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.     

Force variability in isometric responses

In the present study we examined the contribution of different impulse parameters to peak force variability in an isometric task. Five experiments are reported that each held constant a different impulse parameter while allowing the other impulse parameters to vary. The results indicate that change in force level is the parameter that has the greatest effect on peak force variability, although time to peak force and preload also systematically influence response variability. A formula that accommodates the relation between impulse parameters and force variability is proposed. The data suggest that even in isometric tasks, it is the force-time properties of the impulse, rather than discrete parameters such as peak force, that determine the outcome variability.     

Force control is greater in the upper compared with the lower extremity

The authors investigated whether force control is similar between the upper and lower limbs and between contractions that involve 1 or 2 joints. Six volunteers (27.5 +/- 11.2 years of age) attempted to produce consistent discrete rapid force responses of 30, 60, and 90 N by using 6 different body postures, 3 with the upper and 3 with the lower limb. One of the postures for each limb involved 2 joints. The standard deviation of peak force and impulse (aggregate of the force-time curve) was significantly greater ( approximately 25%) for the lower limb than for the upper limb (p <.01). Contractions that involved 1 or 2 joints within a limb had similar variability. Therefore, the upper limb might have better control of force than the lower limb because of its extensive use in fine motor tasks in daily activities.     

Force Control Is Greater in the Upper Compared With the Lower Extremity

The authors investigated whether force control is similar between the upper and lower limbs and between contractions that involve 1 or 2 joints. Six volunteers (27.5 ± 11.2 years of age) attempted to produce consistent discrete rapid force responses of 30, 60, and 90 N by using 6 different body postures, 3 with the upper and 3 with the lower limb. One of the postures for each limb involved 2 joints. The standard deviation of peak force and impulse (aggregate of the force-time curve) was significantly greater (?25%) for the lower limb than for the upper limb (p < .01). Contractions that involved 1 or 2 joints within a limb had similar variability. Therefore, the upper limb might have better control of force than the lower limb because of its extensive use in fine motor tasks in daily activities.     

The acquisition of maximal isometric plantar flexor strength: a force-time curve analysis

A paradigm involving the static force-time curve was used to study the mechanisms through which gains in maximal isometric strength are achieved during repeated testing. Twelve males performed three maximal contractions of the plantar flexors on each of six test days. Each contraction was executed as rapidly as possible, with the force recorded on a rapidly moving pen recorder. Although highly significant increases in maximal plantar flexor strength occurred over the six days, no changes were seen in the maximal rate of tension development. However, assessment of the amount of force reached at absolute time intervals revealed that more force was attained at the early time intervals on the first few days of testing than on the later days, indicating a distinct change in the shape of the static force-time curve. Several neural mechanisms are suggested to explain the alteration in shape of the static force-time curve which accompanies the acquisition of maximal strength.     

Variability of a “force signature” during windmill softball pitching and relationship between discrete force variables and pitch velocity

This study assessed reliability of discrete ground reaction force (GRF) variables over multiple pitching trials, investigated the relationships between discrete GRF variables and pitch velocity (PV) and assessed the variability of the “force signature” or continuous force-time curve during the pitching motion of windmill softball pitchers. Intraclass correlation coefficient (ICC) for all discrete variables was high (0.86–0.99) while the coefficient of variance (CV) was low (1.4–5.2%). Two discrete variables were significantly correlated to PV; second vertical peak force (r(5) = 0.81, p = 0.03) and time between peak forces (r(5) = −0.79; p = 0.03). High ICCs and low CVs support the reliability of discrete GRF and PV variables over multiple trials and significant correlations indicate there is a relationship between the ability to produce force and the timing of this force production with PV. The mean of all pitchers’ curve-average standard deviation of their continuous force-time curves demonstrated low variability (CV = 4.4%) indicating a repeatable and identifiable “force signature” pattern during this motion. As such, the continuous force-time curve in addition to discrete GRF variables should be examined in future research as a potential method to monitor or explain changes in pitching performance.     

On the Relationship Between Peak Force and Peak Force Variability in Isometric Tasks

An experiment is reported documenting the relationship between peak force and peak force variability with a fixed criterion time to peak force for an isometric task requiring activation of the elbow flexors. The results show that maximum peak force increases with increments in time to peak force and that peak force variability increases with increments of peak force in an exponential type function. Furthermore, despite the presence of peak force and time to peak force feedback, subjects systematically shifted time to peak force as a function of the percentage of peak force being produced. This temporal modulation changes the percentage of peak force represented by any given peak force criterion. When peak force is made proportional to the degree of departure from the criterion time to peak force, a linear relationship is found between peak force and peak force variability. These findings suggest that time to peak force and rate of force production are parameters that influence veridical estimates of the force variability function.     

