Article history:Received 21 July 2011Received in revised form 20 March 2012Accepted 25 March 2012Available online 23 May 2012
PsycINFO codes:233023402343
Keywords:Fitts' lawSpeed-accuracy trade-offCyclical and discrete controlExtended practice
An experiment was designed to determine the degree to which reciprocal aiming movements of the wristand arm with various accuracy requirements (Fitts' tasks) are enhanced by extended practice. The vastmajority of research on motor learning shows performance improvement over practice. However, literatureexamining the effect of practice on Fitts' task performance is limited and inconclusive. Participants wereasked 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 aspossible. 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) of1.5, 3, 4.5, and 6. Contrary to the earlier reports, after 20 days of practice, we found minimal changes inmovement time or the movement time–ID relationships for the arm and wrist over practice. However, thevariability in the movement endpoints decreased over practice and wrist movements at ID=6 werecharacterized by shorter movement times and longer dwell times relative to armmovements with dwell timefor the wrist increasing over practice. These data are consistent with the notion that Fitts' tasks provide astable measure of perceptual-motor capabilities.
Paul M. Fitts' now classical paper published in 1954 entitled “TheInformation Capacity of the Human Motor System in Controlling theAmplitude of Movement” has played an important role in stimulatingresearch and theory on the production of movements of varyingdifficulty. Fitts noted that when participants attempted to move backand forth between two targets that decreases in target width (W)and/or increases in movement amplitude (A) resulted in increasedattentional demands and increased average movement time (MT).This finding led Fitts to develop an index of difficulty (ID) which heproposed was a result of the number of bits of information needed tobe processed to effectively produce the desired level of accuracy. TheID for a given task was determined by the equation Log2(2A/W),where A represents the movement amplitude measured from onetarget center to the other target center andW represents the width ofthe target area in the direction of the movement. Thus, MT across avariety of IDs can be represented in the equation MT=a+b (ID)which yields the nearly ubiquitous linear relationship now charac-teristic of a Fitts' task. In the years following the completion of Fitts'initial experiments, investigators began replicating with great success
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his findings using reciprocal aiming tasks (e.g., Andressien, 1960;Annett, Golby, & Kay, 1958; Crossman, 1960; Vredenbregt, 1959)with numerous replications continuing to the present time (e.g.,Boyle & Shea, 2011; Kwon, Zelaznik, Chiu, & Pizlo, 2011; Wu, Yang, &Honda, 2010).
According to Fitts (1954) original explanation of the speedaccuracy trade-off movement time increases as a function of theadditional bits of information that have to be processed to achieve thetask demands (Shannon & Weaver, 1949). More recent experimentsrelated to Fitts' law have concentrated on the controls processes useto produce the required movements. Single (Beggs & Howarth, 1970,1972) and iterative correction (Keele, 1968) models propose that theinitial phase of the movements were preprogrammed with single oriterative feedback based corrections responsible for achieving thetarget position. Thus, higher ID movements required more time toprocess feedback and formulate corrections than lower ID move-ments. A number of years later Meyer, Kornblum, Abrams, Wright,and Smith (1988) formulated an optimized submovement modelwhich was based on the notion that faster and longer movementsrequired the generation of greater forces than slower and shortermovements and that greater forces exhibited greater output variabil-ity. This proposal maintained that the greater the forces required toaccelerate and decelerate the limb, the greater movement variabilityultimately leading to larger effective target widths. More recentlyWolpert and colleagues (e.g., Davision & Wolpert, 2005; Harris &Wolpert, 1998; Maill & Wolpert, 1996) have proposed internal orforward models which propose that the nervous system compares the
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efferent commands sent to the muscles with an efference copy of thedesired commands in order to generate rapid adjustments through afeedforward process when discrepancies arise. This coupled with aprocess that monitors feedback generated by themovement in order tocompare this with an internal representation of the expected sensoryconsequences of the movement also allows for earlier and moreeffective corrective movements than proposed in earlier models.Through practice the internal model is thought to be refined resultingin enhanced performance with increased practice. In addition, HarrisandWolpert (1998) proposed that “neural control signals are corruptedby noise whose variance increases with the size of the control signal”(p. 780). Given the variability arising from this state dependent noise,they argue that eye and arm trajectories are selected that minimize thevariance of movement endpoints. Recently, Brenner and Smeets (2012)have provided evidence suggesting that near optimal performance isnot contingent on explicit knowledge of this variability.
Importantly, even though Fitts original findings have undergone anincredible amount of experimental scrutiny and additional explana-tions for the findings have emerged over the last 50+ years, thefundamental relationship between MT and ID noted in Fitts' originalproposal have withstood the test of time with very few exceptions tothis relationship noted in literature (e.g., Adam, Mol, Pratt, & Fischer,2006; Fernandez & Bootsma, 2008; Kovacs, Buchanan, & Shea, 2008).The primary question to be addressed in the present paper centers onthe changes that occur in the performance of reciprocal wrist and armFitts' tasks as a result of extended practice. Motor tasks are almostuniformly characterized by improved performance over practice andthis has been repeatedly documented in themotor learning literature atleast since the early work of Woodworth (1899). According to Fitts(1954) original explanation of the speed accuracy trade-off, however,movement time increases as a function of the additional bits ofinformation that have to be processed to achieve the task demands(Shannon &Weaver, 1949). That is, if the rate at which information canbe processed is constant then a participant must compensate forincreases in amplitude and/or decreases in target width by increasingmovement time so that the information required to achieve the targetcan be processed. If movement time is maintained at a level that doesnot permit the relevant information to be processed errors would beexpected. Thus, if information processing capacities could somehow befunctionally increased, the amount of processing required reduced, orprocessing becomes more efficient through practice, movement timewould be decreased with proportionally greater decreases at higher IDsthan lower IDs. This would result in decreased slopes over extendedpractice. If the processing capacity remained constant, however, andthere was noway to effectively reduce the amount of information to beprocessed, movement time would be unaffected by additional practice.
