The effects of temporal-precision and time-minimization constraints on the spatial and temporal accuracy of aimed hand movements

Discrete aimed hand movements, made by subjects given temporal-accuracy and time-minimization task instructions, were compared. Movements in the temporal-accuracy task were made to a point target with a goal movement time of 400 ms. A circular target then was manufactured that incorporated the measured spatial errors from the temporal-accuracy task, and subjects attempted to contact the target with a minimum movement time and without missing the circular target (time-minimization task instructions). This procedure resulted in equal movement amplitude and approximately equal spatial accuracy for the two task instructions. Movements under the time-minimization instructions were completed rapidly (M = 307 ms) without target misses, and tended to be made up of two submovements. In contrast, movements under temporal-accuracy instructions were made more slowly (M = 397 ms), matching the goal movement time, and were typically characterized by a single submovement. These data support the hypothesis that movement times, at a fixed movement amplitude versus target width ratio, decrease as the number of submovements increases, and that movements produced under temporal-accuracy and time-minimization have different control characteristics. These control differences are related to the linear and logarithmic speed-accuracy relations observed for temporal-accuracy and time-minimization tasks, respectively.     

Information entropy analysis of discrete aiming movements

Information entropy and mutual information were investigated in discrete movement aiming tasks over a wide range of spatial (20-160 mm) and temporal (250-1250 ms) constraints. Information entropy was calculated using two distinct analyses: (1) with no assumption on the nature of the data distribution; and (2) assuming the data have a normal distribution. The two analyses showed different results in the estimate of entropy that also changed as a function of task goals, indicating that the movement trajectory data were not from a normal distribution. It was also found that the information entropy of the discrete aiming movements was lower than the task defined indices of difficulty (ID) that were selected for the congruence with Fitts' law. Mutual information between time points of the trajectory was strongly influenced by the average movement velocity and the acceleration/deceleration segments of the movement. The entropy analysis revealed structure to the variability of the movement trajectory and outcome that has been masked by the traditional distributional analyses of discrete aiming movements.     

The direction of bilateral transfer depends on the performance parameter

To acquire a more comprehensive understanding of the learning benefits associated with bilateral transfer and to gain knowledge of possible mechanisms behind bilateral transfer, we investigated the transfer direction of several parameters which are assumed to represent important features of movement control in a visuo-motor task. During the study, participants learned a multidirectional point-to-point drawing task in which the visual feedback was rotated 45° and the gain was increased. Performance changes of the untrained hand in movement time, trajectory length, normalized jerk, initial direction error, ratio of the primary sub-movement time to the total movement time, and the accuracy of the aiming movement after the primary sub-movement were investigated as indices of learning from bilateral transfer. The results showed that performance parameters related to the initial production of the movement, such as the initial direction, ratio of primary sub-movement to the total movement time, and movement accuracy after the primary sub-movement, only transferred to the non-dominant, while hand performance variables related to the overall outcome, such as movement duration, movement smoothness, and trajectory length, transferred in both directions. The findings of the current study support the basic principle of the “dynamic dominance model” because it is suggested that overall improvements in the non-dominant system are controlled by trajectory parameters in visuo-motor tasks, which resulted in transference of the afore mentioned production parameters to rather occur to the non-dominant hand as opposed to transference to the dominant hand.     

Influence of Speed and Accuracy Constraints on Motor Learning for a Trajectory-Based Movement

This study investigated the influences of task constraint on motor learning for a trajectory-based movement considering the speed–accuracy relationship. In the experiment, participants practiced trajectory-based movements for five consecutive days. The participants were engaged in training with time-minimization or time-matching constraints. The results demonstrated that the speed–accuracy tradeoff was not apparent or was weak in the training situation. When the participants practiced the movement with a time-minimization constraint, movement errors did not vary, whereas the movement time decreased. With the time-matching constraint, the errors decreased as a session proceeded. These results were discussed in terms of the combination of signal-dependent noises and exploratory search noises. It is suggested that updating spatial and temporal factors does not appear to occur simultaneously in motor learning.     

Space-time accuracy of rapid movements

The space-time accuracy of an elbow flexion movement task was examined in two experiments over a range of motion extents (1 degrees through 100 degrees ) and short-duration movement times (100, 125, 150, and 400 ms). Nonlinear speed-accuracy functions emerged for both spatial and temporal error over all the movement conditions examined. The results showed that the timing error and spatial error had a high degree of complementarity as predicted by a space-time model of the speed-accuracy relation (Hancock & Newell, 1985). The findings confirm that the frame of reference for measuring movement error determines in part the error functions observed.     

