# Duty Factor Reflects Lower Limb Kinematics of Running
## 3 Results
### Hip, Knee, and Ankle Joint Angles
 } & **DF** & \(t_{b}\) & \(\Delta z_{\rm COM,\emph{e}}\) & \(t_{p}\) & \(\Delta z_{\rm COM,\emph{p}}\) & \(t_{c}\) & \(\Delta z_{\rm COM,\emph{e}}\) & \(t_{d}\) & \(\Delta z_{\rm COM,\emph{d}}\) \\  & **Group** & **(ms)** & **(\%)** & **(ms)** & **(\%)** & **(ms)** & **(\%)** & **(ms)** & **(\%)** \\ \hline \multirow{2}{*}{8} & DF\({}_{\rm high}\) & \(129\pm 14\) & \(-3.7\pm 0.5\) & \(133\pm 11\) & \(3.4\pm 0.4\) & \(61\pm 13\) & \(1.0\pm 0.4\) & \(46\pm 11\) & \(-0.7\pm 0.3\) \\  & DF\({}_{\rm low}\) & \(114\pm 12\)\({}^{*}\) & \(-4.0\pm 0.6\) & \(11\pm 12\)\({}^{*}\) & \(3.4\pm 0.5\) & \(83\pm 11\)\({}^{*}\) & \(2.0\pm 0.5\) & \(68\pm 11\)\({}^{*}\) & \(-1.4\pm 0.4\) \\ \hline \multirow{2}{*}{10} & DF\({}_{\rm high}\) & \(119\pm 13\) & \(-3.8\pm 0.4\) & \(117\pm 8\) & \(3.2\pm 0.3\) & \(70\pm 12\) & \(1.4\pm 0.4\) & \(52\pm 9\) & \(-0.9\pm 0.3\) \\  & DF\({}_{\rm low}\) & \(104\pm 11\)\({}^{*}\) & \(-3.7\pm 0.6\) & \(98\pm 10\)\({}^{*}\) & \(3.1\pm 0.5\) & \(89\pm 11\)\({}^{*}\) & \(2.3\pm 0.6\) & \(74\pm 9\)\({}^{*}\) & \(-1.7\pm 0.4\) \\ \hline \multirow{2}{*}{12} & DF\({}_{\rm high}\) & \(110\pm 11\) & \(-3.5\pm 0.4\) & \(105\pm 7\) & \(2.9\pm 0.2\) & \(74\pm 11\) & \(1.6\pm 0.4\) & \(56\pm 7\) & \(-1.0\pm 0.3\) \\  & DF\({}_{\rm low}\) & \(97\pm 10\)\({}^{*}\) & \(-3.5\pm 0.5\) & \(90\pm 9\)\({}^{*}\) & \(2.8\pm 0.4\) & \(91\pm 9\)\({}^{*}\) & \(2.4\pm 0.4\) & \(76\pm 11\)\({}^{*}\) & \(-1.8\pm 0.4\) \\ \hline \multirow{2}{*}{14} & DF\({}_{\rm high}\) & \(99\pm 10\) & \(-3.2\pm 0.5\) & \(95\pm 7\) & \(2.6\pm 0.3\) & \(78\pm 11\) & \(1.7\pm 0.4\) & \(60\pm 6\) & \(-1.1\pm 0.3\) \\  & DF\({}_{\rm low}\) & \(89\pm 10\)\({}^{*}\) & \(-3.2\pm 0.5\) & \(82\pm 8\)\({}^{*}\) & \(2.6\pm 0.4\) & \(93\pm 9\)\({}^{*}\) & \(2.5\pm 0.5\) & \(78\pm 12\)\({}^{*}\) & \(-1.9\pm 0.5\) \\ \hline \multirow{2}{*}{16} & DF\({}_{\rm high}\) & \(90\pm 9\) & \(-2.9\pm 0.7\) & \(87\pm 7\) & \(2.3\pm 0.4\) & \(79\pm 10\) & \(1.8\pm 0.5\) & \(62\pm 7\) & \(-1.3\pm 0.2\) \\  & DF\({}_{\rm low}\) & \(82\pm 9\)\({}^{*}\) & \(-2.8\pm 0.4\) & \(75\pm 8\)\({}^{*}\) & \(2.3\pm 0.4\) & \(92\pm 10\)\({}  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Running