Rapoport Svetlana, Mizrahi Joseph, Kimmel Eitan, Verbitsky Oleg, Isakov Eli
Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel.
J Biomech Eng. 2003 Aug;125(4):507-14. doi: 10.1115/1.1590358.
The present study deals with the stiffness and damping profiles of the leg joints during the ground-contact phase of hopping. A two-dimensional (sagittal plane) jumping model, consisting of four linked rigid segments and including the paired feet, shanks, thighs, and the head-arms-trunk segment, was developed. The segments were interconnected by damped torsional springs, representing the action of the muscles, tendons and ligaments across the joint and of the other joint tissues. A regressive function was used to express stiffness and damping, and included second-order dependence on angle and first-order dependence on angular velocity. By eliminating redundancies in the numerical solution using multicollinearity diagnostic algorithms, the model results revealed that the correct and sufficient nonlinearity for the joint stiffness is of the first order. Damping was found negligible. The stiffness profiles obtained were bell-shaped with a maximum near midstance and nonzero edge values. In predicting the joint moments, the obtained variable joint stiffnesses provided a closer agreement compared to a constant stiffness model. The maximal stiffness was found to be in linear correlation with the initial stiffness in each joint, providing support to the of muscles' preactivation strategy during the flight phase of hopping. All stiffnesses increased with increasing hopping frequency. The model presented provides an effective tool for future designing of artificial legs and robots and for the development of more accurate control strategies.
本研究探讨了单足跳地面接触阶段腿部关节的刚度和阻尼特性。建立了一个二维（矢状面）跳跃模型，该模型由四个相连的刚性节段组成，包括双脚、小腿、大腿以及头-臂-躯干节段。这些节段通过阻尼扭转弹簧相互连接，代表了跨越关节的肌肉、肌腱、韧带以及其他关节组织的作用。采用回归函数来表达刚度和阻尼，该函数包括对角度的二阶依赖性和对角速度的一阶依赖性。通过使用多重共线性诊断算法消除数值解中的冗余，模型结果表明关节刚度的正确且充分的非线性为一阶。发现阻尼可忽略不计。所获得的刚度特性呈钟形，在支撑中期附近达到最大值，边缘值非零。在预测关节力矩时，与恒定刚度模型相比，所获得的可变关节刚度提供了更紧密的一致性。发现最大刚度与每个关节的初始刚度呈线性相关，这为单足跳飞行阶段肌肉的预激活策略提供了支持。所有刚度都随着单足跳频率的增加而增加。所提出的模型为未来人工腿和机器人的设计以及更精确控制策略的开发提供了一个有效的工具。