Another possible change that could occur as a result of extensivepractice is that the control processes change such that more efficientcontrol schemes replace less efficient ones resulting in fastermovementtimes. Numerous theoretical perspectives argue that the processingand/or control of movements change as a result of practice (e.g., Elliott,Hansen, Mendoza, & Tremblay, 2004; Glover, 2004; Hikosaka et al.,1999; Schmidt, 1975; see Elliott et al., 2010 for recent review)presumably resulting in more efficient movement control. Wolpert,for example, has argued that the internal model is refined or tuned as aresult of practice and that movement trajectories are chosen tominimize endpoint variability. There are also clear indications in theliterature that control processes are different for the lower and higherIDs (e.g., Buchanan, Park, & Shea, 2006; Guiard, 1993, 1997; Mottet &Bootsma, 1999) and these control processes may be modified withadditional practice (Buchanan, Park, & Shea, 2004). Note that lower IDmovements in reciprocal Fitts' tasks are often characterized as harmonicmotionwith values for harmonicity (H) of 1 indicating the lack of subtlecorrections in the movement trajectory as the participant approachesthe target, approximately the same proportion of time devoted toacceleration and deceleration, and little if any dwell time present at
movement reversal. Alternatively, higher ID movements are charac-terized by additional zero crossings in velocity indicating on-lineadjustment to the movement trajectory resulting in values for H≈0,a greater proportion of movement time utilized in the decelerationphase than acceleration phase, and increased dwell times. Thesefindings are consistent with a shift from cyclical units of action toconcatenated series of discrete units of action as the ID is increased.Using a target width scaling paradigmwhere the ID was increased ordecreased during a trial, Buchanan and colleagues (Buchanan et al.,2004, 2006) found that participants transitioned from cyclical todiscrete or vice versa between ID=4.0 and ID=4.9. This finding ledthem to propose IDc≈4.5 as a critical boundary where movementvariability is increased prior to transition to an alternative mode ofcontrol. Further, the Buchanan et al. (2004) data for two days ofpractice indicated that additional practice resulted in a modest shiftin the critical boundary to higher IDs on the ID continuum. Inaddition, they proposed that movement of the wrist and fingers, forexample, may exhibit a critical range that is at slightly higher IDsthan that observed for arm movements.
Discrete single joint movements to a target often termed “discreteFitts tasks”have also been studied across practice. Corcos and colleagues(Corcos, Jaric, Agarwal, & Gottieb, 1993; Jaric, Corcos, Agarwal, &Gottieb, 1993) investigated the myoelectric and mechanical changesacross practice as participants attempted to move to a target as fast aspossible (A=54°, W=3, ID=5.16). Prior to practice and followingextended practice they also administered tests at IDs=3.58, 4.58, 5.16,5.58, and 5.90 by varyingA andholdingW=3° constant. Over the sevenpractice sessions with the ID=5.16 task, each session consisting of 10blocks of 20 trials, participants reducedmovement time, increased peakvelocity, and decreased the proportion on time spent decelerating (alsosee Elliott et al., 2004; Gottieb, Corcos, Jaric, & Agarwal, 1988; Jaric,Corcos, & Latash, 1992). These changes were accompanied by fasterbuild-up of EMG activity in the agonist muscle and an earlier andmore focused activity of the antagonist muscle. Movement timeperformances for the five participants on the pre- and post-testwere variable. While movement time on the practiced task(ID=5.16) generally improved across participants, the analysis ofmovement time on the pre- and post-tests across the range of IDsfailed to detect a main effect of practice or a Distance×Practiceinteraction. The standard deviation of the final position and peakvelocity were reduced over practice indicatingmore stable performance,but movement time was not significantly reduced.
What these findings indicate is that some changes in processingand control appear to occur over practice but the extent to whichthese changes directly influences movement time and the movementtime–ID relationship is not clear. Indeed, the relevant question withinthe context of this paper is do these changes also result in decreasedmovement time resulting in changes in the intercept, slope, orlinearity of the movement time–ID relationship. The lack of under-standing of changes that might occur as a result of extended practice isillustrated in the following quote:
“The slope of the Fitts equation can be reduced considerably withpractice: B. Kelso (1984) found that the slope was reduced to nearlyzero following 40,000 trials conducted over 20 days of practice”(Schmidt & Lee, 1999, p175).
Clearly, the slope of the movement time–ID relationship could notbe reduced to near zero over extended practice. This would result insimilar movement times for low and high ID conditions which do notseem reasonable even following extensive practice.