Speed** & **DF** & \(\theta_{\text{FS}}\) & \(\theta_{\text{IA}}\) & \(\theta_{\text{MS}}\) & \(\theta_{\text{TO}}\) & \(\Delta\theta_{a}\) & \(\Delta\theta_{b}\) & \(\Delta\theta_{p}\) \\ (**km/h**) & **Group** & **(deg)** & **(deg)** & **(deg)** & **(deg)** & **(deg)** & **(deg)** & **(deg)** & **(deg)** \\ \hline \multirow{2}{*}{8} & DFhigh & \(11.9\pm 4.2\) & \(24.7\pm 4.6\) & \(36.8\pm 4.0\) & \(19.2\pm 4.5\) & \(12.8\pm 2.1\) & \(24.9\pm 4.4\) & \(-17.6\pm 3.6\) \\  & DFlow & \(13.1\pm 3.5\) & \(27.1\pm 4.0\) & \(34.8\pm 4.5\) & \(18.3\pm 3.9\) & \(13.9\pm 2.4\) & \(21.7\pm 4.6\) & \(-16.5\pm 3.9\) \\ \hline \multirow{2}{*}{10} & DFhigh & \(11.3\pm 4.1\) & \(26.5\pm 4.3\) & \(38.2\pm 3.9\) & \(19.3\pm 4.9\) & \(15.2\pm 2.2\) & \(26.9\pm 4.5\) & \(-18.9\pm 3.4\) \\  & DFlow & \(13.4\pm 3.5\) & \(29.2\pm 4.2\) & \(36.1\pm 4.4\) & \(18.8\pm 4.1\) & \(15.8\pm 2.7\) & \(22.7\pm 4.8\) & \(-17.3\pm 3.8\) \\ \hline \multirow{2}{*}{12} & DFhigh & \(11.2\pm 4.1\) & \(28.3\pm 4.3\) & \(39.1\pm 3.5\) & \(19.7\pm 4.4\) & \(17.0\pm 2.4\) & \(27.9\pm 4.1\) & \(-19.4\pm 3.1\) \\  & DFlow & \(13.2\pm 3.9\) & \(30.5\pm 4.7\) & \(36.8\pm 4.2\) & \(19.0\pm 3.8\) & \(17.2\pm 3.1\) & \(23.5\pm 4.8\) & \(-17.7\pm 3.8\) \\ \hline \multirow{2}{*}{14} & DFhigh & \(11.8\pm 3.9\) & \(30.6\pm 4.3\) & \(40.0\pm 4.0\) & \(20.1\pm 4.7\) & \(18.8\pm 2.6\) & \(28.2\pm 4.3\) & \(-19.9\pm 3.0\) \\  & DFlow & \(13.4\pm 4.1\) & \(32.0\pm 4.7\) & \(37.5\pm 4.1\) & \(19.9\pm 3.7\) & \(18.6\pm 3.2\) & \(24.1\pm 4.9\) & \(-17.7\pm 3.7\) \\ \hline \multirow{2}{*}{16} & DFhigh & \(12.5\pm 3.5\) & \(32.6\pm 4.2\) & \(40.7\pm 3.7\) & \(20.4\pm 4.6\) & \(20.1\pm 2.6\) & \(28.2\pm 3.7\) & \(-20.3\pm 3.1\) \\  & DFlow & \(13.6\pm 4.0\) & \(33.2\pm 4.7\) & \(37.8\pm 4.2\) & \(20.3\pm 3.6\) & \(19.6\pm 3.3\) & \(24.2\pm 4.7\) & \(-17.5\pm 4.0\) \\ \hline \multirow{2}{*}{18} & DFhigh & \(13.5\pm 3.5\) & \(34.4\pm 4.1\) & \(41.1\pm 4.1\) & \(20.9\pm 4.6\) & \(20.9\pm 3.0\) & \(27.6\pm 4.1\) & \(-20.2\pm 2.8\) \\  & DFlow & \(14.0\pm 3.6\) & \(34.3\pm 4.4\) & \(38.2\pm 4.3\) & \(21.1\pm 3.3\) & \(20.3\pm 3.5\) & \(24.2\pm 4.9\) & \(-17.2\pm 4.3\) \\ \hline \multirow{2}{*}{DF groups effect (\(p\)) running speed effect (\(p\)) interaction effect (\(p\))} & 0.123 & 0.159 & **0.019** & 0.717 & 0.886 & **\textless  
A larger plantar flexion was observed at FS for DFlow than for DFhigh (DF groups main effect, \(p<0.001\); large effect size, \(d=1.39\); Table 5 and Figure 2C).