## 5 Discussion  
In our research, we have identified optimal delayed dorsiflexion assistance timing after toe-off and conducted an experiment to verify the assistance effects on healthy participants with restricted swing-phase dorsiflexion. Our previous study indicated a trade-off relation between ensuring voluntary efforts and preventing compensatory movements [26]. Later swing-phase dorsiflexion assistance timing could induce voluntary effort but could also exacerbate compensatory movements. On the other hand, earlier assistance could prevent compensatory movements but could hinder voluntary efforts. Thus, we assumed that there is an assistance timing that could induce voluntary efforts while suppressing compensatory movements, which we sought to identify. With the identified assistance delay (ASTy), the sEMG amplitude results showed an improvement in voluntary effort during swing-phase dorsiflexion, and the swing width and hip hike results show suppression of compensatory movements. Some differences were observed with shorter (AST0.Sy) and longer assistance delays (AST1.5y). sEMG amplitude results with AST0.5y for Participants C and D also significantly increased compared with those with AST0. Meanwhile, the extent of compensatory movements with AST1.5y was also significantly suppressed when compared with those in SCG for some participants, especially Participant A. Figure 13 explains the assumed reason for these results with shorter and longer assistance delays. Instead of a specific suitable assistance timing, there is a range of ideal delay times for dorsiflexion assistance. For Participants C and D, their sEGM amplitudes increased with not only ASTy but also AST0.5y, which indicates that assistance delay times 0.5y and y are both in the range of suitable dorsiflexion delay. On the other hand, Participant A's swing-phase and hip hike were suppressed with both ASTy and AST1.5y, which indicates that y and 1.5y assistance delay times were both suitable for Participant A. It should also be noted that Participant F's sEMG result with ASTy was marginally increased compared to AST0. This suggests that the identified timing for Participant F is at the lower bound of the suitable timing zone, also shown in Figure 13. Despite such differences, our goal of inducing voluntary dorsiflexion and suppressing compensatory movement with identified assistance delay was met. Figure 12: Ankle dorsiflexion angle in the swing phase. Limb shortening results are also consistent among participants, and those with the identified assistance delay time (ASTy) were significantly larger when compared to the restricted dorsiflexion walking condition (SCG). This is consistent with an observed trade-off between limb shortening and compensatory movements from a related study [6]. The study also notes that ankle angle is one of the factors that affects limb shortening. However, results of our experiment are not consistent with that theory. For Participants B and C, their swing-phase ankle dorsiflexion angles in ASTy had no significant difference compared to those in SCG. Since limb shortening could also be affected by knee movement, we reanalyzed participants' knee flexion angles in the swing phase. Two examples of knee flexion angle from Participants B and E are shown in Figure 14. Both data sets show knee flexion differences between conditions, which is expected. Past studies have also pointed out that resistance or assistance in ankle movements also affects knee and hip kinematics [37; 38]. However, Participant B's knee flexion angle in SCG is 18.95\({}^{\circ}\)\(\pm\) 2.32\({}^{\circ}\), which is abnormally small when compared with the average angle of a healthy person, between 45\({}^{\circ}\) and 55\({}^{\circ}\)[39]. Therefore, it is clear that Participant B did not only exhibit circumduction and hip hiking but also decreased knee flexion during the swing phase. Therefore, Participant B's limb shortening might be dominated by knee flexion instead of ankle dorsiflexion during the swing phase.