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Journal of Motor Behavior

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Force Control Characteristics for Generation andRelaxation in the Lower Limb

Chiaki Ohtaka & Motoko Fujiwara

To cite this article: Chiaki Ohtaka & Motoko Fujiwara (2018): Force Control Characteristicsfor Generation and Relaxation in the Lower Limb, Journal of Motor Behavior, DOI:10.1080/00222895.2018.1474337

To link to this article: https://doi.org/10.1080/00222895.2018.1474337

Published online: 29 May 2018.

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RESEARCH ARTICLE

Force Control Characteristics for Generation and Relaxationin the Lower LimbChiaki Ohtaka, Motoko FujiwaraDepartment of Health Sciences, Faculty of Human Life and Environment, Nara Women’s University, Nara, Japan.

Summary. We investigated the characteristics for force generationand relaxation using graded isometric contractions of the knee exten-sors. Participants performed the following tasks as quickly and accu-rately as possible. For the force generation task, force was increasedfrom 0% to 20%, 40% and 60% of the maximal voluntary force(MVF). For the force relaxation task, force was decreased from 60%to 40%, 20% and 0%. The following parameters of the recorded forcewere calculated: error, time, and rate of force development. The errorwas consistently greater for force relaxation than generation. Reactionand adjustment times were independent of the tasks. The control strat-egy was markedly different for force relaxation and generation, thistendency was particularly evident for the lower limb compared to theupper limb.

Keywords: Voluntary force control, Relaxation, Accuracy,Quickness

Introduction

Performance of smooth, accurate and well-coordinated

movement requires control over both force generation

(muscle contraction) and force relaxation (muscle relaxa-

tion). Therefore, the ability to accurately control both force

generation and relaxation, quickly, is essential to the skill-

ful performance of various movements (Kato, Muraoka,

Higuchi, Mizuguchi, & Kanosue, 2014; Li, 2013; Spraker,

Corcos, & Vaillancourt, 2009). However, when performing

unfamiliar movements, force relaxation is typically more

difficult to accurately control than force generation (Sakurai

& Ohtsuki, 2000; Sewa & Kizuka, 2006).

Various studies have investigated the control of force using

different paradigms, including the control of pulse height and

width (Freund & B€udingen, 1978; Ghez, 1979; Gordon &

Ghez, 1987). It has been reported that as themagnitude of force

to be controlled increases, the strategy changes from one of

controlling pulse height (control of the rate of force develop-

ment) to controlling pulse width (control of the timing of the

force) (Bahill, Clark, & Stark, 1975). Gottlieb, Corcos, and

Agarwal (1989) described the control of pulse height and width

as a strategy for the control of force for single joint movements.

Strategies of force generation and relaxation have also been

investigated through the measurement of muscle activation

using electromyography and functional magnetic resonance

imaging. Using functional magnetic resonance imaging,

Spraker et al. (2009) demonstrated that different neural sub-

strates were activated for muscle contraction and relaxation

during an isometric pinch task. Harbst, Lazarus, and Whitall

(2000) used a periodic isometric bimanual self-paced pinch

task, performed at two force magnitudes, 10%–30% of maxi-

mal voluntary force (MVF) and 20%–40% ofMVF, to investi-

gate force-time control in adults and children. They reported

greater variability in the timing and force level for force

relaxation than force generation. This finding of a higher vari-

ability in force relaxation than force generation has been sup-

ported by several other researchers (Masumoto & Inui, 2010;

Moritou, Inui, & Masumoto, 2009; Spiegel, Stratton, Burke,

Glendinning, & Enoka, 1996). However, these findings have

been reported only for isometric motor tasks involving small

muscles and relatively small force levels, such as finger-grasp-

ing movements, with no reports of control strategies for whole

limb, with tasks requiring a relatively high level of force. Other

studies have evaluated the characteristics underlying the accu-

racy and quickness of force control for various muscle groups

(ranging from the small muscles of the hand and digits to the

large muscles of the thigh), using different force levels and

tasks. Therefore, it is difficult to systematically compare results

from these various studies. Moreover, in these studies, the con-

trol of force generation and relaxationwas evaluated as compo-

nents of one task, with relaxation analyzed as the relaxation

phase during a periodic force generation (Harbst et al., 2000;

Masumoto & Inui, 2010; Moritou et al., 2009; Spiegel et al.,

1996). As such, the characteristics of force relaxation have not

been systematically evaluated as a discrete component of force

control.