A secondary question addressed in the present experiment iswhether changes over practice, if any, are the same for wrist andelbow movements. Fitts (1954), for example, hypothesized that“the motor system probably varies considerably for different
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movements, limbs, and muscle groups.” The wrist and fingers werethought to be capable of exhibiting more precise control thanthe arm or leg due to presumed differences in the innervationcharacteristics of the various effectors in the motor cortex (Fitts,1954; Penfield & Rasmussen, 1950). In addition, Henneman (1957)noted that the recruitment of smaller motor units like those in thewrist or fingers offers greater force control than the recruitment oflarge motor units like those in the leg or arm. Even though thesehypotheses were proposed over 50 years ago, little research hasdirectly examined this question and the limited number of studiesthat have contrasted the use of different effectors in Fitts' type taskshave yielded conflicting results (e.g., Balakrishnan & MacKenzie, 1997;Langolf, Chaffin, & Foulke, 1976; Pfann, Hoffman, Gottlieb, Strick, &Corcos, 1998; Smits-Engelsman, Van Galen, & Duysens, 2002). Langolfet al. (1976), for example, studied finger, wrist, and arm movementsusing Fitts' peg transfer and reciprocal tapping tasks. Their results wereconsistent with Fitts' original claim and concluded that the MT–IDslopes forfinger andwrist performanceswere flatter than that found forthe arm. In other words, arm movements were slower than finger andwristmovements for the same ID and this difference increased as the IDincreased. However, more recent experiments by Balakrishnan andMacKenzie (1997) failed to detect movement time differences acrosseffectors and concluded that the number of bits that must be processedto support fingers, wrists, and armsmovements in a Fitts aiming task isnot significantly different. Balakrishnan andMacKenzie argued that thesmall sample size in Langolf and colleagues' study may have been acritical factor in explaining the reason that their results differed.Another argument raised by Kovacs et al. (2008) for Langolf andcolleagues' results was that the tasks the participants were asked toperformusing thewrist and finger, but not the arm,were presented in avisually amplified (10×) environment with participants lookingthrough a stereomicroscope to perform the wrist and finger tasks.Recent work by Kovacs et al. (2008) demonstrated that an increase inthe visual gain of a Fitts' task can functionally decrease MT at high IDs(ID>4.5). Similarly, Fernandez and Bootsma (2008) (also see Brenner &Smeets, 2012) found increasing advantages of applying a non-lineargain to the movement feedback as the ID increased. Thus, altering thevisual feedback provided in the task display may influence the amountof information that has to be processed and/or the control processesused to produce the movements. The result is changes in movementtimes at higher IDs.
Alternative explanations have been formed through EMG analysisof single degree of freedom wrist, elbow, and ankle joint motion.Pfann et al. (1998), for example, had participants make singlemovements over differing distances at variable speeds (fast aspossible, comfortable, inertial load). They concluded that no differ-ences in muscle activation patterns were found when comparingeffectors. These findings led the researchers to “conclude that acommon set of control rules is used at different joints…” and thebiomechanics (i.e. viscoelastic properties, strength) of the engagedeffector (e.g., Hoffmann & Hui, 2010), determine the controlproperties of the movement. Similar conclusions were formed byCharles and Hogan (2010) when they examined path shape during“fast” and “comfortable” wrist rotation and arm movement. Theirfindings show differences in the path utilized by the wrist and armand concluded that these differences can, in part, be attributed todifferences in the biomechanical constraints of the two effectors.
Recently Boyle and Shea (2011) tested participants with the wristand arm in an attempt to account for the differences in findingsbetween Balakrishnan andMacKenzie (1997) and Langolf et al. (1976).Balakrishnan and MacKenzie (1997) failed to find differences betweenwrist and armmovements in a Fitts' task and Langolf et al. (1976) founda reduced slope for the wrist relative to armmovements. The Boyle andShea results indicated that one reason for the conflicting resultswas dueto differences in themanner in whichmovement timewas determined.In the Balakrishnan andMacKenzie's experiments movement time was
determined from the beginning of one movement to the beginning ofthe next. While this was consistent with the way Fitts originallydetermined movement time, this method includes dwell time in themovement time calculation. In the Langolf et al. experimentsmovementtime was determined from the time in which the participant left onetarget to the time they made contact with the next target. Thisdetermination excludes dwell time from the movement time calcula-tion. Note that most Fitts' type experiments today determine move-ment time based on kinematic measures. In these cases, movementtermination is determined by searching forward from the point atwhich peak velocity occurs until velocity decreases to a preset level (5or 10% of peak velocity). Similarly, movement onset is determinedby searching backward from peak velocity until the preset valuewas attained. Thus, this measure of movement time (termination–initiation) does not include dwell time. What Boyle and Shea (2011)found was similar movement times for the wrist and arm movementswhen movement time included dwell time but decreased movementtime for the wrist at the higher IDs when movement time excludeddwell time. The reason for this difference was that dwell time for thewrist increased substantially more at higher IDs than for higher ID armmovements.
In summary, a limited number of studies have investigated theeffect of practice on Fitts' tasks across a variety of ID and effectors.Thus, the purposes of the present experiment were two fold. Theprimary purpose was to determine the changes that occur in themovement time–ID relationship in a reciprocal Fitts' tasks as a resultof practice. The secondary purpose was to determine if differencesacross practice exist for wrist and arm movements. Contrary toreports of substantial decreases in slope with extended practice(Schmidt & Lee, 1999), we predicted minimal improvement for thearm task. However, given the innervation differences in the arm andwrist where the muscles controlling the wrist are thought to becomposed ofmore but smallermotor units than themuscles controllingarm movements, we predict improved performance for wrist tasksespecially at the higher IDs. We make this prediction based on thenotion that more practice may be required to efficiently manage theincreased control complexity resident in the muscles controlling wristmovements.
