Università degli Studi di Milano, Department of Human Physiology and Chair of Physical and Rehabilitation Medicine, Milan, Italy.
J Biomech. 2011 Feb 24;44(4):732-40. doi: 10.1016/j.jbiomech.2010.10.035. Epub 2010 Nov 13.
During straight walking, the body centre of mass (CM) follows a 3D figure-of-eight ("bow-tie") trajectory about 0.2 m long and with sizes around 0.05 m on each orthogonal axis. This was shown in 18 healthy adults walking at 0.3 to 1.4 ms⁻¹ on a force-treadmill (Tesio and Rota, 2008). Double integration of force signals can provide both the changes of mechanical energy of the CM and its 3D displacements (Tesio et al., 2010). In the same subjects, the relationship between the tangential speed of the CM, Vt, the curvature, C, and its inverse--the radius of curvature, r(c), were analyzed. A "power law" (PL) model was applied, i.e. logVt was regressed over logr(c). A PL is known to apply to the most various goal-directed planar movements (e.g. drawing), where the coefficient of logr(c), β, usually takes values around 13. When the PL was fitted to the whole dataset, β was 0.346 and variance explanation, R², was 59.8%. However, when the data were split into low- and high-curvature subsets (LC, HC, arbitrary cut-off of C=0.05 mm⁻¹, r(c)=20mm), β was 0.185 in the LC (R² 0.214) and 0.486 in the HC (R² 0.536) tracts. R² on the whole dataset increased to 0.763 if the LC-HC classification of the forward speed and their interaction entered the model. The β coefficient, the curvature C, and the pendulum-like recovery of mechanical energy were lower during the double foot-ground contact phase, compared to the single contact. Along the CM trajectory, curvature and muscle power output peaked together around the inversions of lateral direction. Non-zero torsion values were randomly distributed along 60% of the trajectory, suggesting that this is not segmented into piecewise planar tracts. It is proposed that the trajectory can be segmented into one tract that is more actively controlled (tie) where a PL fits poorly and another tract which is more ballistic (bow) where a PL fits well. Results need confirmation through more appropriate 3D PL modelling.
在直线行走时，人体质心（CM）沿 3D 数字 8（“蝴蝶结”）轨迹运动，轨迹长度约为 0.2m，每个正交轴的大小约为 0.05m。这在 18 名健康成年人在力跑步机上以 0.3 至 1.4ms⁻¹的速度行走时得到了证明（Tesio 和 Rota，2008）。力信号的双重积分可以提供质心的机械能变化及其 3D 位移（Tesio 等人，2010）。在相同的受试者中，分析了质心的切向速度 Vt、曲率 C 及其倒数——曲率半径 r(c)之间的关系。应用了“幂律”（PL）模型，即 logVt 回归于 logr(c)。众所周知，PL 适用于各种有目标的平面运动（例如绘图），其中 logr(c)的系数β通常取 13 左右的值。当 PL 拟合整个数据集时，β为 0.346，方差解释度 R²为 59.8%。然而，当将数据分为低曲率和高曲率子集（LC、HC，任意 C=0.05mm⁻¹，r(c)=20mm 的截止值）时，LC 中的β为 0.185（R²为 0.214），HC 中的β为 0.486（R²为 0.536）。如果将低速高速分类和它们的相互作用纳入模型，整个数据集的 R²增加到 0.763。β系数、曲率 C 和机械能的钟摆式恢复在双足触地阶段较低，与单足接触相比。沿着质心轨迹，曲率和肌肉功率输出在横向反转处同时达到峰值。非零扭转值随机分布在轨迹的 60%，这表明轨迹没有分段成分段的平面轨迹。提出轨迹可以分为一个主动控制较差（领带）的轨迹和一个被动控制较好（蝴蝶结）的轨迹。结果需要通过更合适的 3D PL 模型来验证。