Based on the above, Ohtaka and Fujiwara (2016) system-

atically investigated the characteristics and motor strategies

for force generation and relaxation in the upper limb, dem-

onstrating that for tasks requiring accurate control of force,

the magnitude of error was greater for force relaxation than

force generation, especially under conditions of low magni-

tude of force. They also demonstrated that although the tim-

ing of force adjustments was dependent on the magnitude

of the target force level for both force generation and relax-

ation, the reaction time was consistently shorter for force

relaxation than for force generation. They concluded that

force generation and relaxation are controlled by two differ-

ent strategies, with the need to control both the timing and

the peak rate of force development increasing the difficulty

of the control of force relaxation.

As mentioned above, the characteristics of force control in

the upper limb were clarified, but there have been no reports of

the characteristics of force generation and relaxation in the

lower limb.While the upper limbs play a part of relatively high

Correspondence address: Chiaki Ohtaka, Department ofHealth Sciences, Nara Women’s University, Kitauoya-NishiMachi, Nara, 630–8506, Japan. e-mail: ohtaka@cc.nara-wu.ac.jp

Color versions of one or more of the figures in the article canbe found online at www.tandfonline.com/vjmb.

1

Journal of Motor Behavior, Vol. 0, No. 0, 2018

Copyright© Taylor & Francis Group, LLC

operability, the lower limbs support the upper body, as well as

move the body, such in walking and running. In addition to

having different functions, the force levels to be controlled are

also relatively larger at the lower than at the upper limbs.

Our aim in this study was to evaluate if the control of

force generation and relaxation for the lower limb uses the

same characteristics and strategies as identified for the

upper limb. A priori, we hypothesized the following based

on previous studies of force control for the upper limbs and

the points of commonality and difference in the function of

the upper and lower limbs.

Hypothesis 1: Force generation (a). The accuracy of force

generation will be lower under conditions of low than high

force magnitudes. This tendency will be particularly evi-

dent for the lower than upper limb. (b) Reaction time will

be shorter for higher than lower magnitudes of force gener-

ation, with the adjustment time varying as a function of the

magnitude of force generation.

Hypothesis 2: Force relaxation (a). The accuracy of

force relaxation will be lower under conditions of low than

high force magnitudes, and these differences will be more

conspicuous in the lower than upper limb. (b) Reaction

time of force relaxation will be shorter for higher than lower

magnitudes of force, and the adjustment time will again

depend on the magnitude of force.

Hypothesis 3: Comparing force generation and relaxa-

tion (a). The magnitude of error will be significantly higher

for force relaxation than for force generation, and the rela-

tionship between the magnitude of error for force genera-

tion and for force relaxation will be different than those

previously identified for the upper limb. (b) Reaction time

will be significantly shorter for force relaxation than for

force generation, with no differences in the adjustment time

for force generation and relaxation. (c) Motor strategies

controlling force generation and relaxation will be different

between the lower and upper limbs.

Method

Participants

Fifteen healthy women of right foot dominance (mean

age, 20.2 years; standard deviation, 1.1 years) formed our

study group. The procedures were approved by the Aca-

demic Ethics Committee in Nara Women’s University,

Japan. Prior to the experiment, all participants were fully

informed of the purpose of the study and its procedures,

and written informed consent was obtained.

Apparatus

The experimental set-up is shown in Fig. 1. The output

force was measured using a force-measuring device (Takei

Inc., Japan). Participants were seated in the force-measuring

device, with the right knee in 120� of extension (180� is fullknee extension) and the foot placed on the force plate; this

knee angle was selected based on previous research that

reported the highest magnitude of maximal isometric volun-

tary contractions around 120� of knee extension (Lindahl,

Movin, & Ringqvist, 1969; Tsunoda, Watanabe, & Hori-

kawa, 1987). The left leg was maintained in a relaxed posi-

tion, with the foot resting on a cylindrical bar, and the arms

were held along each side of the body. The output of the

force-plate and the target line of the force level were dis-

played on a personal computer (NEC, VJ22LL-D). The tar-

get force level line, along with three light-emitting diodes

(LED) used to indicate the warning signal and ‘go’ signal,

was controlled by a time-programmer (Takei Inc., Japan).

The display of force levels was placed at a distance of

approximately 1.5 m from participants, providing visual

feedback for knowledge of performance.

Experimental Tasks

Participants were instructed to produce an isometric knee

extension force to match the target force level, as quickly

and accurately as possible. This required that force be either

generated or decreased through relaxation. Four target force

levels were used (0%, 20%, 40%, and 60%MVF), with three

conditions presented for force generation and relaxation, as

follows: force generation task (20% magnitude, increase

force from 0% to 20%MVF; 40%magnitude, increase force

from 0% to 40% MVF; and 60% magnitude, increase force

from 0% to 60%MVF) and force relaxation task (20% mag-

nitude, decrease force from 60% to 40% MVF; 40% magni-

tude, decrease force from 60% to 20% MVF; and 60%

magnitude, decrease force from 60% to 0%MVF). The rela-

tionship between the tasks and magnitudes, as well the

abbreviations used, are defined in detail in Table 1. Each

trial began with a 500 ms visual warning signal, with the

500 ms “go” signal presented 2 s following the warning sig-

nal. Participants were informed of the magnitude before

each trial. For the force generation tasks, participants gener-

ated the required force level from baseline resting (0%). For

the relaxation task, participants were instructed to generate a

force level of 60% MVF prior to the warning signal, with

visual feedback of the force level presented. After maintain-

ing the 60%MVF for 1 s, the warning and “go” signals were

Display of force level

LED signal

1.5m

120degree

FIGURE 1. Experimental setup.

