A simulation study of the degrees of freedom of movement in reaching and grasping

The question of independently controlled components in the act of reaching and grasping has attracted interest experimentally and theoretically. Data from 35 studies were recently found consistent with simulated kinematic finger and thumb trajectories optimised for minimum jerk. The present study closely reproduces those trajectories using a discrete-time model based on minimum acceleration. That model was further used to generate two-dimensional trajectories for finger and thumb to reach and grasp an elliptical object with varying position and/or orientation. Orthogonalisation of these four trajectories revealed one degree of freedom when direction of reach was constant and two degrees of freedom when direction of reach varied, irrespective of object distance and orientation. These simulations indicate that reach and grasp movements contain redundancy that is removable by formation of task-dependent synergies. As skilled movement can be planned and executed in a low dimension workspace, control of these independent components lessens central workload.     

Freezing degrees of freedom under stress: kinematic evidence of constrained movement strategies

The present study investigated the effect of psychological stress imposed on movement kinematics in a computer-simulated batting task involving a backward and forward swing of the forearm. The psychological stress was imposed by a mild electric stimulus following poor performance. Fourteen participants hit a moving ball with a horizontal lever and aimed at a distant target with as much accuracy as possible. The kinematic characteristics appearing under stress were delay of movement initiation, small amplitude of movement and low variability of spatial kinematic events between trials. These features were also found in previous studies in which the experimental task required high accuracy. The characteristic kinematics evident in the present study suggested that the movement strategies adopted by the stressed participants were similar to those that appear under high accuracy demand. Moreover, a correlation analysis between the onset times of kinematic events revealed that temporally consistent movements were reproduced under stress. Taken together, the present findings demonstrated that, under psychological stress, movement strategies tend to shift toward the production of more constrained trajectories, as is seen under conditions of high accuracy demand, even though the difficulty of the task itself does not change.     

The freedom of Christ and the problem of deliberation

Call the claim, common to many in the Christian intellectual tradition, that Christ, in virtue of his created human intellect, had certain, infallible exhaustive foreknowledge the Foreknowledge Thesis. Now consider what I will call the Conditional: If the Foreknowledge Thesis is true, then Christ’s created human will lacked an important sort of freedom that we mere humans have. Insofar as many, perhaps all, of the people who affirm the Foreknowledge Thesis also wish to affirm the robust freedom of Christ’s human will, the truth of the Conditional would be most unwelcome to them. I consider an argument in support of the Conditional from the necessary conditions for deliberation, arguing that the argument fails.     

Recruitment of degrees of freedom stabilizes coordination

By showing that transitions may be obviated by recruiting degrees of freedom in the coupled pendulum paradigm, the authors reveal a novel mechanism for coordinative flexibility. In Experiment 1, participants swung pairs of unconstrained pendulums in 2 planes of motion (sagittal and frontal) at 8 movement frequencies starting from either an in-phase or antiphase mode. Few transitions were observed. Measures of spatial trajectory showed recruitment effects tied to the stability of the initial coordinative pattern. When the motion of the pendulums was physically restricted to a single plane in Experiment 2, transitions were more common, indicating that recruitment delays--or even eliminates--transitions. Such recruitment complements transitions as a source of coordinative flexibility and is incorporated in a simple extension of the Haken-Kelso-Bunz (1985) model.     

Change in the organization of degrees of freedom with learning

The authors examined the effects of learning on the change in the organization of the mechanical and dynamical degrees of freedom in 5 men who performed a ski-simulator task. A 3-dimensional analysis of the motion of the total-body center of mass and the segmental centers of mass (head, torso, thighs, and shanks) over practice showed that the recruitment of mechanical degrees of freedom was strongly influenced by anatomical and task constraints. Principal components analysis of the body segments' motions revealed that practice shifted their relative contributions but did not change the number of principal components. The present findings show that there can be independence in the patterns of change in the mechanical and dynamical degrees of freedom that arise from practice.     

Online feedback and the regulation of degrees of freedom in motor control

We tested the hypothesis that the degree to which online feedback is used to control movement influences the regulation of degrees of freedom in a task. Ten participants performed an isometric force production task with their two index fingers with the goal of matching the total force to a target waveform. The role of online feedback was manipulated by changing three factors - the tracking mode, the profile of the target waveform, and the visual gain. The results showed that the coupling between the finger forces was lower in conditions where participants used online feedback to correct their movements compared to conditions where more feedforward strategies were used. The availability of online feedback is dependent on the nature of the task and this contributes to task-dependent changes in the regulation of the degrees of freedom.     

