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Biess, A., Flash, T., & Liebermann, D. G. (2011). Riemannian geometric approach to human arm dynamics, movement optimization, and invariance. Phys Rev E Stat Nonlin Soft Matter Phys, 83(3 Pt 1), 031927.
Abstract: We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparameterized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm's configuration space may provide insights into the emerging properties of the movements generated by the motor system.
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Hoffman, J. R., Liebermann, D., & Gusis, A. (1997). Relationship of leg strength and power to ground reaction forces in both experienced and novice jump trained personnel. Aviat Space Environ Med, 68(8), 710–714.
Abstract: METHODS: There were 14 male soldiers who participated in this study examining the relationship of leg strength and power on landing performance. Subjects were separated into two groups. The first group (E, n = 7) were parachute training instructors and highly experienced in parachute jumping. The second group of subjects (N, n = 7) had no prior parachute training experience and were considered novice jumpers. All subjects were tested for one-repetition maximum (1 RM) squat strength and maximal jump power. Ground reaction forces (GRF) and the time to peak force (TPF) at landing were measured from jumps at four different heights (95 cm, 120 cm, 145 cm, and 170 cm). All jumps were performed from a customized jump platform onto a force plate. RESULTS: No differences were seen between E and N in either IRM squat strength or in MJP. In addition, no differences were seen between the groups for time to peak force at any jump height. However, significantly greater GRF were observed in E compared to N. Moderate to high correlations between maximal jump power and GRF (r values ranging from 0.62-0.93) were observed in E. Although maximal jump power and the TPF was significantly correlated (r = -0.89) at only 120 cm for E, it was interesting to note that the correlations between MJP and the time to peak force in E were all negative and that the correlations between these variables in N were all positive. CONCLUSIONS: These results suggest that experienced parachutists may use a different landing strategy than novice jumpers. This difference may be reflected by differences in GRF generated during impact and a more efficient utilization of muscle power during the impact phase of the landing.
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Melzer, I., Liebermann, D. G., Krasovsky, T., & Oddsson, L. I. E. (2010). Cognitive load affects lower limb force-time relations during voluntary rapid stepping in healthy old and young adults. J Gerontol A Biol Sci Med Sci, 65(4), 400–406.
Abstract: BACKGROUND: Quick step execution may prevent falls when balance is lost; adding a concurrent task delays this function. We investigate whether push-off force-time relations during the execution of rapid voluntary stepping is affected by a secondary task in older and young adults. METHODS: Nineteen healthy older adults and 12 young adults performed rapid voluntary stepping under single- and dual-task conditions. Peak power, peak force, and time to peak force during preparatory and swing phases of stepping were extracted from center of pressure and ground reaction force data. RESULTS: For dual-task condition compared with single-task condition, older adults show a longer time to reach peak force during the preparation and swing phases compared with young adults (approximately 25% vs approximately 10%, respectively). Peak power and peak force were not affected by a concurrent attention-demanding task. CONCLUSION: Older adults have difficulty allocating sufficient attention for fast muscle recruitment when concurrently challenged by an attention-demanding task.
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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., Ben-David, J., Schweitzer, N., Apter, Y., & Parush, A. (1995). A field study of braking reactions during driving I: Triggering and modulation. Ergonomics, 38(9), 1894–1902.
Abstract: The present experiment was carried out to explore the response of driving subjects to emergency braking. The field trial consisted of driving behind a leading vehicle while the following drivers' responses were recorded by telemetry. A group of 51 individuals performed a series of trials at two driving speeds (60 and 80km/h), two following distances (6 and 12 m), and two braking conditions (real and dummy braking). Not all of these subjects completed all conditions or the minimum number of trials. The dependent variables were the total braking time (TBT) and its subcomponents: braking reaction time (BRT), and accelerator-to-brake movement time (MT). These data were analysed in three separate three-way ANOVAs with repeated measures on all factors. The results showed that when subjects were not aware of the forthcoming braking, the distance and braking conditions had major effects on all dependent variables. At the shorter following distance drivers reacted and moved faster. Similarly, when the brakes were real compared with dummy (i.e. brake lights only) drivers reacted faster. In addition, drivers reacted to onset of brake lights in 83% of the cases when dummy braking was applied, compared with 97% when real brakes were applied. Speed of driving did not show any significant effects and did not appear to influence the cognitive or attentional set to anticipate an emergency manoeuvre. These findings suggest that changes in angular velocity during optic expansion of the leading vehicle may be used as a cue to modulate braking movement, while onset of brake lights alone may be enough to trigger a ‘ballistic’ preventive response.
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