C. Ohtaka & M. Fujiwara

2 Journal of Motor Behavior

presented. Once the target force level had been achieved, the

participants were informed to turn their eyes towards the

warning signal. In order to measure and contrast the two

tasks, participants were instructed to adjust the target force

level in an instant under both tasks. As soon as they achieved

the target force level, participants were instructed to relax

their force for the generation task. In the relaxation task, as a

contrast to the generation task, the participants adjusted the

target force level in an instant, subsequently increasing their

voluntary force level.

Procedure

Prior to the presentation of the test conditions, partici-

pants were instructed to produce three maximum isomet-

ric force efforts, with the MVF held for 1 s, and the

maximum value obtained used as the reference MVF for

each participant. Participants then practiced controlling

their force to the target level, with visual feedback pro-

vided to facilitate learning (Masumoto & Inui, 2010).

Up to 10 trials were offered at each target force level.

Once participants were able to accurately control their

force output, one practice session using the warning and

“go” signals was conducted.

For the test conditions, participants were instructed

about the target force level prior to each trial. Partici-

pants did not receive visual feedback of their perfor-

mance during the trial, but did receive knowledge of

their performance using a summary of their force waves

after completion of the 10 trials at each of the three tar-

get force levels. A 1-min rest period was provided

between each force level, with a 5-min rest interval

between the two tasks (force generation and force relax-

ation). The order of the tasks was counterbalanced, with

7/15 of participants performing the force generation

prior to the force-reduction task and, therefore, 8/15 of

participants performed the relaxation task first. With

regard to the magnitude of force, we used a blocked

randomized design, with the 10 trials at a given level

performed as a block, with the order of the “force level”

blocks randomized across participants. After completion

of the two tasks, participants again produced three

MVFs to exclude effects of fatigue.

Data Analysis

Force measurements were acquired using a Biopac

MP150 data acquisition system (1000 Hz sampling rate;

Biopac Systems, United States). From each set of 10 trials

at each of the three target force levels, 8 trials were ran-

domly selected for analysis. The force data were low-pass

filtered (cutoff, 100 Hz) and a mean force curve calculated

from which the variables of interest were measured as

shown in Fig. 2, and described as follows.

The calculation of adjustment time was performed as fol-

lows. Baseline force was calculated as the average force

produced over a 300 ms period prior to the “go” signal.

The average rate of force development (N/s) was then cal-

culated over a 10 ms period following the “go” signal. Sub-

sequently, the force onset was defined as the first time point

within this first 10 ms period during which the average rate

of force development exceeded 50% of baseline force for

the force generation task, or decreased below this 50%

threshold for the force relaxation task (Ohtaka & Fujiwara,

2016). The reaction time was defined as the time interval

between the “go” signal and the force onset. The adjust-

ment time could then be defined as the time between the

force onset and the maximum force (generation task) or the

minimum force (relaxation task). The total adjustment time

was defined as the time between the “go” signal and the

maximum force (generation task) or the minimum force

(relaxation task).

The calculation of accuracy was performed as follows.

The force level (%MVF) was defined as the relative value

of the maximum or minimum force of each participant’s

MVF. The difference in the accuracy of the force level

between the peak force and each target force level was

calculated to evaluate the constant, absolute and variable

error.

The peak rate of force development of force control was

calculated as follows. The peak rate of force development

(peak RFD) was defined as the peak value of the rate of

TABLE 1. The relationship of tasks and magnitudes, and abbreviations used

Force level (%MVF)

Task Start level Target level Magnitude (%) Abbreviation

Force generation(G) 0 20 20 G2040 40 G4060 60 G60

Force relaxation (R) 60 40 20 R2020 40 R400 60 R60

Force Control Characteristics

2018, Vol. 0, No. 0 3

force development over the adjustment time, with the time

to reach peak RFD (time to peak RFD) also calculated.

Statistical Analysis

Prior to applying the evaluating differences between tasks

and force levels, we tested for homoscedasticity in the data set.