Effects of average movement velocity on reaction time and spatiotemporal accuracy in single-aiming and rapid-timing movement tasks

The effects of instructed movement speed were investigated in two experiments. First, rapid-timing and single-aiming movement tasks were compared. Unlike rapid timing, single aiming implies spatial accuracy. The aim of the first experiment was twofold: (a) to examine whether the requirement of accurate placement termination in single aiming affects the negative relationship between instructed average velocity and reaction time found in rapid timing, and (b) to test the speed-accuracy relationships predicted by the symmetric impulse variability model of these movement tasks. For this purpose, four average velocities (5, 24, 75, and 140 cm/s) were investigated in both types of movement tasks in a two-choice reaction task. The effects of average velocity on reaction time were similar in both single-aiming and rapid-timing tasks, and the predicted linear relationship between instructed average velocity and spatial accuracy was not found. The results suggest that the movement control mode, that is, open loop or closed loop, interferes with effects of instructed average velocity. The movement control mode explanation was confirmed in the second experiment with respect to the effect of paired velocities on reaction time. It is argued that the type of movement control mode must be considered in the interpretation of effects of instructed average velocity on reaction time and spatiotemporal measures.     

Search Strategies in Practice: Movement Variability Affords Perception of Task Dynamics

Practice has been conceptualized in terms of a search process through an evolving perceptual-motor workspace. The experiment was set up to examine whether the inherent variability of the system would influence perception of the relevant properties of the task space. We reanalyzed the data from Hsieh, Liu, Mayer-Kress, and Newell (2013) in which participants performed a speed-accuracy aiming task and feedback emphasized either temporal or spatial accuracy in different conditions. The maximum variability in spatial error during practice differentiated individual's best performance in the fast speed-accuracy conditions. Additionally, we found that a threshold of variability predicted discontinuities during practice within individuals. The findings support the proposition that inherent variability affords perception of the relevant dimension of the task. The search motion through the perceptual-motor workspace was continuous or discontinuous depending on the constraints of the movement speed-accuracy condition.     

Movement Speed and Accuracy in Space and Time: The Complementarity of Error Distributions

Movement speed-accuracy trade-off is a function of the space-time constraints of the task. We investigated the space-time account of Hancock and Newell (1985) and the hypothesis of complementarity between the four moments of the error distribution in space and time. Twelve participants performed 15 conditions in a line drawing task composed of different spatial (10, 20, and 30 cm) and temporal (250 to 2,500 ms) criteria. The results showed that all moments of distributions changed systematically between conditions but there were some departures from the Hancock and Newell predictions. In contrast, individual analysis revealed the complementarity of the spatial and temporal error including a trade-off between the four moments of error. These findings support a complementary space-time account of movement speed and accuracy.     

Information entropy and the variability of space-time movement error

The authors investigated the effects of movement time and movement distance on the information entropy and variability of spatial and temporal error in a discrete aiming movement. In Experiment 1, the authors held movement distance (100 mm) constant and manipulated 11 movement times (300-800 ms) of 8 participants. In Experiment 2, the authors tested 6 movement distances at 2 given movement times (15-60 mm at 300 ms; 40-240 mm at 800 ms) in 8 participants. The variability and entropy for spatial error increased with average movement velocity, whereas the variability and entropy for temporal error decreased as a function of average movement velocity. The common variance between variable error and entropy averaged about 84% and 72% for spatial and temporal errors, respectively, suggesting that the probabilistic approach of entropy reveals features that are not present in the standard deviation index of variability. The findings provide further evidence that information entropy may be a useful single-index representation of variability in the movement speed-accuracy relation.     

Aiming error under transformed spatial mappings suggests a structure for visual-motor maps

Transformed spatial mappings were used to perturb normal visual-motor processes and reveal the structure of internal spatial representations used by the motor control system. In a 2-D discrete aiming task performed under rotated visual-motor mappings, the pattern of spatial movement error was the same for all Ss: peak error between 90 degrees and 135 degrees of rotation and low error for 180 degrees rotation. A two-component spatial representation, based on oriented bidirectional movement axes plus direction of travel along such axes, is hypothesized. Observed reversals of movement direction under rotations greater than 90 degrees are consistent with the hypothesized structure. Aiming error under reflections, unlike rotations, depended on direction of movement relative to the axis of reflection (see Cunningham & Pavel, in press). Reaction time and movement time effects were observed, but a speed-accuracy tradeoff was found only for rotations for which the direction-reversal strategy could be used. Finally, adaptation to rotation operates at all target locations equally but does not alter the relative difficulty of different rotations. Structural properties of the representation are invariant under learning.     

