Soechting J F, Lacquaniti F, Terzuolo C A
Neuroscience. 1986 Feb;17(2):295-311. doi: 10.1016/0306-4522(86)90248-4.
In this paper data are presented concerning the motion of limb segments during drawing movements executed in different planes in free space. The technique used allows the determination of the wrist and elbow positions in space as well as the measurement of the elbow angle of extension. Other kinematic variables are determined trigonometrically. Elbow and shoulder torque is also calculated. For circles and ellipses, it was found that the motion at the wrist is sinusoidal in two orthogonal directions in the plane of motion. Angular motion, when described by a set of angles previously identified psychophysically as constituting an appropriate coordinate system, is also sinusoidal. Although the number of degrees of freedom of the arm affords many possible ways of performing the task, there is a fixed phase relation between the angles of elevation of the upper arm and forearm for naturally executed movements in all planes of space. Also, the phase of the yaw angles of the upper arm and forearm relative to the angles of elevation are related to the plane of motion and to the slant of ellipses in a fixed manner. There is a simple mapping between angular motion and intended wrist trajectory. Because this mapping is not valid for all planes of space, the actual trajectory can deviate from the intended one. However, the subject has no cognizance of the distortion. The calculated torque deviates substantially from sinusoidal and does change significantly when the same movement is executed in different planes. Results of simulations and mathematical analysis indicate that the fixed phase relationship between angles of elevation leads to a minimal distortion from sinusoidal motion at the wrist in an average sense and that the characteristic distortions observed in the sagittal plane result inevitably from this constraint on the phase relations. The results support the assumption that the topology of the sensorimotor map used for the production of the movement and for its perception is the same. The problem of invariant relationships between kinematic parameters is discussed and the suggestion is made that they represent a general constraint, leading through learning and practice to an optimal solution in an average sense.
本文呈现了关于在自由空间中不同平面执行绘图动作时肢体节段运动的数据。所使用的技术能够确定空间中的手腕和肘部位置，以及测量肘部伸展角度。其他运动学变量通过三角学方法确定。还计算了肘部和肩部扭矩。对于圆形和椭圆形，发现在运动平面内，手腕在两个正交方向上的运动是正弦曲线形式。当用一组先前通过心理物理学确定为构成合适坐标系的角度来描述角运动时，它也是正弦曲线形式。尽管手臂的自由度数量提供了许多执行任务的可能方式，但对于在空间所有平面自然执行的动作，上臂和前臂的仰角之间存在固定的相位关系。此外，上臂和前臂相对于仰角的偏航角相位以固定方式与运动平面和椭圆的倾斜度相关。角运动和预期的手腕轨迹之间存在简单的映射关系。由于这种映射关系并非对所有空间平面都有效，实际轨迹可能会偏离预期轨迹。然而，受试者并未意识到这种扭曲。计算得到的扭矩与正弦曲线有很大偏差，并且当在不同平面执行相同动作时会有显著变化。模拟和数学分析结果表明，仰角之间的固定相位关系在平均意义上导致手腕处正弦运动的扭曲最小，并且在矢状面观察到的特征性扭曲不可避免地源于对相位关系的这种限制。这些结果支持了这样一种假设，即用于产生运动及其感知的感觉运动映射的拓扑结构是相同的。讨论了运动学参数之间不变关系的问题，并提出它们代表一种一般约束，通过学习和实践在平均意义上导致最优解。