On the relationship between peak force and peak force variability in isometric tasks

An experiment is reported documenting the relationship between peak force and peak force variability with a fixed criterion time to peak force for an isometric task requiring activation of the elbow flexors. The results show that maximum peak force increases with increments in time to peak force and that peak force variability increases with increments of peak force in an exponential type function. Furthermore, despite the presence of peak force and time to peak force feedback, subjects systematically shifted time to peak force as a function of the percentage of peak force being produced. This temporal modulation changes the percentage of peak force represented by any given peak force criterion. When peak force is made proportional to the degree of departure from the criterion time to peak force, a linear relationship is found between peak force and peak force variability. These findings suggest that time to peak force and rate of force production are parameters that influence veridical estimates of the force variability function.     

Preload and isometric force variability

Two experiments are reported, which examined the relative contributions of preload (resting force level), change of force, and the time taken to achieve the force in determining isometric force variability. The findings showed that change of force is the strongest determiner of peak force variability but that preload and time to peak force have smaller though systematic effects. A formula that predicts peak force variability is proposed, with preload as an additive effect to the ratio between the change of force level and the square root of time to peak force. These findings confirm that these three impulse variables are significant in predicting force variability and that the impact of rate of force on peak force variability is nonlinear.     

Preload and Isometric Force Variability

Two experiments are reported, which examined the relative contributions of preload (resting force level), change of force, and the time taken to achieve the force in determining isometric force variability. The findings showed that change of force is the strongest determiner of peak force variability but that preload and time to peak force have smaller though systematic effects. A formula that predicts peak force variability is proposed, with preload as an additive effect to the ratio between the change of force level and the square root of time to peak force. These findings confirm that these three impulse variables are significant in predicting force variability and that the impact of rate of force on peak force variability is nonlinear.     

Time but not force is transferred between ipsilateral upper and lower limbs

The authors compared the force and time endpoint accuracy of goal-directed ipsilateral upper and lower limb isometric contractions and determined the components of motor performance that can be transferred from 1 limb to the other after practice. Ten young adults (27.4 +/- 4.4 years) performed 100 trials that involved their matching peak force to a force-time target with ankle dorsiflexor and elbow flexor muscles. The peak force error and variability was greater for ankle dorsiflexor contractions than for elbow flexor contractions, whereas the timing error and variability did not significantly vary with limb. There was transfer of timing, but not force, of motor output between upper and lower limbs. The timing error of the elbow flexor contractions decreased by 23% when those contractions were preceded by ankle dorsiflexor contractions, and the timing error of the ankle dorsiflexors decreased by 24% when those contractions were preceded by elbow flexor contractions. These finding therefore suggest that timing of an aiming isometric contraction may be organized at a common part of the brain for the upper and lower limbs.     

The relationship of impulse to response timing error

This paper examines the relationship between response impulse and timing error in 200 msec discrete timing responses over a range of movement velocities and system masses. The results from two experiments showed that variable timing error decreased as both movement velocity and the mass of the system to be moved increased. The variability of force proportional to force (measured either as impulse or peak force) decreased curvilinearly as force out-put increased. The correlations between each of these parameters and variable timing errors, calculated on a group mean basis, ranged between.91 and.95. The ability to predict the movement time outcome of each individual trial from impulse-related parameters was considerably reduced, although the relationship between the various kinematic and kinetic parameters did strengthen as the movement velocity approached maximum. Collectively, the findings show the size of impulse is related to movement timing error, although it is premature argue that impulse variability is a causal agent of timing error.     

The Relationship of Impulse to Response Timing Error

This paper examines the relationship between response impulse and timing error in 200 msec discrete timing responses over a range of movement velocities and system masses. The results from two experiments showed that variable timing error decreased as both movement velocity and the mass of the system to be moved increased. The variability of force proportional to force (measured either as impulse or peak force) decreased curvilinearly as force output increased. The correlations between each of these parameters and variable timing errors, calculated on a group mean basis, ranged between .91 and .95. The ability to predict the movement time outcome of each individual trial from impulse-related parameters was considerably reduced, although the relationship between the various kinematic and kinetic parameters did strengthen as the movement velocity approached maximum. Collectively, the findings show that size of impulse is related to movement timing error, although it is premature to argue that impulse variability is a causal agent of timing error.     

Tempo,Rhythm, and Aging in Golf

Older (n = 12) and younger (n = 12) golfers attempted to hit a golf ball into a target net a short distance away. An accelerometer attached to the back of the clubhead measured the applied force. In contrast to the more typical finding of slower perceptual-motor performance by older adults, older golfers reached their peak downswing force earlier in the shot and also exhibited a trend toward a faster overall speed or tempo of the shot. Additionally, older golfers exhibited greater changes in applied force and greater variability. A pattern of divergence among the force-time histories from multiple shots suggested that the overall person-plus-golf-club dynamics were unstable during a part of the shot. Older adults may be slower in controlling this instability. Half of the participants heard a tone whose pitch was proportional to their force. These participants had a slower follow through; however, they did not make significantly more or fewer shots than participants who had not been presented with the tone. Analyses of the temporal covariation among the backswing, downswing, and follow-through favored a chain-like temporal structure over a hierarchical, proportional structure. The pattern of covariation suggests that the tempo and rhythm of the shot are not independent and that changing one's tempo may disrupt rhythm.     