Goal-directed aiming under restricted viewing conditions with confirmatory sensory feedback

A substantial body of research has examined the speed-accuracy tradeoff captured by Fitts’ law, demonstrating increases in movement time that occur as aiming tasks are made more difficult by decreasing target width and/or increasing the distance between targets. Yet, serial aiming movements guided by internal spatial representations, rather than by visual views of targets have not been examined in this manner, and the value of confirmatory feedback via different sensory modalities within this paradigm is unknown. Here we examined goal-directed serial aiming movements (tapping back and forth between two targets), wherein targets were visually unavailable during the task. However, confirmatory feedback (auditory, haptic, visual, and bimodal combinations of each) was delivered upon each target acquisition, in a counterbalanced, within-subjects design. Each participant performed the aiming task with their pointer finger, represented within an immersive virtual environment as a 1 cm white sphere, while wearing a head-mounted display. Despite visual target occlusion, movement times increased in accordance with Fitts’ law. Though Fitts’ law captured performance for each of the sensory feedback conditions, the slopes differed. The effect of increasing difficulty on movement times was least influential in the haptic condition, suggesting more efficient processing of confirmatory haptic feedback during aiming movements guided by internal spatial representations.     

Impulse and Movement Space-Time Variability

In 3 experiments, the authors examined movement space-time variability as a function of the force-time properties of the initial impulse in a movement timing task. In the range of motion and movement time task conditions, peak force, initial rate of force, and force duration were manipulated either independently or in combination across a range of parameter values. The findings showed that (a) impulse variability is predicted well by the elaboration of the isometric force variability scaling functions of L. G. Carlton, K. H. Kim, Y. T. Liu, and K. M. Newell (1993) to movement, and (b) the movement spatial and temporal outcome variability are complementary and well predicted by an equation treating the variance of force and time in Newton's 2nd law as independent random variables. Collectively, the findings suggest that movement outcome variability is the product of a coherent space-time function that is driven by the nonlinear scaling of the force-time properties of the initial impulse.     

Speed-accuracy tradeoff and information processing dynamics

For a long time, it has been known that one can tradeoff accuracy for speed in (presumably) any task. The range over which one can obtain substantial speed-accuracy tradeoff varies from 150 msec in some very simple perceptual tasks to 1,000 msec in some recognition memory tasks and presumably even longer in more complex cognitive tasks. Obtaining an entire speed-accuracy tradeoff function provides much greater knowledge concerning information processing dynamics than is obtained by a reaction- time experiment, which yields the equivalent of a single point on this function. For this and other reasons, speed-accuracy tradeoff studies are often preferable to reaction-time studies of the dynamics of perceptual, memory, and cognitive processes. Methods of obtaining speed-accuracy tradeoff functions include: instructions, payoffs, deadlines, bands, response signals (with blocked and mixed designs), and partitioning of reaction time. A combination of the mixed-design signal method supplemented by partitioning of reaction times appears to be the optimal method.     

Kinematic analysis of multiple constraints on a pointing task

The current experiment suggests that the speed/accuracy tradeoff is composed of two classes of constraints, effector and task. We examined the effects of movement distance, target size, orientation of the movement in the workspace, and C-D gain on the kinematics of discrete pointing movements made with computer mouse. It was found that target size influenced the shape of velocity profiles by elongating the duration of the corrective sub-movement phase, while movement distance scaled the entire velocity curve without affecting its shape. C-D gain and orientation of the movement exhibited two kinds of effects: an overall scaling of the velocity curve and a change in its shape. We conclude that target size is a task constraint and movement distance is an effector constraint, while movement orientation exhibited characteristics of both. C-D gain by itself was not a constraint, but interacted with both task and effector constrains. These results highlight the roles of biomechanical and information processing factors in the speed/accuracy tradeoff.     

Kinematics properties of rapid aimed hand movements

Generalized motor program theory and the models of Schmidt, Zelaznik, and Frank (1978), and Meyer, Smith, and Wright (1982) of speed-accuracy relationships in aimed hand movements require that the underlying acceleration-time patterns exhibit time rescalability, in which all acceleration-time functions in an aimed hand movement are generated from one rescalable pattern. We examined this property as a function of movement time in Experiment 1, and as a function of movement time and movement distance in Experiment 2. Both experiments failed to demonstrate strict time rescalability in acceleration-time patterns, with the time to peak positive acceleration being invariant across movement time. This suggests that time rescalability is not a necessary condition for the linear relation between speed and spatial variability. A second major finding was that the variability in distance traveled at the end of positive acceleration was independent of movement time, contrary to the symmetric-impulse-variability model of Meyer et al. (1982). The findings of both experiments suggest that the processes involved in decelerating the limb play an important, but yet to be understood, role in determining the linear speed-accuracy trade-off. Finally, these results suggest that generalized motor programs are not based on simple, time-rescalable acceleration patterns.     