2. Method
2.1. Participants
Self-declared right-handed students (N=5: 4 males and 1female: M=24.8 years, SD=3.71 years) with normal or corrected-normal-vision volunteered to participate in the experiment afterreading and signing a consent form approved by the local IRB for theethical treatment of experimental participants. The participants hadno prior experience with the experimental task and were not awareof the specific purpose of the study.
2.2. Apparatus
The apparatus consisted of a horizontal lever supported at theproximal end by a vertical axle that turned in a ball-bearing support.The support was affixed to the right side of the midline of the tableallowing the lever to move in the horizontal plane over the table. Atthe distal end of the lever for the arm condition a vertical handle wasfixed. The handle's position was adjusted so that when grasping thehandle the participant's elbow was aligned with the axis of rotation.The lever used for the wrist condition also had a vertical handlewhich was positioned much closer to the axis of rotation. Thehandle's position in the wrist task was adjusted so that, whengrasping the handle, the participant's wrist was aligned with the axisof rotation. A single turn potentiometer (resolution .02%) wasattached to the lower end of the axis to record position of the lever
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and its output was sampled at 200 Hz. A wooden cover was placedover the table to prevent participants from seeing the lever and theirarm. A video projector was used to display the targets and a cursorindicating the position of the lever on the wall facing the participant.Extension resulted in the cursor moving up the display and flexionmoved the cursor down. Participants were seated at about 2 m fromthe wall and a 1.64×1.23 m image was projected on the wall (seeFig. 1A and B, top). A height adjustable chair ensured the participantshorizontal eye line corresponded with the midway point of the twotargets.
2.3. Procedure
Participants completed 20 practice sessions with the constraintthat each session was completed on a separate day. Each sessionconsisted of the same practice routine. Prior to each session theparticipant was encouraged to reduce their movement time whilemaintaining their error rate at less than or equal to 10%. During eachpractice session participants were seated at a table with their forearmor wrist (depending on the condition) resting on a horizontal leverthat restricted elbow/wrist motion to flexion–extension in thehorizontal plane (Fig. 1A and B, bottom). In the wrist condition theforearm was placed in a restraint to ensure only wrist motion wasused. The position of the handle for both effectors was adjusted toensure the participants' elbow or wrist joint (depending on thecondition) was centered over the axis of rotation. Flexing the elbowor wrist horizontally moved the lever toward the body and extendingthe elbow or wrist horizontally moved the lever away from the body.Note that as the participant moved their arm or wrist the cursor,indicating the position of the limb, left a trace indicating the currentand prior movement of the cursor (see Fig. 1, top). Extension causedthe cursor to move up on the display and flexion caused the cursor tomove down. The cursor and two targets were generated with customsoftware and displayedwith a projectormounted above the participant.
In all sessions the movement amplitude for the right arm andwrist was fixed at 16° and four target widths (11.3°, 4°, 1.415°, and.5°) were used to create four ID conditions (IDs=1.5, 3, 4.5, and 6).The participants moved the horizontal lever back and forth so that thecursor projected on the wall in front of themmoved between the twotarget areas. The two targets were defined by two shaded rectangularshaped areas enhanced by a black background. In each practice
Fig. 1. Illustration of the feedback projection (top–front view) and movement set-up (bottomwas displayed as a cursor with trace and the targets were indicated by the shaded areas.
session the participants initially performed three consecutive 15 sec-ond practice trials at one of the four ID (1.5, 3, 4.5, and 6) conditionswith either the arm or wrist before being tested at the next IDcondition using the same effector. Participants were challenged tomove as fast and accurately as possible on each trial. A 15 s restinterval followed each trial. After completion of all trials with each IDcondition for one effector, the participant switched to the othereffector (arm or wrist depending on the initial effector used) in orderto complete three trials under each ID condition resulting in 12 totaltrials for the wrist and 12 total trials for the arm. Participantscompleted 20 sessions over a period of 60 days with no more than onesession per day. Prior to each session participants were encouraged totry to reduce their movement times from the previous session withoutsacrificing accuracy.
2.4. Measures and data analysis
Movement time (MT), dwell time (DT), percent time to peakvelocity (%TTPV), and endpoint variability (VE) were computed fromthe potentiometer signal. Prior to analysis, the displacement timeseries was dual-passed filtered (Butterworth, 10 Hz). A three-pointcentral difference algorithm was used to compute velocity. Thedisplacement and acceleration signal were then mean centered bysubtracting out the mean of each signal from the signal itself. Thesignals were then normalized by their maximum values (positive ornegative) in order to plot themwithin the samewindow and facilitatecomparisons. All dependent measures of movement extension orflexion were computed on a half-cycle basis (see Fig. 2). In each halfcycle, peak velocity (PV) of the movement was identified and tracedback to 2.5% of its value following the previous movement reversal todetermine movement onset. Movement offset was calculated bytracing forward from peak velocity to a value of 2.5% of peak velocitybefore reversal for the next movement. Variable error (VE), a measureof endpoint variability, was determined as the standard deviation ofthe location at movement offsets about their ownmean. Using VE as ameasure of the function target width, we also calculated an ID' whichwas determined as 2A/VE. Dwell time was calculated by the equationDT=movement onseti+1−movement offseti. Utilizing the parame-ters of movement onset, offset and dwell time, movement time (MT)was calculated from the onset of one movement to the offset of thatmovement and thus, excludes dwell time (MT=movement offseti−
–top view) for the arm (A) and wrist (B) conditions. Note that the position of the limb
Fig. 2. Illustration of normalized arm (A) and wrist (B) displacements and velocity at ID=6. Note that movement initiation (triangle), peak velocity (circle), and movementtermination (square) are provided. ID=6 is used in the illustration because of the unusual waveform produced by participants using the wrist.
