THE SPRING MASS MODEL FOR RUNNING AND HOPPING
THE SPRING MASS MODEL FOR RUNNING AND HOPPING
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DOI：
10.1016/0021-9290(89)90224-8
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发表时间：
1989-01-01
影响因子：
2.4
通讯作者：
BLICKHAN, R
中科院分区：
文献类型：
--
作者：
BLICKHAN, R
一个由连接到质点的无质量弹簧组成的简单弹簧 - 质量模型，描述了作为速度函数的人类跑步和跳跃的力学参数之间的相互依存关系。弹跳机制本身导致了可以找到解的自由参数空间受到限制。特别是，弹跳频率和垂直位移密切相关。只有少数几个参数，比如特定着陆速度矢量和特定腿长，就足以确定系统的运行点。生理约束比独立参数要多。由于约束限制了可能发生跳跃的参数空间，它们必须相互调整才能实现跳跃。在生理上可能的跳跃频率范围内，人类跳跃者会选择一个能传递最大能量且仍能弹性储存能量的频率。在跑步和跳跃过程中，动物利用着陆速度的平角，从而使接触长度最大。在这种情况下，地面反作用力与特定接触时间成正比，总位移与步长持续时间的平方成正比。接触时间和跳跃频率并非仅仅由弹簧 - 质量系统的固有频率决定，而是在很大程度上受着陆速度矢量的影响。腾空阶段或着陆速度角度的差异导致了在跑步和跳跃过程中观察到的不同运动学和动力学模式。尽管存在这些差异，该模型预测跑步者和跳跃者的质心每单位距离的质量比能量波动是相似的，并且与各种体型动物的实验数据相似。
A simple spring-mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed. The bouncing mechanism itself results in a confinement of the free parameter space where solutions can be found. In particular, bouncing frequency and vertical displacement are closely related. Only a few parameters, such as the vector of the specific landing velocity and the specific leg length, are sufficient to determine the point of operation of the system. There are more physiological constraints than independent parameters. As constraints limit the parameter space where hopping is possible, they must be tuned to each other in order to allow for hopping at all. Within the range of physiologically possible hopping frequencies, a human hopper selects a frequency where the largest amount of energy can be delivered and still be stored elastically. During running and hopping animals use flat angles of the landing velocity resulting in maximum contact length. In this situation ground reaction force is proportional to specific contact time and total displacement is proportional to the square of the step duration. Contact time and hopping frequency are not simply determined by the natural frequency of the spring-mass system, but are influenced largely by the vector of the landing velocity. Differences in the aerial phase or in the angle of the landing velocity result in the different kinematic and dynamic patterns observed during running and hopping. Despite these differences, the model predicts the mass specific energy fluctuations of the center of mass per distance to be similar for runners and hoppers and similar to empirical data obtained for animals of various size.