Differences in measured variables (error, time, and peak RFD)

between the magnitudes (20%, 40%, and 60% magnitudes)

and the two tasks (force generation and force relaxation) were

evaluated using a two-way repeated measures analysis of vari-

ance (ANOVA). The within-participant factors were the mag-

nitude of force (20%, 40%, and 60%) and task (force

generation and relaxation). When significant effects were iden-

tified, pairwise comparisons were carried out, using a Bonfer-

roni post hoc test. Differences in the slope of the force wave

(RFD) between target force levels for the two force tasks were

evaluated using one-way repeated measures ANOVA. All

analyses were performed using SPSS for Windows (SPSS

Inc.). Statistical analysis was conducted at the 0.05 level of

significance.

Results

Accuracy

Themeans and standard deviations of the force levels for the

force-generation and force-relaxation tasks for all participants

are summarized in Fig. 3. For the force generation task, the dif-

ference between the force level and the target force level was

influenced by a main effect of force magnitude (F2, 18 D2640.753, p< .001) and an interaction between force level and

the target force level (F1, 9 D 5.698, p < .05). The force level

increased as a function of an increase in the target force level,

FIGURE 2. Definition and measurement of force for (A) the force generation task and (B) force relaxation task.

0

10

20

30

40

50

60

70

80

90

G20 G40 G60

%M

VF

0

10

20

30

40

50

60

70

80

90

R20 R40 R60

%M

VF

*** *** ***

*** *** ***

††

††

†

†

A B

FIGURE 3.Mean values and standard deviations of the force levels for (A) the force-generation task and (B) force-relaxation task.*: Significant difference between the magnitude of the force controlled, ***: p <.001. y: Significant difference between the forcelevel and the target force level, y: p <.05, yy: p <.01.

4 Journal of Motor Behavior

C. Ohtaka & M. Fujiwara

from magnitudes of 20% through to 60% (p < .001), with the

force level being significantly higher than the target force level

at the 20%magnitude (p< .05).

For the force relaxation task, the difference between the

force level and the target force level was influenced by a

main effect of force magnitude (F2, 18 D 546.113, p <

.001) and level (F1, 9 D 7.172, p < .001), as well as by an

interaction between the force level and the target force level

(F2, 18 D 26.721, p < .001). Again, the force level

decreased as a function of the target force level, from mag-

nitudes of 20% through to 60% (p < .001), with the force

level being significantly lower than the target force level

for the 20% and 40% magnitudes (p < .01), and higher at

the target force level of 60% magnitude (p < .05). There-

fore, for the force generation task, the force level was sig-

nificantly higher than the target force level at the 20%

magnitude. By comparison, for the force relaxation task,

the force level was significantly lower than the target force

level at the 20% and 40% magnitudes.

Error

The means and standard deviations of the constant, abso-

lute, and variable error for all participants and for both tasks

are shown in Fig. 4. The constant error was influenced by a

significant interaction (F2, 18 D 18.620, p < .001) as well as

by significant main effects of the magnitude of force (F2, 18

D 30.722, p < .001) and task (F1, 9 D 8.224, p < .01). The

constant error was significantly higher at the 20% magni-

tude than the 40% magnitude for the force generation task

(p < .05), and higher at the 60% magnitude than the 20%

and 40% magnitudes for the force relaxation task (p < .05).

Moreover, the constant error was significantly higher for

the force generation than relaxation task at the 20% and

40% magnitudes (20%: p < .01; 40%: p < .05).

In terms of the absolute error, a significant interaction

was identified (F2, 18 D 6.327, p < .01), with the magnitude

of the absolute error being significantly higher for the force

relaxation than force-generation task at the 20% magnitude

(p < .05), but with the magnitude of the absolute error

being significantly higher for the force generation than

relaxation task at the 60% magnitude (p < .05).

In terms of the variable error, the interaction (F 2, 18 D13.467, p< .001) and the main effect of the magnitude (F2, 18D 4.360, p< .05) were again significant factors. For the force-

relaxation task, the variable error was significantly greater at

the 20% and 40% magnitudes than at the 60% magnitude (p<

.01). The variable error was also greater for the force relaxation

than generation task at the 20% magnitude (p < .01). In con-

trast, the variable error was greater for the generation than

force-relaxation task at the 60%magnitude (p< .01).