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movement onseti). Percent time to peak velocity was determined bythe equation, %TTPV=(PVi−onseti) /(offseti−onseti) where PVi isthe time at which peak velocity occurs in the half cycle.
MT, DT, %TTPV, and VE were analyzed in separate Effector (arm,wrist)×Day (1, 10, 20)×ID (1.5, 3.0, 4.5, 6) analyses of variance(ANOVAs) with repeated measures on all factors. In addition,regression analyses were conducted for each participant on eachday of practice using MT at each ID and MT at each ID' to determinethe intercepts and slopes and to determine if a linear relationshipbetween MT–ID and MT–ID' best fit the data for each day and effectorcombination. Duncan's new multiple range tests and simple maineffects analyses were utilized when appropriate as post-hoc pro-cedures to follow up on significant main effect and interactions,respectively. An α=.05 was used for all tests.
3. Results
The data from Trial 3 at each ID and effector condition for eachparticipant were subjected to analysis unless the error rate for thattrial was greater than 10%. An error occurred in the event thatmovement endpoint was outside the target area. In the event that theerror rate for Trial 3 exceeded 10%, the data from Trial 2 was used foranalysis. The error rate on Trial 3 exceeded 10% for only oneparticipant on Day 1. On Days 10 and 20 all participants met theerror rate condition on Trial 3.
Examples of normalized displacement and velocity profiles for thearm (A–D) and wrist (E–H) movements at IDs 1.5 and 6, respectively,for one participant on Days 1 (left panels) and 20 (right panels) areprovided in Fig. 3. Mean MT (A), DT (B), %TTPV (C), and VE (D) byeffector, day, and ID are provided in Fig. 4. Regression lines for MT–ID
relationship for the arm (A–D) and wrist (E–H) movements acrossDays 1, 10, and 20 are provided in Fig. 5. Also included in Fig. 5 are theregression lines for the MT–ID' relationship for the arm (I–K), andwrist (M–O)movements across days. In order to facilitate comparisonacross days, the regressions lines for each method of determining IDand the two effectors are overlaid (D, H, L, P). Note that ID' wasdetermined using VE (variability of the movement endpoint whichhas been termed the functional target width) rather than thepredefined target width (W).
3.1. Movement time (MT)
The analysis indicated a main effect for the ID F(3,92)=755.53,pb .01. The Effector×ID interaction, F(3,92)=3.25, pb .05, was alsosignificant. Duncan's new multiple range test on ID indicated that MTincreased for each increase in ID. Simple main effects analysis of theEffector×ID interaction for MT failed to detect differences betweeneffectors at the 1.5, 3, and 4.5 IDs, but did determine that lowermovement times were produced for the wrist (M=860 ms,STD=109 ms) at ID=6 than for the arm (M=988 ms, STD=100 ms)at ID=6. All other main effects and interactions failed significance.
3.2. Dwell time (DT)
The analysis indicated a main effect of ID F(3,92)=139.99, pb .01,with DTs higher for the higher IDs although no difference wasdetected between IDs 1.5 and 3. The main effect of Effector, F(1,92)=37.71, pb .01, was also significant with DTs longer for the wrist(M=93 ms, STD=111 ms) than arm (M=50 ms, STD=53 ms). TheEffector×ID interaction, F(3,92)=19.67, pb .01 was also significant.
Fig. 3. Normalized displacement (black) and velocity (red) for arm (A–D) and wrist (E–H) movements at IDs 1.5 and 6, respectively, on Day 1 (left) and Day 20 (right). Note that thewindow for the ID=1.5 waveforms is shorter (2 s) than for the ID=6.0 waveforms (5 s).
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Simple main effects analysis failed to detect differences in DTbetween effectors at the 1.5, 3, and 4.5 IDs but did detect higherDTs for the wrist (M=264 ms STD=80 ms) than for the arm(M=127 ms, STD=25ms) at ID=6. All other main effects andinteractions failed significance.
3.3. Time to peak velocity (% TTPV)
The analysis indicated only a main effect for ID, F(3,92)=205.16,pb .01. Duncan's new multiple range test indicated that %TTPVdecreased for each ID as IDs increased. All other main effects andinteractions failed significance.
3.4. Variable error (VE)
The analysis indicated main effects of day, F(2,92)=18.51, pb .01,and ID, F(3,92)=69.51, pb .01. Duncan's new multiple range testsindicated that VE was reduced from Day 1 (M=1.07°, STD=0.48°) toDay 10 (M=.81°, STD=0.33°) with no further decrease on Day 20(M=0.69°, STD=0.34°) with VE larger for each increase in ID. Allother main effects and interactions failed significance.
3.5. MT–ID regression analysis with ID calculated as (2A/W)
The MT–ID regression analyses for the arm (Fig. 5A–D) indicat-ed strong linear relationships between MT and ID for the arm on Day
Fig. 4. Mean movement time (A), dwell time (B), time to peak velocity (%) (C), and VE (D) for Days 1, 10, and 20 for each effector.
