The dynamics of rhythmical aiming in 2D task space: relation between geometry and kinematics under examination

We explored a two-dimensional task space variant of the classical rhythmical Fitts' task in which participants were asked to sequentially cross four targets arranged around the extreme points of the major axes of an ellipse. Fitts' law was found to adequately describe the changes in movement time with the variations in task difficulty (ID), but the 1/3 power-law relating curvature and tangential velocity of the trajectory did not resist the increase in ID. Kinematic analyses showed that the behavioral adaptation to the ID resulted in an increase in the contribution of non-linear terms to the kinematics along the two axes of task space. Moreover, a limit cycle model (combining Rayleigh damping and Duffing stiffness, as in one-dimensional Fitts' task) captured such a behavior. In such a context, Fitts' law and the 1/3 power law appear as surface relations that emerge from parametric changes in a dynamical structure that captures the nature of Fitts' task.     

Performance on a reciprocal tapping task with variations in intertapping interval

Fitts' law was investigated in a study of the effect of the index of difficulty (ID) and intertapping interval upon reaction time (RT) and movement time (MT) for a reciprocal tapping task. ID showed its well-established relationship with MT as described by Fitts' law: MT = aID + b. Improvement in the linearity of this relationship was, however, demonstrated by expressing MT in logarithmic units. While ID had an unsubstantial (though significant) effect on RT, increases in intertapping interval from zero to any level of discrete tapping led to significant increases in RT of about 135 msec. The results are interpreted as lending support to Fitts' thesis that RT and MT reflect independent phases of information processing.     

Deficits in executed and imagined aiming performance in brain-injured children

Motor disorders are a frequent consequence of acquired brain injury (ABI) in children and much effort is currently invested in alleviating these deficits. The aim of the present study was to test motor imagery (MI) capabilities in children with ABI (n=25) and an age- and gender-matched control group (n=25). A computerized Virtual Radial Fitts Task (VRFT) was used to investigate the speed-accuracy trade-offs (or Fitts' law) that occur as target size is varied for both executed and imagined performance. In the control group, the speed for accuracy trade-off for both executed and imagined performance conformed to Fitts' law. In the ABI group, only executed movements conformed to Fitts' law. These findings suggest that children with ABI show an inferior ability to imagine the time needed to complete goal-directed movements with differential difficulty levels.     

Fitts' reciprocal tapping task, a measure of motor capacity?

Employing Fitts' reciprocal tapping task, the capacity of the motor system in bits processed/second was assessed across different ages. In Exp. I a comparison was made among Grades 1, 5, 9, and university females. Motor capacity and average movement time/tap were significantly lower for Grade 1 girls than the other three grades. In addition, within-subject variability and percentage error rate decreased with increasing grade level. These findings were discussed in comparison to other studies looking at motor capacity changes across ages. Exp. II was designed to study the changes in motor capacity throughout 25 days of practice by two 5-yr.-old children. Two different methods were used to calculate motor capacity. One method (Kay, 1962) which assessed motor capacity separately for each tapping condition led to the conclusion that capacity increased with practice. A second method (Fitts & Peterson, 1964) treating all tapping conditions together in a regression equation and measuring capacity as the reciprocal of the slope (1/b) showed capacity to decrease with practice for one subject and oscillate with practice for the other subject. The general conclusion drawn from the two experiments was that motor capacity, as assessed by Fitts' tapping task, is not an extremely useful measure. Consideration of movement time is usually just as informative.     

Increasing the efficiency of instruction for a person with severe disabilities: The applicability of Fitts' law in predicting response time

The purpose of this study was to demonstrate the applicability of Fitts' law in predicting the response duration of instruction-specific head movements for a person with severe multiple disabilities. Fitts' law is a motoric algorithm that calculates an index of difficulty (ID) for responses in relation to the variables of stimulus width and stimulus amplitude. Four functional tasks from the learner's current continuing education plans were targeted: photocopying, using a paint well, model painting, and communication symbol sequencing. For each of the four tasks, two sets of indices were calculated by (1) holding constant stimulus width while varying amplitude, and (2) holding constant stimulus amplitude while varying width. Results showed that response duration varied as a function of ID variation.     

Feedback versus motor programming in the control of aimed movements.

In the Fitts paradigm the subject moves a stylus to the left or right of an initial rest position to reach targets that vary in size and in distance from the initial position. The classic finding for relatively long movements is that movement time, measured from leaving the initial position until contact with the target, depends on both distance and target size according to a relationship known as "Fitts' law." By contrast, reaction time, measured from the signal to move until the stylus leaves the initial position, is independent of these parameters. While replicating these results for long movements, the present data show a different pattern for very short movements, for which Fitts' law no longer holds and for which reaction time increases as the size of the target is decreased. These findings were interpreted as implying that long movements are under feedback control, whereas short movements are predominately programmed and ballistic. This conclusion was supported by the additional finding that elimination of visual feedback was more disruptive to the long than to the short movements.     