Overall, for the force-generation task, no differences in

absolute and variable error values were observed across the

three levels of force magnitude (20%, 40%, and 60%), with

the constant error being higher at the 20% magnitude than

at the 40% magnitude. For the force-relaxation task, the

constant error was lower at the 20% and 40% magnitudes

than at the 60% magnitude, and with the variable error

being higher at the 20% and 40% magnitudes than at the

60% magnitude. Moreover, when comparing the force gen-

eration and relaxation tasks at the same magnitude, the con-

stant error was lower for force relaxation than generation at

the 20% and 40% magnitudes, and the absolute and variable

errors were greater for force relaxation than generation at

the 20% magnitude. However, the absolute and variable

-20

-10

0

10

20

G R G R G R

20 40 60

Cons

tant

Err

or (%

MVF

)

magnitude

†††

*

**

0

10

20

G R G R G R

20 40 60Ab

solu

te E

rror

(%M

VF)

magnitude

††

0

10

G R G R G R

20 40 60

Varia

ble

Erro

r (%

MVF

)

magnitude

††††

**

**

A

B

C

FIGURE 4. Mean values and standard deviations of (A)the constant error, (B) absolute error, and (C) the variableerror. *: Significant difference between the magnitude ofthe force controlled, *: p <.05, **: p <.01. y: Significantdifference between the tasks, y: p <.05, yy: p <.01.

2018, Vol. 0, No. 0 5

Force Control Characteristics

errors were lower for force relaxation than generation task

at the 60% magnitude.

Quickness

The means and standard deviations of the reaction time,

adjustment time and total adjustment time are shown for all

participants for the two tasks in Fig. 5. Reaction timewas influ-

enced mainly by the magnitude of force (F2, 18 D 21.931, p <

.001), with significantly longer reaction time at the 20% and

40% magnitudes than at the 60% magnitude for both tasks

(20%: p < .001; 40%: p < .01). Adjustment time was influ-

enced mainly by the magnitude (F2, 18 D 106.999, p < .001)

and the task (F1, 9 D 26.620, p < .01). The adjustment time

was increasingly longer from the 20% through to the 60%mag-

nitudes (p< .001), with longer adjustment times for force gen-

eration than relaxation at all magnitudes (p < .01). Similarly,

total adjustment time was influenced mainly by the magnitude

of force (F2, 18 D 95.971, p < .001) and the task (F1, 9 D11.331, p < .01). The total adjustment time was increasingly

longer from the 20% through to the 60%magnitudes (20% and

40%, 60%: p< .001; 40% and 60%: p< .05), and being longer

for force generation than relaxation at all magnitudes (p< .01).

Overall, the adjustment time increased as the magnitude

of force increased for both tasks, whereas the reaction time

tended to decrease as the magnitude increased. Comparing

the two tasks, the adjustment time and the total adjustment

time were consistently shorter for force relaxation than gen-

eration at all magnitudes.

The means and standard deviations of the peak RFD and the

time to peak RFD for all participants during both tasks are

shown in Fig. 6. Peak RFD was influenced by a significant

main effect of the magnitude of force (F2, 18 D 52.141, p <

.001) and the task (F1, 9 D 23.110, p < .01). For both tasks,

peak RFD significantly increased from the 20% through to the

60% magnitudes (20%, 40%, and 60%: p < .001; 20% and

40%: p < .01), with a significantly higher peak RFD for force

relaxation than generation at all magnitudes (p< .01). Time to

peak RFD was influenced by a significant interaction (F2, 18 D11.930, p< .001) and a main effect of the magnitude (F2, 18D27.239, p < .001) and of the task (F1, 9 D 36.622, p < .001).

Time to peak RFD was significantly longer for the 40% and

60% than the 20% magnitudes for the force-generation task

(40%: p< .001; 60%: p< .01). As well, the time to peak RFD

was significantly longer for force generation than force relaxa-

tion at all magnitudes (20%: p< .01; 40% and 60%: p< .001).

Overall, for the force-generation task, peak RFD

increased as the magnitude increased, which was associated

with an increase in the time to peak RFD. In contrast, for

the force-relaxation task, as the magnitude increased,

although the peak RFD increased, the time to peak RFD

remained constant. Comparing the two tasks, the relaxation

task showed greater peak RFD than the generation task,

while the generation task showed longer time to peak RFD

compared to the relaxation task at all magnitudes.

Force Wave

Representative average force waves during the adjustment

time for all magnitudes and for the two tasks are shown in

Fig. 7. Of note, each force wave is contributed by a different

participant. For analysis, we used the average force wave for

each participant, without consideration for outlying values.

Two patterns of force waves were observed, the first (pattern

A

B

0

100

200

300

400

500

G R G R G R

20 40 60

Reac

�on

�me

(ms)

magnitude

***

**

0

100

200

300

400

500

600

700

G R G R G R

20 40 60Ad

just

men

t �m

e (m

s)magnitude

******

***

†† ††††

C

0

200

400

600

800

1000

1200

G R G R G R

20 40 60

Tota

l adj

ustm

ent �

me

(ms)

magnitude

****

***

†† ††††

Adjustment �me Reac�on �me

FIGURE 5. Mean values and standard deviations of (A)the reaction time, (B) adjustment time, and (C) total adjust-ment time. *: Significant difference between the magnitudeof the force controlled, *: p <.05, **: p <.01, ***: p<.001. y: Significant difference between the tasks, yy: p<.01.