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1, F(1,18)=181.69, pb .01, R2=.91, Day 10, F(1,18)=260.36, pb .01,R2=.93, and Day 20, F(1,18)=189.96, pb .01, R2=.91. The regres-sion analyses for the wrist (Fig. 5E–H) also indicated strong linearrelationships between MT and ID for the arm on Day 1, F(1,18)=161.39, pb .01, R2=.90. However, the linear relationship between MTand ID on Day 10, F(1,18)=132.71, pb .01, R2=.88, and Day 20,F(1,18)=129.47, pb .01, R2=.85, resulted in decreasing R2 values.
A Limb×Day ANOVA with repeated measures on both factors onthe slopes from the individual participants MT–ID failed to detectmain effects of limb, F(1,20)=2.24, p>.05, and Day, F(2,20)=1.14,p>.05, or a Limb×Day interaction, F(2,20)b1, p>.05.
3.6. MT–ID' regression analysis with ID calculated as (2A/VE)
Using the functional targetwidth (VE) in the determination of the IDprovides an estimate of the observed difficulty of the tasks. The MT–ID'regression analyses for the arm (Fig. 5I–L) indicated strong linearrelationships between MT and ID' for the arm on Day 1, F(1,18)=118.46, pb .01, R2=.93, Day 10, F(1,18)=101.05, pb .01, R2=.92, andDay 20, F(1,18)=93.14, pb .01, R2=.91. The regression analyses for thewrist (Fig. 5M–P) also indicated strong linear relationshipsbetween MT and ID' for the arm on Day 1, F(1,18)=88.74,pb .01, R2=.93, Day 10, F(1,18)=135.15, pb .01, R2=.90, and Day20, F(1,18)=173.48, pb .01, R2=.91.
A Limb×Day ANOVAwith repeatedmeasures on both factors on theslopes from the individual participants MT–ID' regression indicatedmain effects of limb, F(1,20)=6.02, pb .05, and Day, F(2,20)=14.70,
pb .01. In addition, the Limb×Day interaction, F(2,20)=7.90, pb .05,was significant. Simple main effects analysis failed to detect differencesin slope for the arm, but indicated that the slope decreased from Day 1to Day 20 for the wrist.
4. Discussion
We initially predicted thatmovement time for the various IDswoulddecrease with practice with the decreases for the wrist movementsproportionally larger at the higher IDs than that for the arm move-ments. These predictions were based on the notion that practicetypically results in enhanced performance, reports in the literature ofprofound decreases in slope (Schmidt & Lee, 1999) with extendedpractice, and that the motor units producing wrist movements may bebetter adapted to precise movement control but may also involvegreater control complexity than arm movements with the increasedcomplexity requiring substantial practice to be fully exploited(Henneman, 1957). Note that Boyle and Shea (2011) found that wristmovements at ID=6 were produced more quickly than arm move-ments at ID=6. In the present experiment which involved 20 days ofpractice with approximately 30,000 movements for the wrist and30,000movements for the arm, there were no indications in theMT–IDdata of a pattern of decreased intercept and/or slope for either the armor wrist across the range of IDs as a result of the extended practice.However, there were significant decreases in endpoint variability (VE)from Day 1 to Day 10 across all IDs and a significant reduction in slopefor the MT–ID' relationship for wrist movements.
Fig. 5. Data and regression lines for the movement time–ID (2A/W) relationship on Days 1, 10, and 20 for the arm (A–C) and wrist (E–G) and the movement time-ID(2A/VE)relationship determined based on the functional target width (VE) on Days 1, 10, and 20 for the arm (I–K) and wrist (M–O). Regressions lines across days are provided for the arm(D,L) and wrist (H,P) for both MT–ID and MT–ID'.
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Subtle, but perhaps important changes in the MT–ID relationshipwere noted for wrist movements over practice. Regression analysesindicated a reduction in the R2 for the linear MT–ID relationship fromR2=0.90 on Day 1 to R2=0.89 on Day 10 and R2=0.85 Day 20. Thedecreased in R2 appeared to be related to reductions over practice inMT for IDs=3 and 6, but not for IDs 1.5 and 4.5. The pattern of changein MT coupled with decreases over practice in within and between
participants variability appears to account for the reduced R2.Conceptually, a linear relationship, such as that typically derived forFitts' tasks, indicate that the predicted values for MT increases by thesame amount for each equal increases in ID with this increase per bitcharacterized by the slope of the linear equation. After 20 days ofpractice the increase in MT from ID=1.5 to 3, ID=3 to 4.5, andID=4.5 to 6 were 89.38 ms, 514.06 ms, and 128 ms, respectively.
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Interestingly, this pattern was apparent even at the beginning ofpractice (157.97, 420.74, and 183.08, respectively) although after1 day of practice the regression analysis indicated a relatively stronglinear relationship (R2=.90). Note also, that the minor changes in MTover practice were not detected by the ANOVA analysis, althoughconsistent with Boyle and Shea (2011) an Effector×ID interaction didreveal that wrist movements were faster than arm movements atID=6.
