歩行運動の平面法則が成立する座標系について

抄録

The three-dimensional plot of the time sequences of the elevation angles of the thigh, shank, and foot during human walking has been reported to lie close to a plane, called the planar law showing the intersegmental coordination. For evaluating such coordination, the elevation angle has been regarded as an important coordinate system. However, there exist many other coordinate systems for describing the limb configuration. Even for the same data, the difference of the coordinate system may change the degree of planarity, and also affect the evaluation of the coordination. Here we aim to study the effect of the coordinate system on the planar law. We measure lower limb kinematics during steady walking on a treadmill with various speeds. Then we compare the degrees of planarity of the measured data described in various coordinate systems generated from the measured angles between the vertical and the thigh, the thigh and the shank, and the shank and the foot, and the linear transformations described by regular-three-dimensional matrices composed of elements { 0, 1, -1 }. The result shows that the different coordinate system can lead to a wide range of the planarity, and there exist many coordinate systems yielding higher or lower planarity than the elevation angles. Additionally, we elucidate the mathematical aspects of the planarity that depends on the coordinate systems. It is concluded that the planar law does not necessarily imply the importance of the information described by the elevation angles.