6 Journal of Motor Behavior

C. Ohtaka & M. Fujiwara

A) having a different slope for each of the three magnitudes

(Fig. 7A), with the slopes being comparable at all three magni-

tudes in the second pattern (pattern B; Fig. 7B). Based on these

findings, and using a one-way repeated measures ANOVA for

both tasks, we classified the force waves into these two patterns

for both tasks (Ohtaka & Fujiwara, 2016). For the force-gener-

ation task, pattern A was consistently identified for all partici-

pants. By comparison, for the force-relaxation task, pattern A

was identified in 2/10 participants, with pattern B identified in

the other 8 participants. Therefore, the ratio of pattern A to pat-

tern B was 10:0 for force generation, compared to 1:4 for force

relaxation.

Discussion

With a focus on force control, we describe the character-

istics for the control of force generation and relaxation for

the lower limb. Moreover, we compared the characteristics

of force control for the lower limb to those previously

described for the upper limb (Ohtaka & Fujiwara, 2016).

The Accuracy of Force Control

In terms of force generation, at the 20% magnitude, force

level overshot the target level (Fig. 3A), with the magni-

tude of error being significantly higher than at the 40%

magnitude (Fig. 4A). This finding is indicative of a lower

accuracy of force generation at lower than mid-levels of

magnitude, which is opposite to the control characteristics

for the upper limb. However, our findings were consistent

with previous studies which have reported an increase in

self-reported sensation of effort (and hence greater error) to

control higher magnitudes of mechanical force during a

graded handgrip task (Stevens & Mack, 1959) or an

increase in jump distance task (Sadamoto & Ohtsuki,

1977). Therefore, the error in generated force (objective) is

influenced by the magnitude of force to be controlled

(subjective).

In terms of force relaxation, for the 20% and 40% magni-

tudes, force level undershot the target force level greatly

(Fig. 3B), with the magnitude in force error being signifi-

cantly higher than at the 60% magnitude (Fig. 4A). More-

over, the variability of force relaxation was also

significantly higher at the 20% and 40% magnitudes than at

the 60% magnitude (Fig. 4C). Consistent with previous

findings for the upper limb, we demonstrated greater diffi-

culty in accurately controlling force relaxation than genera-

tion at low magnitude in the lower limb. Therefore, the

error in force control (objective) is influenced by the magni-

tude of force to be controlled by muscle relaxation

(subjective).

Furthermore, at the 20% magnitude, the error was signifi-

cantly greater for force relaxation than for force generation

(Fig. 4). In other words, accurate control at low magnitude

of force is more difficult for force relaxation than for force

generation. Several studies have demonstrated that decreas-

ing isometric force results in greater variability in force and

timing than for increasing isometric force (Harbst et al.,

2000; Masumoto & Inui, 2010; Moritou et al., 2009;

Spiegel et al., 1996). Harbst et al. (2000)) investigated how

children and adults control force and timing using periodic

isometric bimanual self-paced pinch tasks of 10–30% MVF

and 20–40% MVF. Masumoto and Inui (2010) also exam-

ined the control of force and timing utilizing a periodic iso-

metric force task of the right index finger in adults. They

related the variability in force and timing to the isometric

condition of the task itself. Specifically, as force is pro-

duced without an overt change in muscle length during an

isometric contraction, the proprioceptive feedback of force

is reduced, which would contribute to the variability in

maintaining a consistent force output. That this variability

is greater in the force relaxation than force generation task

reflects the further decrease in tactile cues on the index and

thumb as the magnitude of force of the pinch is decreased

under force relaxation. Although these studies used rela-

tively small force levels, our findings were consistent with

the outcomes of these studies, as well as for larger forces at

A

B

0

100

200

300

400

G R G R G R

20 40 60

Tim

e to

Pea

k RF

D (m

s)

magnitude

†† ††††††

*****

0

1000

2000

3000

4000

5000

G R G R G R

20 40 60

Peak

RFD

(N/S

)

magnitude

†† ††††

******

**

FIGURE 6. Mean values and standard deviations of (A)peak rate of force development and (B) time to peak rate offorce development. *: Significant difference between themagnitude of the force controlled, **: p <.01, ***: p<.001. y: Significant difference between the tasks, yy: p<.01, yyy: p <.001.

2018, Vol. 0, No. 0 7

Force Control Characteristics

the upper limb (Ohtaka & Fujiwara, 2016), confirming the

greater difficulty in controlling force relaxation than gener-

ation. However, we did identify a specific difference

between force control between the upper and lower limbs.