Relatively small but systematic deviations in the linearity of theMT–ID relationship, particularly at the lower IDs, have also been noted inFitts' task data as early as Fitts (1954) paper. This is seen in themovement time at low ID (IDsb3) which tends to be slower thanpredicted given the best fit linear regression line derived from a widerrange of IDs. Indeed, this finding for lower IDs is not only observed forwrist movements but also for arm movements in the presentexperiment. That is, the difference between IDs 1.5 and 3 is substantiallysmaller than between IDs 3 and 4.5 and IDs 4.5 and 6 even though alinear equationwould characterize these differences as equal. However,with arm movements in the present experiment and most typically inthe literature linearity tends to be well maintained at higher IDs. Wesuggest this finding may be related to refinements in the controlprocesses used to produce the lower and higher ID movements.
When the MT–ID' relationship was assessed the findings werequite different for the wrist but not for the arm. Using VE in thedetermination of ID' resulted in a significant decrease in slope for thewrist across practice with a slope reduction of nearly 250 ms fromDay 1 to Day 20. This reduction occurred while the strength of thelinear relationship (R2) was maintained across practice. While thisappears quite interesting it should be remembered that the cause of thedecreased slope was not primarily due to a reduction in movementtime, but rather an decreases across practice in the functional targetwidth (VE) used to determine ID'.
4.1. Critical ID: cyclical and discrete control
The control processes involved in reciprocal motion of the limbs areoften described as cyclical or discrete. Descriptions of discrete controlprocesses typically utilize an information processing or motor pro-gramming approach arguing online knowledge of previousmovementscombined with anticipation of future movements results in theparticipants issuing new motor commands to compensate for errorsdetected in the movement pattern (Fitts, 1964; Meyer et al., 1988;Meyer, Smith, & Wright, 1982; Plamondon, 1993; Plamondon & Alimi,1997; Schmidt, Heuer, Ghodsian, & Young, 1998; Schmidt, Zelaznik,Hawkins, Frank, & Quinn, 1979). In theory, discrete control couldbe thought of as the fundamental basis of movement control(i.e., discrete motor primitive). Theories regarding discrete movementcontrol propose that all movements, whether discrete or reciprocal, areconstructed from initial goal directed movements plan followed bycorrective sub-movements (Crossman & Goodeve, 1963; Meyer et al.,1988; Plamondon & Alimi, 1997). These perspectives argue that a seriesof discrete movements can be concatenated to achieve reciprocalmotion. Alternatively, proponents of cyclical control often describereciprocal motion using a coordination dynamics approach wherebystored elastic kinematic energy and the retuning of the ongoingmovement result in adjustments to the on-going movement pattern(Buchanan, Park, Ryu, & Shea, 2003, 2004, 2006; Buchanan et al., 2004,2006; Crossman, 1960; Fitts, 1954; Kelso, 1995; Langolf et al., 1976;Turvey, 1990; Welford, 1968). Moving from a start position to a targetsimply represents a special case of cyclical controlwhere themovementis terminated after reaching the target. Mottet and Bootsma (1999)have demonstrated that both harmonic (cyclical) and non-harmonic(discrete) repetitive aiming movements can be modeled as the samenon-linear oscillator. This work is consistent with the notion thatcyclical movements are a basic unit of action.
The findings related to low IDs, which are evident in both wristand arm movement, and the advantage at ID=6, which was evidentonly in wrist movements following substantial practice appear to berelated to the control processes utilized to produce the reciprocalmovements. As noted above, these findings appear to be consistentwith the notion that low ID movements are controlled differentlythan higher ID movements, utilize different information, and rely ondifferent neural pathways (e.g., Glover, 2004; Hikosaka, Nakamura,Sakai, & Nakahara, 2002; also see Schaal, Sternad, Osu, & Kawato,2004). Indeed, Buchanan et al. (2006) have proposed that there is acritical boundary between the control processes used for low andhigh ID movements which they term IDc. In the Buchanan et al.experiment, when the ID was relatively low, participant's movementpattern was characterized as harmonic motion with relatively little, ifany, dwell time and the percent movement time utilized to achievepeak velocity (%TTPV) was nearly equal to the percent of movementtime devoted to deceleration. The short dwell times were consistentwith a trade-off between kinetic and potential energy that allows forthe saving and releasing of elastic energy during rapid movementreversals characteristic of harmonic motion assembled from a cyclicalunit of action (Adam et al. 1993; Buchanan et al., 2003, 2004, 2006;Guiard, 1993, 1997). Buchanan et al. (2006) noted that as the IDincreased movement variability increased and then stabilized at thehigher IDs. However, the motion at higher IDs was best characterizedas discrete motion with increased dwell time and a substantiallylarger percent of the movement time devoted to the decelerationphase of the movement as movement corrections were initiated toachieve the target location (e.g., Elliott & Chua, 1995; Elliott, Helsen, &Chua, 2001; Woodworth, 1899). The increased dwell time reflects thedissipation of elastic energy to stop the motion in one direction andinitiate an independent discrete motion in the opposite direction(Adam & Paas, 1996; Buchanan et al., 2003, 2004, 2006; Guiard, 1993,1997). This coupled with additional pre-planning time required togenerate the discrete motion in the opposite direction could accountfor the increased dwell time. The control processes used at the lowerIDs have been variously described as open-loop (e.g., Schmidt, 1975),preplanned (Glover, 2004), or cyclical (e.g., Guiard, 1997) control andthe control processes at the higher IDs have been described as closed-loop (e.g., Adams, 1971), feedback (e.g., Crossman & Goodeve, 1963),online (e.g., Glover, 2004), or discrete (e.g., Guiard, 1997) control.Buchanan et al. determined the critical value for arm movements tobe IDc=4.5+/− .5, but found this critical value slightly reduced on asecond day of practice.