Conditions for a linear speed-accuracy trade-off in aimed movements

A linear speed-accuracy trade-off has been found for rapid, precisely timed movements from a home position toward a target point. In this trade-off, W_e = K₁ + K₂(D/T), where D is the distance between the home position and the target, T is a pre-specified movement time, and W_e is the standard deviation of the distances actually moved. This result differs from Fitts' law, the commonly observed logarithmic trade-off in aimed movements. A new experiment with wrist rotations was performed to determine what conditions induce the linear trade-off rather than Fitts' law. Three types of condition are considered: movement brevity, feedback deprivation, and temporal precision. The experiment yielded a linear trade-off for precisely timed movements even when their durations significantly exceeded an amount of time (200 ms) sufficient to process visual feedback. This result suggests that the linearity does not depend on movement brevity and/or feedback deprivation per se. Instead it supports a temporal-precision hypothesis that the linear trade-off occurs when aimed movements must have precisely specified durations.

A linear speed-accuracy trade-off has been found for rapid, precisely timed movements from a home position toward a target point. In this trade-off, W_e = K₁ + K₂(D/T), where D is the distance between the home position and the target, T is a pre-specified movement time, and W_e is the standard deviation of the distances actually moved. This result differs from Fitts' law, the commonly observed logarithmic trade-off in aimed movements. A new experiment with wrist rotations was performed to determine what conditions induce the linear trade-off rather than Fitts' law. Three types of condition are considered: movement brevity, feedback deprivation, and temporal precision. The experiment yielded a linear trade-off for precisely timed movements even when their durations significantly exceeded an amount of time (200 ms) sufficient to process visual feedback. This result suggests that the linearity does not depend on movement brevity and/or feedback deprivation per se. Instead it supports a temporal-precision hypothesis that the linear trade-off occurs when aimed movements must have precisely specified durations.     

Extended practice of reciprocal wrist and arm movements of varying difficulties

An experiment was designed to determine the degree to which reciprocal aiming movements of the wrist and arm with various accuracy requirements (Fitts' tasks) are enhanced by extended practice. The vast majority of research on motor learning shows performance improvement over practice. However, literature examining the effect of practice on Fitts' task performance is limited and inconclusive. Participants were asked to flex/extend their limb/lever in the horizontal plane at the wrist (arm stabilized) or elbow joint (wrist stabilized) in an attempt to move back and forth between two targets as quickly and accurately as possible. The targets and current position of the limb were projected on the screen in front of the participant. Target width was manipulated with amplitude constant (16°) in order to create indexes of difficulty (ID) of 1.5, 3, 4.5, and 6. Contrary to the earlier reports, after 20 days of practice, we found minimal changes in movement time or the movement time-ID relationships for the arm and wrist over practice. However, the variability in the movement endpoints decreased over practice and wrist movements at ID=6 were characterized by shorter movement times and longer dwell times relative to arm movements with dwell time for the wrist increasing over practice. These data are consistent with the notion that Fitts' tasks provide a stable measure of perceptual-motor capabilities.     

Extending Fitts' law to a three-dimensional pointing task

An attempt was made to extend Fitts' law to a three-dimensional movement (pointing) task to enhance its predictive performance in this domain. An experiment was conducted in which 10 subjects performed three-dimensional pointing movements under the manipulation of target size, distance to target and direction to target. As expected, the duration of these three-dimensional movements was rather variable and affected markedly by direction to target. As a result, the variance in the movement times produced was not satisfactorily explained by the conventional Fitts' model. The conventional model was extended by incorporating a directional parameter into the model. The extended model was shown to better fit the data than the conventional Fitts' model, both in terms of r(2) and the standard error of the residual between the measured movement time and the value predicted by model fit.     

Chaos and God's Abundance: An Ontology of Variety in the Divine Life

The primordial chaos of Genesis 1 may be understood as the Pandemonium Tremendum (or PT), the infinite field of variety or abundance within God. The concept of variety is taken from Claude Shannon's theory of communication. Especially significant is Shannon's notion that communication is the limitation of variety through decision processes. In one model of the divine life suggested by the theory, the PT is the boundless source of potential reaped by an agential God in the act of creation as a communication process. Other models for creation include the PT in a biased mode and creatures themselves as decision agents.     