Specifically, at the 60% magnitude, errors in force genera-

tion were significantly higher compared to those for force

relaxation, with errors being comparatively higher for force

relaxation than generation at the 20% magnitude (Fig. 4B,

Fig. 4C). Therefore, the magnitude of error and variability

in force control decreases as the target force level

approaches 0%, regardless of the direction of force control,

which likely reflects the better estimation of effort that

enhances force reproducibility.

The Quickness of Force Control

The reaction time was shorter for the 60% magnitude

than for the 20% and 40% magnitudes, for both force gener-

ation and relaxation (Fig. 5A). Using an isometric pinch

grasp task, Haagh, Spijkers, Boogaart, and Boxtel (1987)

reported a negative correlation between the premotor reac-

tion time and the peak amplitude of force. Our findings

were consistent with this previous finding, indicative that

the quickness of force control improves as the magnitude of

force to be controlled increases for the lower limb. This

inverse association between reaction time and the magni-

tude of force to be controlled was significant for force

relaxation. This might reflect differences in the complexity

of control for high and low magnitude forces. Specifically,

for high magnitudes of force, the control of force is first ini-

tiated, with adjustments to the target level following. How-

ever, for low magnitudes of force, the control of force and

the final adjustment to the target level must occur concur-

rently, which would increase the reaction time as attention

must be paid to both components of force control. How-

ever, we did not identify differences in reaction time

between force generation and relaxation at high force mag-

nitudes (Fig. 5A). This finding is in contrast to the findings

of Buccolieri, Avanzino, Trompetto, and Abbruzzese

(2003) who reported reaction time to be shorter for force

relaxation than for force generation for the proximal

muscles of the arm (biceps brachii and triceps brachii). In

contrast, for the lower limb, the quickness of force control

was comparable for both force generation and relaxation.

This difference between the upper and lower limb might

reflect differences in absolute force capacity, with the MVF

being greater for the lower limb than upper limb.

The adjustment time for both force generation and relax-

ation increased from the 20% through to the 60% magni-

tude as well as being positively associated to the magnitude

of force to be controlled (Fig. 5B). This finding is consis-

tent with those of previous studies (Bahill et al., 1975; Got-

tlieb et al., 1989; Ono, Okada, Kizuka, & Tanii, 1997), and

is indicative of a common effect of force magnitude on

adjustment time for the upper and lower limbs and this for

both force generation and relaxation. As well, the

Force genera�on Force relaxa�on A

B

0

800

Forc

e (N

)

Time 100ms

0

800

Forc

e (N

) Time

100ms

0

800

Forc

e (N

)

Time 100ms

FIGURE 7. Ensemble average of the force waves for force generation and force relaxation of (A) a pattern with different inclina-tions and (B) a pattern with the same inclinations, shown for three force magnitudes: 20% (light gray line), 40% (dark gray line),and 60% (black line).

8 Journal of Motor Behavior

C. Ohtaka & M. Fujiwara

adjustment time was consistently shorter for force relaxa-

tion than generation at all magnitudes, this consistency in

the lower limb being different than for the upper limb.

When we consider that peak RFD was greater for force

relaxation than generation at all magnitudes, we confirm a

quicker control of force relaxation than generation, with a

greater control of force per unit time than for force

generation.

The Force Control Strategy

Applying findings of force control process and peak

RFD for the upper limb (Ohtaka & Fujiwara, 2016), we

identified two control strategies that were differentially

used for force generation and relaxation (Fig. 8). For force

generation, a single strategy was observed, in which tim-

ing and RFD are controlled for different magnitudes

(Fig. 7A, Fig. 8A). In other words, the force is controlled

by changing the RFD from the beginning of the adjust-

ment for each magnitude. This pattern is similar to the

pulse height control strategy which has previously been

described (Freund & B€udingen, 1978; Ghez, 1979; Gordon& Ghez, 1987; Gottlieb et al., 1989), and is comparable to

the control strategy of force generation of the upper limb

(Ohtaka & Fujiwara, 2016). In contrast, for force relaxa-

tion, two strategies were observed, namely, the control of

timing and RFD, as for force generation, and control of

only timing, irrespective of the magnitude (Fig. 7B,

Fig. 8B). Thus, the force is controlled by a fixed RFD,

which is determined from the onset of the adjustment time

for each magnitude. The concomitant control of timing

and RFD is similar to the pattern of control for force

relaxation which has previously described (Bahill et al.,

1975; Gottlieb et al., 1989), and is comparable to the strat-

egy for the upper limb (Ohtaka & Fujiwara, 2016). Of

note, however, was the obvious difference in the pattern

of control for force generation and relaxation in the lower

limb, which was quite different than previously reported

findings for the upper limb. Specifically, all participants

selected to control both the timing and RFD of force gen-

eration, while controlling only timing for force relaxation.

