Anderson F C, Pandy M G
Department of Kinesiology and Health Education, University of Texas at Austin 78712.
J Biomech. 1993 Dec;26(12):1413-27. doi: 10.1016/0021-9290(93)90092-s.
Based upon the optimal control solutions to a maximum-height countermovement jump (CMJ) and a maximum-height squat jump (SJ), this paper provides a quantitative description of how tendons and the elastic elements of muscle store and deliver energy during vertical jumping. After confirming the ability of the model to replicate the major features of each jump (i.e. muscle activation patterns, body-segmental motions, ground reaction forces, jump height, and total ground contact time), the time histories of the forces and shortening velocities of all the musculotendon actuators in the model were used to calculate the work done on the skeleton by tendons as well as the series-elastic elements, the parallel-elastic elements, and the contractile elements of muscle. We found that all the elastic tissues delivered nearly the same amount of energy to the skeleton during a CMJ and an SJ. The reason is twofold: first, nearly as much elastic strain energy was stored during the SJ as the CMJ; second, more stored elastic strain energy was lost as heat during the CMJ. There was also a difference in the way energy was stored during each jump. During the CMJ, strain energy stored in the elastic tissues came primarily from the gravitational potential energy of the skeleton as the more proximal extensor muscles were stretched during the downward phase of the jump. During the SJ, on the other hand, energy stored in the elastic tissues came primarily from the contractile elements as they did work to stretch the tendons and the series-elastic elements of the muscles. Increasing tendon compliance in the model led to an increase in elastic energy storage and utilization, but it also decreased the amount of energy delivered by the contractile elements to the skeleton. Jump height therefore remained almost the same for both jumps. These results suggest that elastic energy storage and utilization enhance jumping efficiency much more than overall jumping performance.
基于对最大高度反向运动跳跃（CMJ）和最大高度深蹲跳跃（SJ）的最优控制解，本文定量描述了肌腱和肌肉的弹性元件在垂直跳跃过程中如何储存和传递能量。在确认模型能够复制每次跳跃的主要特征（即肌肉激活模式、身体节段运动、地面反作用力、跳跃高度和总地面接触时间）之后，利用模型中所有肌肉-肌腱驱动装置的力和缩短速度的时间历程，计算肌腱以及肌肉的串联弹性元件、并联弹性元件和收缩元件对骨骼所做的功。我们发现，在CMJ和SJ过程中，所有弹性组织向骨骼传递的能量几乎相同。原因有两方面：第一，SJ过程中储存的弹性应变能与CMJ过程中几乎一样多；第二，CMJ过程中更多储存的弹性应变能以热量形式损失掉了。每次跳跃过程中能量储存的方式也存在差异。在CMJ过程中，弹性组织中储存的应变能主要来自骨骼的重力势能，因为在跳跃的下降阶段，近端伸肌被拉伸。另一方面，在SJ过程中，弹性组织中储存的能量主要来自收缩元件，因为它们在拉伸肌腱和肌肉的串联弹性元件时做功。增加模型中肌腱的顺应性会导致弹性能量储存和利用增加，但同时也会减少收缩元件向骨骼传递的能量。因此，两种跳跃的跳跃高度几乎保持不变。这些结果表明，弹性能量的储存和利用对跳跃效率的提升比整体跳跃性能的提升要大得多。