Visual control of discrete aiming movements

An experiment is reported which investigated the visual control of discrete rapid arm movements. Subjects were required to move as rapidly as possible to several target width-movement distance combinations under both visual and non-visual conditions. The movement time (MT) data were supportive of Fitts' Law in that MT was linearly related and highly correlated to the Index of Difficulty (ID). MT was also similar for different target width-distance combinations sharing the same ID value. The error rate analysis, which compared visual to non-visual perfromance, indicated that vision was only used, and to varying degrees, when MT exceeded 200 ms (3.58 ID level). There was some evidence that vision was differentially used within target width-distance combinations sharing the same ID. Estimates of endpoint variability generally reflected the results of the error rate analysis. These results do not support the discrete correction model of Fitts' Law proposed by Keele (1968).     

Organization of drinking: postural characteristics of arm-head coordination

Postural characteristics of components of a natural movement-taking a sip from a mug filled with water-were studied. The authors hypothesized that important postural characteristics of each of the components involved in natural drinking can be described with a single or a few significant parameters. Seated participants (N = 7) took a small sip from a mug (selected from a set of 4) placed in front of them on the table. Movement components selected for analysis were transporting the mug, tilting the mug, moving and tilting the head, and opening the mouth. The ratio of mug diameter to the distance from the level of water to the rim of the mug was introduced as an index of difficulty (ID). ID showed significant logarithmic relationships to a number of parameters that described different components of the movement, including movement time (MT). Significant logarithmic relationships between ID and MT were observed during movements performed under visual control and with eyes closed. The authors tentatively suggest that those relationships are consequences of Fitts' law and that Fitts' law be expanded to tasks that are characterized by permissible error margin, not necessarily related to the size of a spatial target, and that are not constrained by the typical instruction "as fast and accurate as possible". A possible interpretation of the present observations is that the task constraints imposed on a number of movement parameters during the task of drinking can be described with a single parameter.     

Fitts' law with an isometric controller: effects of order of control and control-display gain

Twenty-four male subjects performed a discrete positioning task using an isometric controller. Two levels of order of control (position and velocity) were factorially crossed with two levels of control-display gain. Fitts' law functions were found for each of the four conditions. The velocity control conditions had significantly steeper slopes than the corresponding position control conditions, but there was no main effect for gain. A predicted interaction between control-display gain and order of control was found, indicating that the relative benefit of high gain is greater for velocity control than for position control. The reaction time (RT) regression lines had steeper negative slopes than those attained by Jagacinski, Repperger, Moran, Ward, and Glass (1980), who used an isotonic controller. This is in agreement with the results of Falkenberg and Newell (1980), who found that as average velocity increases, RT decreases. The components of Fitts' law were investigated, and this showed that the RT finding was due to the amplitude of the target, which covaried with average velocity, but was not due to the width.     

Feedback control of hand-movement and Fitts' law

Fitt's empirical result is stated and its information theoretic interpretation briefly discussed. An alternate derivation from a model assuming continous velocity control of hand position is shown to fit the motion time data equally well. Detailed studies of hand motion trajectories in Fitts' reciprocal tapping task have confirmed the exponential target approach predicted by this model but also revealed systematic fluctuations that it cannot explain. A further alternate model is therefore presented, based on intermittent feedback with target approach by a sequence of discrete positional corrective motion “impulses”. The second model also predicts motion times in accord with Fitts' Law.

Detailed studies of target aimed translational hand and rotary wrist motions have shown that the intermittent corrective impulses are of approximately Gaussian integral form, with minimum s.d. on the order of 30 msec. for wrist rotation, and recurrence rate about 10/s. Mechanical and physiological interactions capable of explaining this corrective impulse trajectory are discussed, and a model based on balance of forces between agonist and antagonist muscles is briefly developed. The interaction between external (visual) and internal (proprioceptive or kinaesthetic) feedback channels determining impulse amplitude is discussed in the light of results obtained using force disturbance and with amplified, attenuated or delayed visual feedback. It seems that an internal “secondary positional reference” must be postulated to explain results obtained when S is deprived of visual feedback.     

The coordination of bimanual aiming movements: Evidence for progressive desynchronization

It is known that when simultaneous bimanual aiming movements are made to targets with different IDs (Index of Difficulty), Fitts' Law is violated. There is massive slowing of the easy target hand, but a debate has arisen over the degree of synchronization between the hands and whether this effect represents a coordinative structure or interference due to neural cross-talk. This issue was investigated in an experiment with 12 subjects who moved styli forward in the sagittal plane to pairs of targets that differed in difficulty (0.77/3.73 ID and 0.77/5.17 ID). Reaction time, movement time, and kinematic measures of resultant velocity and acceleration were analysed. The results showed clear-cut timing differences between the hands that depended on both the ID difference between target pairs and elapsed time of the movement. The violation of Fitts' Law was confined to the easy target hand. Pronounced individual differences in both timing differences and left-right asymmetry were also noted. Neither the coordinative structure nor the neural cross-talk models can fully account for these data, and it is possible that the initial constraints on movement are moderated by visually driven corrective movements.     

