Nontrivial Impact

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Karsai, Andras
Goldman, Daniel I.
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The purpose of this investigation is to identify and calculate the forces that occur on an impulsive object as it intrudes into granular media. The system analyzed is a computational model of a sinusoidally actuated spring-mass system jumping on a bed of granular material. Various types of ground reaction forces on the robot's foot are investigated and their parameters are systematically varied to compare to experimental data taken from the real-world jumping robot system. Different types and combinations of ground reaction forces are investigated since a single force type was found to be insufficient to fully explain the experimental system's dynamics. The mechanics of this setup are modeled as a set of ordinary differential equations, which are computationally solved to determine the jumping mechanics. Maximal jump heights are calculated across a wide variety jumping motions and granular media densities with different types of ground reaction force laws.The relations that are investigated include a depth-dependent spring-like force, a velocity-squared-dependent force, and an added-mass force. The results of finding a well-fitting combination of force laws across many jump types and volume fractions can be used to imply a valid comprehensive force law for impulsive motion on a granular surface. The anticipated outcome is that there exists such a comprehensive force law, but each force type's contribution will vary as a function of volume fraction. Finding optimal jumping motions using this comprehensive law may lead to better implementations of impulsive commands in fields such as robotics and biomechanics where granular material is involved.
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