The control of both timing and RFD would provide a

quicker and more accurate control of force generation,

compared to force relaxation. It might be that as force

relaxation is more difficult to control at the level of the

muscle, opting for a strategy that controls only timing

(rather than control of both timing and RFD) might lower

the attentional demand required. The effect of the differ-

ence in control strategy for force generation and relaxation

on peak RFD and time to peak RFD is clearly evident in

Fig. 6, with peak RFD being greater for force relaxation

than force generation (Fig. 6A), with the time to peak

RFD being almost twice as short for force relaxation than

force generation (Fig. 6B). The fact that a higher RFD is

organized more quickly likely explains the decrease in

accuracy of force relaxation as magnitude was decreased

to 20% (requiring a greater change in force per unit of

time). This finding is comparable to the strategies that

have previously been reported for the upper limb, and

agree with the mechanism of a speed-accuracy trade-off

that has previously been well described (Fitts, 1954;

Schmidt, 1982). Therefore, although participants can

Force genera�on Force relaxa�on A

B

0% MVF

60% MVF

40% MVF

20% MVF

Forc

e

Peak RFD

60% MVF

0% MVF

20% MVF

40% MVF

60% MVF

0% MVF

20% MVF

40% MVF

Time

Peak RFD

Peak RFD

FIGURE 8.Motor strategies for force generation and force relaxation focused on the force wave and peak RFD of (A) a strategy tocontrol both the time and RFD and (B) a strategy to control only the time. “Peak RFD” in the figure shows the time at which peakRFD occurred. The peak RFD occurred in the latter half of the adjustment time for all magnitude in the force-generation task, butoccurred during the early stage of the adjustment time for all magnitudes in the force-relaxation task.

2018, Vol. 0, No. 0 9

Force Control Characteristics

quickly control force relaxation at higher RFD, this comes

at a cost of lower accuracy due to the short time available

to organize the force response.

With regard to the issue of lower accuracy with force

relaxation than generation, differences in motor unit

recruitment and derecruitment must also be considered.

According to Henneman’s size principle (Henneman, Som-

jen, & Carpenter, 1964), during ramped force generation,

smaller motor units are recruited before larger ones. In con-

trast, during force relaxation, motor units are derecruited in

reverse order, from the largest to the smallest motor units

(Latash, 1998). This reverse order would further contribute

to the lower accuracy for force relaxation than generation,

as the early derecruitment of large motor units would not

allow rapid adjustments in force level. Several studies have

previously reported greater variability in the force and tim-

ing of force relaxation than generation (Harbst et al., 2000;

Masumoto & Inui, 2010; Moritou et al., 2009), but without

providing insight onto possible mechanisms. We provide

evidence for the lower limb that this variability likely

reflects a trade-off of control speed during force relaxation,

compared to force generation, with this effect being greater

for the lower than upper limb.

The following limitations of this study are recognized.

Foremost, we did not consider the effect of providing feed-

back of force and of visual feedback of the target force lev-

els on the characteristics of force generation and relaxation.

In future studies, we also should compare force control

characteristics for the upper and lower limb at the same

magnitude of force in each force direction to reliably evalu-

ate differences in accuracy, quickness and strategy.

In conclusion, the findings of the present study indicate

marked differences in the accuracy, quickness, and motor

control for force generation and relaxation for the lower

limb, which were not evident for the upper limb.

Verification of the Hypotheses

Force Generation

Accuracy of force generation is lower for low than high

magnitudes of force output. Moreover, quickness and reac-

tion time are negatively associated with the magnitude of

force output, with the adjustment time being dependent on

the control strategy selected. Accuracy can be improved by

controlling both timing and RFD, which is a strategy that is

consistently used for force generation.

Force Relaxation

Again, accuracy decreased as the magnitude of force

decreased. With regard to quickness, reaction time was neg-

atively associated with force magnitude. Again, adjustment

time varied depending on the control strategy used. A strat-

egy in which only time was controlled (with RFD remain-

ing constant) was principally used for force relaxation.

Comparison between Force Generation and Relaxation

The magnitude of error in controlling the target force

level was significantly higher for force relaxation than force

generation, especially at low magnitudes of force. Reaction

time and adjustment time (which together characterize

quickness) were independent of the direction of force con-

trol (generation or relaxation). However, the control strat-

egy was markedly different for force relaxation and

generation, with consequent differences in peak RFD and

the time to peak RFD. This tendency was particularly evi-

dent for the lower limb compared to the upper limb.

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Received October 24, 2017Revised April 2, 2018

Accepted April 28, 2018

2018, Vol. 0, No. 0 11

Force Control Characteristics