benefit this gives them is the ability to hide in narrow spaces under branches and leaves.  To move along flat ground, snakes use a variety of limbless "gaits" analogous to a horse's walk, trot and gallop.   We study here the simplest of the snake's gaits, slithering.

Figure 2.  Have you ever run your hand over a cat's fur?  The fur feels smooth in one direction and rough in another.  Similarly, the bodies of snakes are covered by smooth scales, resembling the overlapping shingles on a house.   These are important to locomotion because they engage with bumps on the ground while the snake is moving. Using simple friction measurements, we find that arrangement of the scales causes the snakes to slide twice as easily forwards than sideways.  This property is called frictional anisotropy.  Many everyday items share this property, like wheels, ice skates and cross-country skis.   For example, wheels roll easily in the forward direction, but skid in the sideways direction.

Figure 3. Methods: snakes on a plane.  We temporarily put the snakes to sleep and slide them down inclined planes. By placing them in various orientations, we can measure their resistance to sliding. VIDEO: in the movie, we incline a plane with an awake snake. Notice that the ruler, because it is smooth, slides first. The snake's scales cause it to slide second.

Figure 4--VIDEOS. The necessity of snake scales to locomotion can be shown by putting snakes on smooth surfaces or enveloping their scales in cloth.  In both of these cases, snakes are unable to slither forward. This is because their scales cannot gain purchase in the ground.

Figure 5--VIDEO.  Snakes can slither on flat ground if the roughness of the surface is similar to that of the snake scales.  The small bumps in the ground allow the scales to catch when the snake is pushing sideways.  This may explain how snakes can be observed to cross sand, bare rock, and roads.

Figure 6. Have you ever tried running uphill?  Snakes can also slither up a cloth-covered hill, but not if it is very steep.  Here, the limit is 7 degrees of inclination.  At higher inclinations, they begin sliding backwards.

Figure 7.  Using a mathematical model incorporating the frictional properties of the snake scales, we can account for about 70% of the snake's forward speed. The arrows in the video above indicate the direction and magnitude of the propulsive frictional force applied by the snake to the ground. The red dot indicates the center of mass.
We found that a simple observation of the way snakes move could bring the theoretical model into even closer agreement with our measurements.

Figure 8.
Looking at the snakes from the side, we see that they will often lift parts from the ground while slithering, as shown in the video above.  The snake's weight is then concentrated on the remaining areas of contact.  When we incorporated this behavior into our theoretical model, we found increases in both body speed and efficiency.

Figure 9.
The ability of a snake to redistribute its weight can also be seen using force visualizations with a photoelastic gelatin.  When polarized light is shone through this material and viewed through cross-polarizing film, forces applied by the snake become visible.  Specifically, bright regions indicate high force.  While the snake undoubtedly sticks to the gelatin as it tries to move across it, it is clear that it tends to lift the peaks and troughs of its body, as we observe in normal slithering.

Figure 10.
By adjusting our model to incorporate this dynamic weight-balancing by the snake, we find improvements in speed of 35% and in mechanical efficiency of 50%. This is illustrated in the video above, where the body is colored red if the snake has lifted its body, and blue if it has concentrating its weight on the ground.  Why is the lifted snake faster?  By pressing its weight in places where the friction force is greatest in the backwards direction, it can increase its speed.   This result shows that snake locomotion is similar to the way we walk or run: we continually redistribute our weight from the left to right foot as we move.  Similarly, snakes are always redistributing their weight so they can slither the fastest.

Figure 11. Other investigators (Hirose, Choset, Miller) have built numerous snake robots for search and rescue.  Many of these robots rely on wheels to slither over flat surfaces.  The mechanisms of propulsion found in this research, the use of overlapping scales and the use of body-lifting, may find application in these devices.

Figure 12.
For a given surface, what is the best snake gait?  We have studied the simplest possible gait, slithering by waving the body.  We find that snakes change gaits like car changes gears.  The video above shows a snake changing from slithering to an accordion-like gait, as it traverses through two walls of decreasing spacing.   We plan to our apply our mathematical methods to studying other snake gaits.

snake fans ( http://www.digits.com/)

References

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3. A Bellairs. Life of reptiles, volume 2, pages 283–331. Universe books, 1970.

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7. C Gans. Slide-pushing: a transitional locomotor method of elongate squamates. Symp. Zool. Soc. Lond., 52:12–26, 1984.

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9. S Renous, E Hoﬂing, and J P Gasc. Analysis of the locomotion pattern of two microteiid lizards with reduced limbs, Calyptommatus leiolepis and Nothobachia ablephara (Gymnophthalmidae). Zool., 99:21–38, 1995.

10. S. Hirose. Biologically Inspired Robots: Snake-Like Locomotors and Manipulators. Oxford University Press, Oxford, 1993.

11. J Hazel, M Stone, M S Grace, and V V Tsukruk. Nanoscale design of snake skin for reptation locomotions via friction anisotropy. J. Biomech., 32:477–84, 1999.

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