RESEARCH PROJECTS

Dynamic Properties of Biological Rubbers

Passive Mechanics Dominate Active Responses

Dynamic Properties of Biological Rubbers

Elastic proteins are used in animals where long-range elasticity is needed for either energy storage, for damping of vibrations, for restoring structures to their resting position without involving muscles, and for allowing frequent, repeated, rapid deformations of material. The majority of soft biological materials used in both the circulatory and locomotor structures of animals have evolved to have frequency independent energy loss or material properties over the physiological usage range. Despite the clear advantages such properties have for structures used over a range of heart rates, stride frequencies, and temperatures, we lack a clear understanding of how such properties arise and are controlled by animals.

To begin to understand the molecular origins of frequency independent properties in biomaterials, I am characterizing the dynamic mechanical properties of resilin, a nearly pure protein of major importance in insects, under varying conditions of pH, temperature, and hydration. I hypothesize that by controlling the degree of hydration via pH and solute concentrations, insects that use resilin at 5, 50, or 500 cycles per second all use a material with similar properties. An understanding of how insects exploit the entire property range of resilin via chemical or evolutionary control will lead to a better understanding of how all elastomeric proteins function in animals.

Synthesizable, self-aggregating biological materials are of current interest for pharmaceutical delivery, medical devices, and robotics. Resilin is bacterially synthesizable but it cannot be used in biologically inspired engineering applications until a database for the range of properties of this biomaterial is available. This project will provide that database.

Passive Mechanics Dominate Active Responses

A wide array of morphologically diverse runners, from insects to large mammals, display the dynamics of a spring-mass system with the same dimensionless leg stiffness. The two major benefits of bouncing while running are: 1) improving mechanical efficiency by storing and returning elastic strain energy, and 2) simplifying the neural control of locomotion. My research on the material properties of the cockroach musculoskeletal system show that the passive mechanical properties of individual legs dominate the whole body behavior during running and are well tuned to both improve energetic efficiency and simplify control.

Dynamic Oscillations

Despite the potential benefits, direct evidence of spring-like function during running in arthropod legs was lacking. I oscillated passive cockroach legs (left) and found that as much as 40% of the mechanical energy expended to lift and accelerate the center of mass each step may be stored and returned by all three legs. The material properties, resilience, and hysteresis are all independent of frequency, so I applied the two-parameter hysteretic damping model to capture the response of the leg and predict its response to different perturbation conditions.

Cockroaches run using an alternating tripod gait. I dynamically oscillated the thorax (right) while the animal ran on an inertial treadmill. The stiffness and damping of the support tripod are almost exactly three times that of a single leg.

Paper: Dudek, D. M., and Full, R. J. (2006) Dynamic Mechanical Properties of Legs from Running Insects. J Exp Bio, 209: 1502-1515. (pdf, 524 kb)

Impulse Perturbations

The stiffness and damping parameters derived from dynamic oscillations predicted that the leg should recover from an impulse perturbation (shown at left) in less time than a single swing phase. Indeed, passive legs begin to recover from an impulse within 5 ms, and fully recover in as little as 15 ms. Using the simplest, 1 dimensional, frequency independent model to predict the response of the leg to an impulse revealed the importance of off-axis rotation in leg damping.

When the hind leg is subjected to an impulsive perturbation during swing (shown at right), it recovers in less than 16 ms. This is faster than the fastest reflexes in these animals. Therefore, the passive mechanical properties of individual legs determine the system behavior and are well suited to both improving mechanical efficiency during stance and simplifying control of locomotion during swing.

Paper: Dudek, D. M., and Full, R. J. (2007) An isolated insect leg’s passive recovery from dorso-ventral perturbations. J Exp Bio, 210: 3209-3217. (pdf, 397 kb)

Biological Inspiration

Models of biological materials and their role in locomotion can be used to generate design rules for creating engineered structures with the desired properties. The legs of SPRAWL were inspired in this manner and helped develop a fast, stable, and robust legged robot.

Paper: Xu, X., Cheng, W., Dudek, D., Cutkosky, M., Hatanaka, M., and Full, R.J. (2000) Material modeling for shape deposition manufacturing of biomimetic components. Proceedings of DETC/DFM, DETC2000/DFM-14022. (pdf, 553 kb)

Dynamics of Rapid Climbing

The first measurements of the forces insects and reptiles exert during rapid climbing revealed that both animals produce similar dynamics, despite differences in adhesive mechanism, morphology, and leg number. All legs pull upward and towards the body’s midline, while fore legs pull towards the wall and hind legs push away to counteract an overturning moment. This led to the development of the first general model for the dynamics of rapid, legged climbing analogous to the spring-mass model used to characterize level running. The general force patterns used by cockroaches and geckos have provided biological inspiration for the design of a climbing robot named RiSE (Robots in Scansorial Environments).

Papers: Goldman, D. I., Dudek, D. M., Chen, T. S., and Full, R. J. (2006) Dynamics of Rapid Vertical Climbing in Cockroaches Reveals a Template. J Exp Bio, 209: 2990-3000. (pdf, 947 kb)

Autumn, K.; Hsieh, S. T.; Dudek, D. M.; Chen, J.; Chitaphan, C.; and Full, R. J. (2006) Dynamics of geckos running vertically. J Exp Bio, 209:260-272. (pdf, 641 kb)