The dimensionality of the convenience phenomenon: A qualitative reexamination

Empirical investigations that have adhered to a unidimensional, time-oriented conceptualization of convenience have often yielded weak findings. This research explains 1) the rationale for and 2) the results of a study that qualitatively reexamines the convenience phenomenon. Diary responses are used to develop and test a reconceptualization of convenience that includes temporal, spatial, and effort dimensions. The dimensions are shown to reliably elaborate upon the unidimensional conceptualization. Implications of the three-dimensional scheme are explained. Other managerial implications of the findings are delineated; among them, the study reveals that, contrary to popular wisdom, convenient products can be dissatisfying. This relates to instances in which the choice of a convenient product entails a tradeoff of environmental or nutritional concerns. Consequently, companies must strive to develop convenient products which do not force consumers to compromise environmental, nutritional, and other concerns.     

Changes in the variability of movement trajectories with practice

We studied variability in movement phase plane trajectories (velocity-position relation) during movement. Human subjects performed 10 degrees and 30 degrees elbow flexion and extension movements in a visual step tracking paradigm. The area of ellipses with radii equal to one standard deviation in position and velocity was taken as a measure of trajectory variability. Trajectory variability was determined at 10-ms intervals throughout movements. Trajectory variability in both the acceleration and deceleration phases of movement decreased with practice. The average trajectory variability during deceleration was greater than that during acceleration even after extended practice (1000 trials). During practice, subjects usually increased movement speed while maintaining end-position accuracy. Trajectory variability was also related to movement speed when equal amounts of practice were given. Short duration (fast) movements had greater trajectory variability than long duration movements. Thus there is a tradeoff between movement speed and trajectory variability similar to the classical speed-accuracy tradeoff. Trajectory variability increased rapidly during the acceleratory phase of movement. The rate of increase was positively related to both movement amplitude and speed. Thus, the forces producing limb acceleration were variable and this variability was more marked in faster and larger movements. In contrast, trajectory variability increased more slowly or actually decreased during the deceleratory phase of movements. Forces involved in limb deceleration thus appeared to compensate to a greater or lesser degree for the variability in accelerative forces. The experiments indicate that the entire trajectory of simple limb movements is controlled by the central nervous system. Variations in accelerative forces may be compensated for by associated variations in decelerative forces. The linkage between accelerative and decelerative forces is progressively refined with practice resulting in decreased variability of the movement trajectory.     

Degrees of freedom and motor planning in purposive movement

This paper presents empirical evidence suggesting that healthy humans can perform a two degree of freedom visuo-motor pursuit tracking task with the same response time delay as a one degree of freedom task. In contrast, the time delay of the response is influenced markedly by the nature of the motor synergy required to produce it. We suggest a conceptual account of this evidence based on adaptive model theory, which combines theories of intermittency from psychology and adaptive optimal control from engineering. The intermittent response planning stage has a fixed period. It possesses multiple optimal trajectory generators such that multiple degrees of freedom can be planned concurrently, without requiring an increase in the planning period. In tasks which require unfamiliar motor synergies, or are deemed to be incompatible, internal adaptive models representing movement dynamics are inaccurate. This means that the actual response which is produced will deviate from the one which is planned. For a given target-response discrepancy, corrective response trajectories of longer duration are planned, consistent with the principle of speed-accuracy trade-off. Compared to familiar or compatible tasks, this results in a longer response time delay and reduced accuracy. From the standpoint of the intermittency approach, the findings of this study help make possible a more integral and predictive account of purposive action.     

The dimensionality of the flanker compatibility effect: A psychophysiological analysis

The psychophysiological approach was used to evaluate the effects of feature similarity and intrinsic response mapping on the flanker compatibility effect. Symbol (e.g., < > < and < / <) and letter arrays (e.g., HCH and SCS) were used. Results showed that delays in stimulus evaluation and both peripheral and central response competition contributed to the compatibility effect, with the contribution of these processes depending on feature similarity and the intrinsic response mapping of the stimuli. For letter stimuli, the difference in the size of the compatibility effect for similar and dissimilar arrays could be accounted for in terms of stimulus evaluation. For symbol arrays, differences in size of the compatibility effect could be accounted for by response competition. Thus, symbol and letter arrays do not appear to be processed differently; what is different is the degree to which stimulus and response-related processes are affected by incompatibility.     

