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Liebermann, D. G., Krasovsky, T., & Berman, S. (2008). Planning maximally smooth hand movements constrained to nonplanar workspaces. J Mot Behav, 40(6), 516–531.
Abstract: The article characterizes hand paths and speed profiles for movements performed in a nonplanar, 2-dimensional workspace (a hemisphere of constant curvature). The authors assessed endpoint kinematics (i.e., paths and speeds) under the minimum-jerk model assumptions and calculated minimal amplitude paths (geodesics) and the corresponding speed profiles. The authors also calculated hand speeds using the 2/3 power law. They then compared modeled results with the empirical observations. In all, 10 participants moved their hands forward and backward from a common starting position toward 3 targets located within a hemispheric workspace of small or large curvature. Comparisons of modeled observed differences using 2-way RM-ANOVAs showed that movement direction had no clear influence on hand kinetics (p < .05). Workspace curvature affected the hand paths, which seldom followed geodesic lines. Constraining the paths to different curvatures did not affect the hand speed profiles. Minimum-jerk speed profiles closely matched the observations and were superior to those predicted by 2/3 power law (p < .001). The authors conclude that speed and path cannot be unambiguously linked under the minimum-jerk assumption when individuals move the hand in a nonplanar 2-dimensional workspace. In such a case, the hands do not follow geodesic paths, but they preserve the speed profile, regardless of the geometric features of the workspace.
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Liebermann, D. G., & Hoffman, J. R. (2005). Timing of preparatory landing responses as a function of availability of optic flow information. J Electromyogr Kinesiol, 15(1), 120–130.
Abstract: This study investigated temporal patterns of EMG activity during self-initiated falls with different optic flow information ('gaze directions'). Onsets of EMG during the flight phase were monitored from five experienced volunteers that completed 72 landings in three gaze directions (downward, mid-range and horizontal) and six heights of fall (10-130 cm). EMG recordings were obtained from the right gastrocnemius, tibialis anterior, biceps femoris and rectus femoris muscles, and used to determine the latency of onset (L(o)) and the perceived time to contact (T(c)). Impacts at touchdown were also monitored using as estimates the major peak of the vertical ground reaction forces (F(max)) normalized to body mass, time to peak (T(max)), peak impulse (I(norm)) normalized to momentum, and rate of change of force (dF(max)/dt). Results showed that L(o) was longer as heights of fall increased, but remained within a narrow time-window at >50 cm landings. No significant differences in L(o) were observed when gaze direction was changed. The relationship between T(c) and flight time followed a linear trend regardless of gaze direction. Gaze direction did not significantly affect the landing impacts. In conclusion, availability of optic flow during landing does not play a major role in triggering the preparatory muscle actions in self-initiated falls. Once a structured landing plan has been acquired, the relevant muscles respond relative to the start of the fall.
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