Liebermann, D. G., Biess, A., Friedman, J., Gielen, C. C. A. M., & Flash, T. (2006). Intrinsic joint kinematic planning. I: reassessing the Listing's law constraint in the control of three-dimensional arm movements. Exp Brain Res, 171(2), 139–154.
Abstract: This study tested the validity of the assumption that intrinsic kinematic constraints, such as Listing's law, can account for the geometric features of three-dimensional arm movements. In principle, if the arm joints follow a Listing's constraint, the hand paths may be predicted. Four individuals performed 'extended arm', 'radial', 'frontal plane', and 'random mixed' movements to visual targets to test Listing's law assumption. Three-dimensional rotation vectors of the upper arm and forearm were calculated from three-dimensional marker data. Data fitting techniques were used to test Donders' and Listing's laws. The coefficient values obtained from fitting rotation vectors to the surfaces described by a second-order equation were analyzed. The results showed that the coefficients that represent curvature and twist of the surfaces were often not significantly different from zero, particularly not during randomly mixed and extended arm movements. These coefficients for forearm rotations were larger compared to those for the upper arm segment rotations. The mean thickness of the rotation surfaces ranged between approximately 1.7 degrees and 4.7 degrees for the rotation vectors of the upper arm segment and approximately 2.6 degrees and 7.5 degrees for those of the forearm. During frontal plane movements, forearm rotations showed large twist scores while upper arm segment rotations showed large curvatures, although the thickness of the surfaces remained low. The curvatures, but not the thicknesses of the surfaces, were larger for large versus small amplitude radial movements. In conclusion, when examining the surfaces obtained for the different movement types, the rotation vectors may lie within manifolds that are anywhere between curved or twisted manifolds. However, a two-dimensional thick surface may roughly represent a global arm constraint. Our findings suggest that Listing's law is implemented for some types of arm movement, such as pointing to targets with the extended arm and during radial reaching movements.
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Friedman, J., & Flash, T. (2007). Task-dependent selection of grasp kinematics and stiffness in human object manipulation. Cortex, 43(3), 444–460.
Abstract: Object manipulation with the hand is a complex task. The task has redundancies at many levels, allowing many possibilities for the selection of grasp points, the orientation and posture of the hand, the forces to be applied at each fingertip and the impedance properties of the hand. Despite this inherent complexity, humans perform object manipulation nearly effortlessly. This article presents experimental findings of how humans grasp and manipulate objects, and examines the compatibility of grasps selected for specific tasks. This is accomplished by looking at the velocity transmission and force transmission ellipsoids, which represent the transmission ratios of the corresponding quantity from the joints to the object, as well as the stiffness ellipsoid which represents the directional stiffness of the grasp. These ellipsoids allow visualization of the grasp Jacobian and grasp stiffness matrices. The results show that the orientation of the ellipsoids can be related to salient task requirements.
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Friedman, J., SKM, V., Zatsiorsky, V. M., & Latash, M. L. (2009). The sources of two components of variance: an example of multifinger cyclic force production tasks at different frequencies. Exp Brain Res, 196(2), 263–277.
Abstract: In a multifinger cyclic force production task, the finger force variance measured across trials can be decomposed into two components, one that affects the combined force output (“bad variance”) and one that does not (“good variance”). Previous studies have found similar time patterns of “bad variance” and force rate leading to an approximately linear relationship between them. Based on this finding and a recently developed model of multifinger force production, we expected the “bad variance” during cyclic force production to increase monotonically with the rate of force change, both within a cycle and across trials at different frequencies. Alternatively, “bad variance” could show a dependence on task frequency, not on actual force derivative values. Healthy subjects were required to produce cyclic force patterns to prescribed targets by pressing on unidimensional force sensors, at a frequency set by a metronome. The task was performed with only the index finger, and with all four fingers. In the task with all four fingers, the “good variance” increased approximately linearly with an increase in the force magnitude. The “bad variance” showed within-a-cycle modulation similar to that of the force rate. However, an increase in the frequency did not lead to an increase in the “bad variance” that could be expected based on the natural relationships between action frequency and the rate of force change modulation. The results have been interpreted in the framework of an earlier model of multifinger force production where “bad variance” is a result of variance of the timing parameter. The unexpected lack of modulation of the “bad variance” with frequency suggests a drop in variance of the timing parameter with increased frequency. This mechanism may serve to maintain a constant acceptable level of variance under different conditions.
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Friedman, J., Latash, M. L., & Zatsiorsky, V. M. (2009). Prehension synergies: a study of digit force adjustments to the continuously varied load force exerted on a partially constrained hand-held object. Exp Brain Res, 197(1), 1–13.
Abstract: We examined how the digit forces adjust when a load force acting on a hand-held object continuously varies. The subjects were required to hold the handle still while a linearly increasing and then decreasing force was applied to the handle. The handle was constrained, such that it could only move up and down, and rotate about a horizontal axis. In addition, the moment arm of the thumb tangential force was 1.5 times the moment arm of the virtual finger (VF, an imagined finger with the mechanical action equal to that of the four fingers) force. Unlike the situation when there are equal moment arms, the experimental setup forced the subjects to choose between (a) sharing equally the increase in load force between the thumb and VF but generating a moment of tangential force, which had to be compensated by negatively co-varying the moment due to normal forces, or (b) sharing unequally the load force increase between the thumb and VF but preventing generation of a moment of tangential forces. We found that different subjects tended to use one of these two strategies. These findings suggest that the selection by the CNS of prehension synergies at the VF-thumb level with respect to the moment of force is non-obligatory and reflects individual subject preferences. This unequal sharing of the load by the tangential forces, in contrast to the previously observed equal sharing, suggests that the invariant feature of prehension may be a correlated increase in tangential forces rather than an equal increase.
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Friedman, J., & Flash, T. (2009). Trajectory of the index finger during grasping. Exp Brain Res, 196(4), 497–509.
Abstract: The trajectory of the index finger during grasping movements was compared to the trajectories predicted by three optimization-based models. The three models consisted of minimizing the integral of the weighted squared joint derivatives along the path (inertia-like cost), minimizing torque change, and minimizing angular jerk. Of the three models, it was observed that the path of the fingertip and the joint trajectories, were best described by the minimum angular jerk model. This model, which does not take into account the dynamics of the finger, performed equally well when the inertia of the finger was altered by adding a 20 g weight to the medial phalange. Thus, for the finger, it appears that trajectories are planned based primarily on kinematic considerations at a joint level.
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