Haptic perception: A tutorial

This tutorial focuses on the sense of touch within the context of a fully active human observer. It is intended for graduate students and researchers outside the discipline who seek an introduction to the rapidly evolving field of human haptics. The tutorial begins with a review of peripheral sensory receptors in skin, muscles, tendons, and joints. We then describe an extensive body of research on “what” and “where” channels, the former dealing with haptic perception of objects, surfaces, and their properties, and the latter with perception of spatial layout on the skin and in external space relative to the perceiver. We conclude with a brief discussion of other significant issues in the field, including vision-touch interactions, affective touch, neural plasticity, and applications.     

The interference problem for the betting interpretation of degrees of belief

The paper’s target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there’s one crucial feature that all these cases have in common: The agent’s degree of belief in a proposition A does not coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent’s rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent’s degree of belief in A cannot be interpreted as her betting rate for A.     

Three-dimensional movement trajectories in Fitts' task: Implications for control

According to Fitts (1954), movement time (MT) is a function of the combined effects of movement amplitude and target width (index of difficulty). Aiming movements with the same index of difficulty and MT may have different planning and control processes depending on the specific combination of movement amplitude and target size. Trajectories were evaluated for a broad range of amplitudes and target sizes. A three-dimensional motion recording system (WATSMART) monitored the position of a stylus during aiming movements. MT results replicated Fitts' Law. Analysis of the resultant velocity profiles indicated the following significant effects: As amplitude of movement increased, so did the time to peak resultant velocity; peak resultant velocity increased slightly with target size, and to a greater extent with increases in the amplitude of movement; the time after peak resultant velocity was a function of both amplitude and target size. Resultant velocity profiles were normalized in the time domain to look for scalar relation in the trajectory shape. This revealed that: the resultant velocity profiles were not symmetrical; the proportion of time spent prior to and after peak speed was sensitive to target size only, i.e. as target size decreased, the profiles became more skewed to the right, indicating a longer decelerative phase; for a given target size, a family of curves might be defined and scaled on movement amplitude. These results suggest that a generalized program (base trajectory representation) exists for a given target width and is parameterized or scaled according to the amplitude of movement.     

Limiting the recruitment of degrees of freedom reduces the stability of perception-action patterns

The goal of the present study was to examine how recruiting/suppressing degrees of freedom affects the (differential) stability of two rhythmic perception-action patterns. In particular, participants synchronized either adduction-on-the-beat or abduction-on-the-beat movements of the right index finger with an auditory metronome. The stability of both patterns as performed in the horizontal plane was predicted to depend on the utilization, or recruitment, of the vertical plane of motion. Movements of the index finger were either free or physically restricted to the horizontal plane. The results showed that in the free condition, the vertical plane was recruited more in the more stable pattern (abduction-on-the-beat) than in the less stable pattern (adduction-on-the-beat). In the constrained condition, abduction-on-the-beat pattern was destabilized, whereas the stability of the adduction-on-the-beat pattern was preserved. These results suggest that the recruitment of the vertical plane of motion in the abduction-on-the-beat movements brought about an increase in the stability of this pattern. More generally, the trade-off between the stability of coordination patterns in the horizontal plane is based on a self-organizing process of recruitment in which neuromuscular factors are an intrinsic aspect.     

Stabilization and destabilization of perception--action patterns influence the self-organized recruitment of degrees of freedom

The recruitment of an additional biomechanical degree of freedom in a unimanual rhythmic task was explored. Subjects were asked to synchronize adduction or abduction of their right index finger with a metronome, the frequency of which was increased systematically. In addition, haptic contact on or off the metronome beat was provided. Results showed that the pattern exhibiting the highest intrinsic stability recruited the vertical plane more than did the less stable one. Moreover, presence and location of haptic contact modulated coordination stability and therefore induced changes in the recruitment of the vertical plane. Thus, a trade-off was shown between coordination stability on the horizontal plane and recruitment of the vertical one. These findings suggest that recruitment of degrees of freedom is governed by general principles of coordination dynamics.