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Berman, S., Liebermann, D. G., & McIntyre, J. (2014). Constrained Motion Control on a Hemispherical Surface – Path Planning. J Neurophysiol, 111(5), 954–968.
Abstract: Surface-constrained motion, i.e., motion constraint by a rigid surface, is commonly found in daily activities. The current work investigates the choice of hand paths constrained to a concave hemispherical surface. To gain insight regarding the paths and their relationship with task dynamics, we simulated various control policies. The simulations demonstrated that following a geodesic path is advantageous not only in terms of path length, but also in terms of motor planning and sensitivity to motor command errors. These stem from the fact that the applied forces lie in a single plane (that of the geodesic path itself). To test whether human subjects indeed follow the geodesic, and to see how such motion compares to other paths, we recorded movements in a virtual haptic-visual environment from eleven healthy subjects. The task was comprised of point-to-point motion between targets at two elevations (30 degrees and 60 degrees ). Three typical choices of paths were observed from a frontal plane projection of the paths: circular arcs, straight lines, and arcs close to the geodesic path for each elevation. Based on the measured hand paths, we applied k-means blind separation to divide the subjects into three groups and compared performance indicators. The analysis confirmed that subjects who followed paths closest to the geodesic produced faster and smoother movements, compared to the others. The 'better' performance reflects the dynamical advantages of following the geodesic path, as shown by the simulations, and may also reflect invariant features of the control policies used to produce such a surface-constrained motion.
Keywords: Constrained motion; geodesics; path planning
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Liebermann, D. G., Berman, S., Weiss, P. L. T., & Levin, M. F. (2012). Kinematics of reaching movements in a 2-d virtual environment in adults with and without stroke. IEEE Trans Neural Syst Rehabil Eng, 20(6), 778–787.
Abstract: Virtual reality environments are increasingly being used for upper limb rehabilitation in poststroke patients. Our goal was to determine if arm reaching movements made in a 2-D video-capture virtual reality environment are similar to those made in a comparable physical environment. We compared arm and trunk kinematics for reaches made with the right, dominant arm to three targets (14 trials per target) in both environments by 16 adults with right poststroke hemiparesis and by eight healthy age-matched controls. Movement kinematics were recorded with a three-camera optoelectronic system at 100 samples/s. Reaching movements made by both control and stroke subjects were affected by viewing the targets in the video-capture 2-D virtual environment. Movements were slower, shorter, less straight, less accurate and involved smaller ranges of shoulder and elbow joint excursions for target reaches in the virtual environment compared to the physical environment in all subjects. Thus, there was a decrease in the overall movement quality for movements made in the 2-D virtual environment. This suggests that 2-D video-capture virtual reality environments should be used with caution when the goal of the rehabilitation program is to improve the quality of movement patterns of the upper limb.
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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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Issurin, V. B., Liebermann, D. G., & Tenenbaum, G. (1994). Effect of vibratory stimulation training on maximal force and flexibility (Vol. 12).
Abstract: In this study, we investigated a new method of training for maximal strength and flexibility, which included exertion with superimposed vibration (vibratory stimulation, VS) on target muscles. Twenty-eight male athletes were divided into three groups, and trained three times a week for 3 weeks in one of the following conditions: (A) conventional exercises for strength of the arms and VS stretching exercises for the legs; (B) VS strength exercises for the arms and conventional stretching exercises for the legs; (C) irrelevant training (control group). The vibration was applied at 44 Hz while its amplitude was 3 mm. The effect of training was evaluated by means of isotonic maximal force, heel-to-heel length in the two-leg split across, and flex-and-reach test for body flexion. The VS strength training yielded an average increase in isotonic maximal strength of 49.8%, compared with an average gain of 16% with conventional training, while no gain was observed for the control group. The VS flexibility training resulted in an average gain in the legs split of 14.5 cm compared with 4.1 cm for the conventional training and 2 cm for the control groups, respectively. The ANOVA revealed significant pre-post training effects and an interaction between pre-post training and 'treatment' effects (P < 0.001) for the isotonic maximal force and both flexibility tests. It was concluded that superimposed vibrations applied for short periods allow for increased gains in maximal strength and flexibility.
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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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