Visual regulation of manual aiming: A comparison of methods

Visual regulation of upper limb movements occurs throughout the trajectory and is not confined to discrete control in the target area. Early control is based on the dynamic relationship between the limb, the target, and the environment. Despite robust outcome differences between protocols involving visual manipulations, it remains difficult to identify the kinematic events that characterize these differences. In this study, participants performed manual aiming movements with and without vision. We compared several traditional approaches to movement analysis with two new methods of quantifying online limb regulation. As expected, participants undershot the target and their movement endpoints were more variable when vision was not available. Although traditional measures such as reaction time, time after peak velocity, and the presence of discontinuities in acceleration were sensitive to the visual manipulation, measures quantifying the trial-to-trial spatial variability throughout the trajectory were the most effective in isolating the time course of online regulation.     

Men are more accurate than women in aiming at targets in both near space and extrapersonal space

Men excel at motor tasks requiring aiming accuracy whereas women excel at different tasks requiring fine motor skill. However, these tasks are confounded with proximity to the body, as fine motor tasks are performed proximally and aiming tasks are directed at distal targets. As such, it is not known whether the male advantage on tasks requiring aiming accuracy is because men have better aim or is better in the proximal domain in which the task is usually presented. 18 men (M age = 20.6 yr., SD = 3.0) and 20 women (M age = 18.7 yr., SD = 0.9) performed 2 tasks of extrapersonal aiming accuracy (>2 m away), 2 tasks of aiming accuracy performed in near space (< 1 m from them), and a task of fine motor skill. Men outperformed women on both the extrapersonal aiming tasks, and women outperformed men on the task of fine motor skill. However, a male advantage was observed for one of the aiming tasks performed in near space, suggesting that the male advantage for aiming accuracy does not result from proximity.     

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.     

Asymmetries in the discrete and pseudocontinuous regulation of visually guided reaching.

An experiment was conducted to examine the contribution of the hemispheres to the organization of aiming movements. The spatial positions of targets were obtained by extrapolating from brief visual displays of geometric patterns. The patterns comprised linear, quadratic, cubic, and quartic mathematical functions and varied in spatial complexity. Vision of the hand was also manipulated. While the hands did not differ in spatial accuracy, movements made by the right hand were of shorter duration and had higher peak velocities. The stimulus pattern strongly influenced kinematics, in particular the number of discrete modifications of the movement trajectory. Vision of the hand resulted in superior accuracy, although subjects were unable to compare the relative positions of the limb and the target. Vision of the hand did not lead to an increase in discrete adjustments, suggesting that visual information was used in a continuous fashion. Movements into ipsilateral space differed from those into contralateral space with respect to a number of parameters.     

Combined visual illusion effects on the perceived index of difficulty and movement outcomes in discrete and continuous fitts’ tapping

The speed-accuracy trade-off is a fundamental movement problem that has been extensively investigated. It has been established that the speed at which one can move to tap targets depends on how large the targets are and how far they are apart. These spatial properties of the targets can be quantified by the index of difficulty (ID). Two visual illusions are known to affect the perception of target size and movement amplitude: the Ebbinghaus illusion and Muller-Lyer illusion. We created visual images that combined these two visual illusions to manipulate the perceived ID, and then examined people’s visual perception of the targets in illusory context as well as their performance in tapping those targets in both discrete and continuous manners. The findings revealed that the combined visual illusions affected the perceived ID similarly in both discrete and continuous judgment conditions. However, the movement outcomes were affected by the combined visual illusions according to the tapping mode. In discrete tapping, the combined visual illusions affected both movement accuracy and movement amplitude such that the effective ID resembled the perceived ID. In continuous tapping, none of the movement outcomes were affected by the combined visual illusions. Participants tapped the targets with higher speed and accuracy in all visual conditions. Based on these findings, we concluded that distinct visual-motor control mechanisms were responsible for execution of discrete and continuous Fitts’ tapping. Although discrete tapping relies on allocentric information (object-centered) to plan for action, continuous tapping relies on egocentric information (self-centered) to control for action. The planning-control model for rapid aiming movements is supported.