Hogan N
Biol Cybern. 1985;52(5):315-31. doi: 10.1007/BF00355754.
The dependence of muscle force on muscle length gives rise to a "spring-like" behavior which has been shown to play a role in the execution of single-joint posture and movement. This paper extends this concept and considers the influence of the apparent mechanical behavior of the neural, muscular and skeletal system on the control and coordination of multiple degree of freedom posture and movement. A rigorous definition of "spring-like" behavior is presented. From it a numerically quantifiable, experimental test of spring-like behavior is formulated. It is shown that if the steady-state force-displacement behavior of a limb is not spring-like, this can only be due to the action of inter-muscular feedback, and can not be due to intrinsic muscle properties. The directional character of the spring-like behavior of a multiple degree of freedom system is described. The unique way in which synergistic coactivation of polyarticular muscles may modulate the directional properties of the spring-like behavior of a multiple degree of freedom system is explained. Dynamic aspects of postural behavior are also considered. The concept of mechanical impedance is presented as a rigorous dynamic generalisation of the postural stiffness of the limb. The inertial behavior of the system is characterised by its mobility. As with the stiffness or impedance, in the multiple degree of freedom case it has a directional property. The way in which the apparent kinematic redundancy of the musculo-skeletal system may be used to modify its dynamic behavior is explained. Whereas the inertial behavior of a single limb segment is not modifiable, it is shown that the apparent inertial behavior of a multiple degree of freedom system may be modulated by repositioning the joints. A unified description of the posture and movement of a multi-joint system is presented by defining a "virtual trajectory" of equilibrium positions for the limb which may be specified by the neuro-muscular system. The way in which this approach may lead to a simplification of some the apparent computational difficulties associated with the control of multi-joint motion is discussed.
肌肉力量对肌肉长度的依赖性产生了一种“弹簧状”行为，这种行为已被证明在单关节姿势和运动的执行中发挥作用。本文扩展了这一概念，并考虑了神经、肌肉和骨骼系统的表观力学行为对多自由度姿势和运动的控制与协调的影响。给出了“弹簧状”行为的严格定义。据此制定了一个数值上可量化的弹簧状行为实验测试。结果表明，如果肢体的稳态力-位移行为不是弹簧状的，这只能归因于肌肉间反馈的作用，而不能归因于肌肉的固有特性。描述了多自由度系统弹簧状行为的方向性特征。解释了多关节肌肉协同共激活可能调节多自由度系统弹簧状行为方向性特性的独特方式。还考虑了姿势行为的动态方面。提出了机械阻抗的概念，作为肢体姿势刚度的严格动态推广。系统的惯性行为由其移动性来表征。与刚度或阻抗一样，在多自由度情况下它具有方向性。解释了肌肉骨骼系统明显的运动冗余性可用于改变其动态行为的方式。虽然单个肢体节段的惯性行为不可改变，但结果表明，多自由度系统的表观惯性行为可通过重新定位关节来调节。通过定义肢体平衡位置的“虚拟轨迹”，给出了多关节系统姿势和运动的统一描述，该轨迹可由神经肌肉系统指定。讨论了这种方法可能如何简化与多关节运动控制相关的一些明显的计算难题。