Effects of differing response-force requirements on food-maintained responding in CD-1 mice

The effect of force requirements on response effort was examined using outbred (CD-1) mice trained to press a disk with their snout. Lateral peak forces greater than 2 g were defined as threshold responses (i.e., all measured responses). Different force requirements were used to define criterion responses (a subclass of threshold responses) that exceeded the requirement. The reinforcer was sweetened, condensed milk, and it was delivered upon response termination. All mice were exposed to two ascending series of criterion force requirements (2, 4, 8, 16, and 32 g). Increasing the force requirement decreased criterion response rates, but increased threshold response rates. The time-integral of force (area under the force-time curve for individual responses, which is proportional to energy expenditure for each response) increased with the increase in the force requirement. These results conflict with the hypothesis that higher force requirements have aversive qualities and suggest that increased force requirements are more analogous to intermittent schedules of reinforcement. These data suggest that estimations of effort or energy expenditure should be measured independently of the force requirement. Individual differences in responding were found for the CD-1 outbred stock.     

The force/force-variability relationship under controlled temporal conditions

Previously, an inverted U relationship between force and force variability was demonstrated in both static and dynamic responses. Recent research suggests that the inverted U function may be due to a lack of control of the temporal aspects of the response. To investigate this hypothesis, we examined the relationship between force and force variability in rapid movements under controlled temporal conditions. Subjects (N = 4) made rapid reversal responses with a horizontal lever (using elbow flexion and extension) such that the time to reversal (160 ms) and the distance to reversal (45 degrees ) were held constant in each of six load conditions (either 0,.260,.780, 1.040, or 1.560 kg added to the lever). When time to reversal and time to peak acceleration were held constant, a curvilinear relationship between force and force variability resulted, suggesting that the inverted U function is related to control of the temporal aspects of the response.     

The Force/Force-Variability Relationship Under Controlled Temporal Conditions

Previously, an inverted U relationship between force and force variability was demonstrated in both static and dynamic responses. Recent research suggests that the inverted U function may be due to a lack of control of the temporal aspects of the response. To investigate this hypothesis, we examined the relationship between force and force variability in rapid movements under controlled temporal conditions. Subjects (N = 4) made rapid reversal responses with a horizontal lever (using elbow flexion and extension) such that the time to reversal (160 ms) and the distance to reversal (45°) were held constant in each of six load conditions (either 0, .260, .520, .780,1.040, or 1.560 kg added to the lever). When time to reversal and time to peak acceleration were held constant, a curvilinear relationship between force and force variability resulted, suggesting that the inverted U function is related to control of the temporal aspects of the response.     

Force and timing variability in rhythmic unimanual tapping

In 3 experiments the interdependencies between timing and force production in unimanual paced and self-paced rhythmic tapping tasks were examined as participants (N = 6 in each experiment) tapped (a) to 1 of 3 target periods (333 ms, 500 ms, and 1,000 ms), while they simultaneously produced a constant peak force (PF) over a 50-s trial; (b) to produce 1 of 3 target forces (5, 10, and 15 N) at their preferred frequency, while keeping their rhythm as invariant as possible; and (c) to all combinations of target force and period. The results showed that (a) magnitudes of force and period were largely independent; (b) variability in timing increased proportionally with tapping period, and the variability in force increased with peak force; (c) force variability decreased at faster tapping rates; and (d) timing variability decreased with increasing force levels. (e) Analysis of tap-to-tap variability revealed adjustments over sequences of taps and an acceleration in the tapping rate in unpaced conditions. The interdependencies of force and time are discussed with respect to the challenges they provide for an oscillator-based account.     

A note on stability in force applied to control a repetitive task with the legs

The forces applied to pedals during cycling were collected every 40 ms from approximately 29,000 movement repetitions. Intra-cycle mean values of force and its variability were significantly correlated, supporting Schmidt's impulse variability theory of within-movement activities of the legs. In addition, as mean forces approached peak values, coefficients of variation decreased. From averages taken minute by minute, intra-cycle forces were seen to rise or fall in concert, implying that the pattern as a whole constituted a significant neuro-muscular unit of control.     

A Note on Stability in Force Applied to Control a Repetitive Task With the Legs

The forces applied to pedals during cycling were collected every 40 ms from approximately 29,000 movement repetitions. Intra-cycle mean values of force and its variability were significantly correlated, supporting Schmidt–s impulse variability theory of within-movement activities of the legs. In addition, as mean forces approached peak values, coefficients of variation decreased. From averages taken minute by minute, intra-cycle forces were seen to rise or fall in concert, implying that the pattern as a whole constituted a significant neuromuscular unit of control.