Anderson FRANK C., Pandy MARCUS G.
Department of Mechanical Engineering and Department of Kinesiology, University of Texas at Austin, Austin, Texas 78712, U.S.A.
Comput Methods Biomech Biomed Engin. 1999;2(3):201-231. doi: 10.1080/10255849908907988.
A three-dimensional model of the human body is used to simulate a maximal vertical jump. The body is modeled as a 10-segment, 23 degree-of-freedom (dof), mechanical linkage, actuated by 54 muscles. Six generalized coordinates describe the position and orientation of the pelvis relative to the ground; the remaining nine segments branch in an open chain from the pelvis. The head, arms, and torso (HAT) are modeled as a single rigid body. The HAT articulates with the pelvis via a 3 dof ball-and-socket joint. Each hip is modeled as a 3 dof ball-and-socket joint, and each knee is modeled as a 1 dof hinge joint. Each foot is represented by a hindfoot and toes segment. The hindfoot articulates with the shank via a 2 dof universal joint, and the toes articulate with the hindfoot via a 1 dof hinge joint. Interaction of the feet with the ground is modeled using a series of spring-damper units placed under the sole of each foot. The path of each muscle is represented by either a series of straight lines or a combination of straight lines and space curves. Each actuator is modeled as a three-element, Hill-type muscle in series with tendon. A first-order process is assumed to model muscle excitation-contraction dynamics. Dynamic optimization theory is used to calculate the pattern of muscle excitations that produces a maximal vertical jump. Quantitative comparisons between model and experiment indicate that the model reproduces the kinematic, kinetic, and muscle-coordination patterns evident when humans jump to their maximum achievable heights.
人体三维模型用于模拟最大垂直跳跃。人体被建模为一个由10个节段、23个自由度（dof）的机械连杆机构，由54块肌肉驱动。六个广义坐标描述骨盆相对于地面的位置和方向；其余九个节段从骨盆以开链形式分支。头部、手臂和躯干（HAT）被建模为单个刚体。HAT通过一个3自由度的球窝关节与骨盆相连。每个髋关节被建模为一个3自由度的球窝关节，每个膝关节被建模为一个1自由度的铰链关节。每只脚由后足和脚趾节段表示。后足通过一个2自由度的万向节与小腿相连，脚趾通过一个1自由度的铰链关节与后足相连。脚与地面的相互作用通过放置在每只脚底的一系列弹簧-阻尼单元来建模。每块肌肉的路径由一系列直线或直线与空间曲线的组合表示。每个驱动装置被建模为一个与肌腱串联的三元件希尔型肌肉。假设采用一阶过程来模拟肌肉兴奋-收缩动力学。动态优化理论用于计算产生最大垂直跳跃的肌肉兴奋模式。模型与实验之间的定量比较表明，该模型再现了人类跳到最大可达到高度时明显的运动学、动力学和肌肉协调模式。
