When falling, geckos are able to right themselves turning their body in mid-air, and always land safely on their feet. It is fascinating to watch the slow-motion videos of the lizard dropping from a belly-up position, then using a swing of the tail to turn around into a skydiving posture. Even more fascinating is to understand the simple physical principle that explains their maneuver: conservation of angular momentum.
The research group of Prof Robert Full at UC Berkeley has conducted exciting work explaining how the lizards use their tail for their mid-air righting prowess—the fastest righting reflex ever measured (about 1/10 of a second). Below is a short video which summarizes the findings.
The results of a first set of experiments, performed by PhD student Ardian Jusufi, were published in the Proceedings of the National Academy of Sciences¹. Among other observations, they describe the air-righting reaction in detail, as follows:
- as soon as it falls (belly-up), the gecko spreads its legs wide
- it then pitches its tail so that it points downward, perpendicular to its body
- the tail now swings around the longitudinal axis of the gecko, which produces a counter-rotation of the body due to conservation of angular momentum
- the body executes a full turn, to end right-side up, and the tail stops turning
- the gecko keeps falling, arms extended like a skydiver
The scientists then built an analytical model of the righting mechanics. The angular momentum of a body is the product of its moment of inertia and its angular velocity:
At the start of the fall, the gecko has zero angular momentum (there are no external torques acting on it). If one considers the body segment separate from the tail, then the sum of the angular momentum of each piece must continue to be zero:
A simple geometrical model can be used: the body as a rigid elliptical slab, and the tail as a thin cone rotating perpendicular to the body. With biometric data, a realistic estimate of the moments of inertiaof body and tail are entered into the equations, and then a change in the angle of the body is obtained from a change in the angle of the tail:
This simple model correctly predicts the reorientation of the body of the gecko! Now, there is enough information to build a device that can emulate the behavior of the gecko: the RightingBot².
¹ ”Active tails enhance arboreal acrobatics in geckos”, A Jusufi, D Goldman, S Revzen, R Full, PNAS Vol. 105, pp. 421-–4219 (2008) [pdf]
² ”Righting and turning in mid-air using appendage inertia: reptile tails, analytical models and bio-inspired robots”, A Jusufi, D T Kawano, T Libby, R J Full, Bioinspiration & Biomimetics, Vol. 5, pp. 1–12 (2010) [doi]