Fitts' Law in two dimensions with hand and head movements

Subjects performed two-dimensional discrete movements either with a helmet-mounted sight or with a joystick. Fitts' Law was found to be a good predictor of the speed-accuracy tradeoff for both systems. The joystick produced faster movement times than the helmet-mounted sight. For both systems, horizontal and vertical movements were slightly faster than diagonal movements. Two dimensional generalizations of Fitts' Law were discussed in terms of multidimensional scaling. The obtained pattern of movement times was found to be intermediate to the predictions of Euclidean and City-block models of the movement space. Muscle coordination strategies were considered, and a strictly serial coordination model was rejected. A strictly parallel model was also rejected for the helmet-mounted sight, but not for the joystick.     

Note on Fitts' law for manipulative temporal motor responses with path constraints.

This paper presents a first-order version of an earlier model by Kv?lseth (1973) of manipulative motor responses involving serial hand movements with different types of movement-path constraints. This model represents a generalization of Fitts' law. Comparisons are also made between experimental movement times obtained and predetermined and motion-time systems predictions.     

Abnormalities of motor and praxis imagery in children with DCD

In an earlier study using the visually guided pointing task (VGPT) the authors showed that the timing of imagined movement sequences in children with developmental coordination disorder (DCD) does not conform to the conventional speed-for-accuracy trade-off (or Fitts' law [P.M. Fitts, Journal of Experimental Psychology 47 (1954) 381-391]) that occurs when the distance and accuracy requirements of movements are varied [P. Maruff, P.H. Wilson, M. Trebilcock, J. Currie, Neuropsychologia 37 (1999b) 1317-1324]. The present study sought to replicate this earlier finding and to examine (using a weight manipulation) whether this deficit was also attributable to inaccurate programming of relative force. The chronometry of real and imagined movements was investigated in a group of 20 children with DCD aged between 8 and 12 years and a group of controls matched on age and verbal IQ (VIQ). Movement duration was tested for real and imagined movements using the preferred hand, with the VGPT performed under two load conditions: with and without the addition of a weight attached to a pen. Group means of each subjects' mean movement duration were calculated and plotted against target width for each of the four conditions [Movement type (2) x Load (2)] and a logarithmic curve was fitted to the data points. In the control group, the speed-for-accuracy trade-off for both real and imagined performance conformed to Fitts' law under each load condition. In the DCD group only real movements conformed to Fitts' law. Moreover, the effect of load differed between groups--for real movements, movement duration did not differ between load and no-load conditions for either group, while for imagined movements, movement duration increased under the load condition for the control group only. These results replicate and extend the results of our earlier study. This pattern of performance suggests that children with DCD have an impairment in the ability to generate internal representations of volitional movements which may reflect an impaired ability to process efference copy signals. The ability to programme both relative force and timing appears to underly this difficulty. Results have implications for the use of (guided) motor imagery training in order to facilitate the development of motor skill in children with DCD.     

Movement control and maturation in elementary-grade children.

Serial tapping by 5-, 7- and 9-yr.-old boys and girls, as measured by Fitts' Law, was recorded. 60 Ss performed a reciprocal tapping task and were assessed developmentally via hand-wrist X-rays. No significant relationship was found between the fine motor task and skeletal age. The results of the motor task suggest an improvement in movement time, with age, due to an ability to plan subsequent movements rather than simply an increase in speed of arm movement.     

Accuracy constraints upon rapid elbow movements

Kinematic and myoelectric variables associated with rapid elbow-flexion movements of various distances to targets of various widths were studied. The movement time in these experiments conformed to Fitts' law: movement time increased with target distance and decreased with target width. Peak movement velocity, electromyograph (EMG) duration, and EMG quantity were poorly described by Fitts' law, for increases in target width were accompanied by increases in these variables. We show with regression equations, using separate weighting coefficients, that kinematic and myoelectric variables can be related to distance and target width. The use of distance and target width as independent variables allows us to suggest that the literature does not agree on the relation between EMG and distance moved partly because of the influences of the target on this relationship. We propose that human voluntary movement involves a subject "strategy," or set of internal constraints, that affect movement outcome. Significant elements of this strategy, such as how accurately to perform the task, may not be recognized or controlled in many movement paradigms, in spite of uniform instruction to subjects and similar apparatus.