(Georgia Institute of Technology, 2012-05)
Li, Chen; Hsieh, S. Tonia; Goldman, Daniel I.
A diversity of animals that run on solid, level, flat, non-slip surfaces appear to bounce on their legs; elastic elements in the limbs
can store and return energy during each step. The mechanics and energetics of running in natural terrain, particularly on surfaces
that can yield and flow under stress, is less understood. The zebra-tailed lizard (Callisaurus draconoides), a small desert
generalist with a large, elongate, tendinous hind foot, runs rapidly across a variety of natural substrates. We use high-speed video
to obtain detailed three-dimensional running kinematics on solid and granular surfaces to reveal how leg, foot and substrate
mechanics contribute to its high locomotor performance. Running at ~10bodylengthss–1 (~1ms–1), the center of mass oscillates
like a spring-mass system on both substrates, with only 15% reduction in stride length on the granular surface. On the solid
surface, a strut-spring model of the hind limb reveals that the hind foot saves ~40% of the mechanical work needed per step,
significant for the lizardʼs small size. On the granular surface, a penetration force model and hypothesized subsurface foot
rotation indicates that the hind foot paddles through fluidized granular medium, and that the energy lost per step during
irreversible deformation of the substrate does not differ from the reduction in the mechanical energy of the center of mass. The
upper hind leg muscles must perform three times as much mechanical work on the granular surface as on the solid surface to
compensate for the greater energy lost within the foot and to the substrate.
(Georgia Institute of Technology, 2010-06)
Ding, Yang; Gravish, Nick; Li, Chen; Maladen, Ryan D.; Mazouchova, Nicole; Sharpe, Sarah S.; Umbanhowar, Paul B.; Goldman, Daniel I.
Terrestrial locomotion can take place on complex substrates such as leaf litter, debris, and soil that flow or solidify in response to stress. While principles of movement in air and water are revealed through study of the hydrodynamic equations of fluid motion, discovery of principles of movement in complex terrestrial environments is less advanced in part because describing the physics of limb and body interaction with such environments remains challenging. We report progress our group has made in discovering principles of movement of organisms and models of organisms (robots) on and within granular materials (GM) like sand. We review current understanding of localized intrusion in GM relevant to foot and body interactions. We discuss the limb-ground interactions of a desert lizard, a hatchling sea turtle, and various robots and reveal that control of granular solidification can generate effective movement. We describe the sensitivity of movement on GM to gait parameters and discuss how changes in material state can strongly affect locomotor performance. We examine subsurface movement, common in desert animals like the sandfish lizard. High speed x-ray imaging resolves subsurface kinematics, while electromyography (EMG) allows muscle activation patterns to be studied. Our resistive force theory, numerical, and robotic models of sand-swimming reveal that subsurface swimming occurs in a “frictional fluid” whose properties differ from Newtonian fluids.