The MT–ID relationship we observe in the present experimentand that has been observed in numerous other experimentsindicates minor deviations from linearity at lower IDs whereparticipants appear to employ open-loop, preplanned or cyclicalcontrol processes (depending on the theoretical perspective). Theslope for the lower IDs is flatter than that which characterizes theMT–ID relationship across all ID conditions. What is particularlyinteresting is that we also see this pattern at higher IDs for the wristfollowing extended practice. That is, wrist movements controlled byclosed loop, on-line, or discrete control processes also exhibit flatterslopes than would be derived by regression equations across all IDconditions. It is tempting to suggest that the wrist and arm exhibitsimilar patterns of movement when using open loop processes at thelower IDs, but that the wrist movements exhibit more efficientclosed-loop control at higher IDs following extended practice.However, it is important to remember that wrist movements athigher IDs are also plagued by substantially increased dwell timewhich functionally offset the advantage gained in the movementsegment of the response. Regardless, the time required to moveunder ID=6 conditions was less for the wrist than for the arm andthis difference increased over practice. This does suggest, however,that after extended practice that the wrist may exhibit a trueadvantage over arm movement on discrete, high ID Fitts' tasks
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although additional time required for planning processing may bemanifest in study or reaction time.
4.2. Dwell time
The time between the end of one movement segment and theinitiation of the reversal movement in reciprocal movement tasks hasdrawn the attention of researchers for some time (e.g., Adam & Paas,1996; Cullen et al., 2001; Fitts & Radford, 1966; Keele, 1968;Woodworth, 1899). In the present experiment dwell time wasgenerally longer in wrist than arm movements with this differencesubstantially increased at IDs 4.5 and 6. Note that the higher IDs alsoresult in a decreased percent time to peak velocity and thus, anincrease in time utilized in the deceleration or corrective phase of themovement. At least three hypotheses have been proposed to accountfor the finding of increased dwell time with increased movementdifficulty (see Adam & Paas, 1996 for discussions; also see Cullenet al., 2001; Elliott et al., 2010). First, a visual feedback hypothesisproposes that increased dwell time is related to the additional timerequired to confirm that the participant has achieved the targetposition. Thus, with smaller targets visual discrimination difficultyrelated to determining if the target position has been achievedincreases resulting in additional dwell time prior to movementreversal (Adam, 1992; Adam & Paas, 1996). Of course, an increase invisual gain, which is sometimes seen in experiments testing high IDfinger or wrist movements, should reduce this time. A secondhypothesis, initially proposed by Fitts and Peterson (1964), proposesthat increased dwell time is a direct result of programming timesnecessary to retrieve, process, and execute the reversal movementwith more precise movement commands required for more difficulttask resulting in increased delays between movement segments (e.g.,Hyman, 1953; Sidaway, Schoenfelder-Zohdi, & Moore, 1990). Thishypothesis is consistent with the notion that wrist control may bemore complex than that for the arm because of the increased numberof smaller motor units. Lastly, an explanation based on movementdynamics suggests that faster movements take advantage of theelastic properties of the muscle-tendon system to store energycoming into a reversal and then utilize that energy to initiate themovement reversal. Because the velocity of high ID movements aresubstantially slower not only peak velocity but especially in theapproach to the reversal point little or no energy is available requiringthe participant to generate through contraction nearly all the forcesrequired to reverse the movement (see Guiard, 1993, 1997).Interestingly, this literature provides no clear evidence for any oneof the hypotheses suggesting that all three types of delays maycontribute to dwell time depending on the specific circumstances.
An intriguing finding in the present experiment was the largedwell times at the higher IDs for the wrist movements compared tothose for the arm movements. Note that the reduced MT for the wristrelative to the arm movements was offset by increased dwell time forthe wrist relative to the arm movements. Thus, the numbers ofmovements produced during each trial were approximately equalacross effectors. The pertinent question is “Why does dwell time, thetime required to transition from movement in one direction (e.g.,extension) to one target to movement back in the other direction(e.g., flexion) to the other target in a reciprocal movement task,increase for the wrist but not for the arm?”
The finding that dwell times were substantially larger at ID=6 forthe wrist than for the arm, but the visual feedback display provided inthe present experiment for arm and wrist movements were identicalsuggests that the visual feedback hypothesis is an unlikely candidatefor the increased dwell time in the wrist condition. Thus, aparticipant's ability to determine the position of the cursor (arm orwrist position) relative to the target was perceptually similar. On theother hand, programming and movement dynamics accounts fordwell time could potentially contribute to the increased dwell times.
Note that in the present experiment arm and wrist movementsinvolved identical amplitudes, target widths, and visual displays. Thisfinding suggests that the differences found are not due to themanipulation of amplitude and proportional changes in target widths,the gain with which the visual feedback was provided, and/or thecontrol characteristics of the wrist. However, these factors mayinteract to produce the unique performance under the wrist conditionand interact to produce the large dwell times for wrist at ID=6.
Indeed, as noted earlier, increases in movement difficulty orcomplexity have been shown to result in increased reaction timesrelative to less difficult or less complex movement and reaction timesin the range of 200–300 ms are not unusual (e.g., Henry & Rogers,1960; Klapp, 1996; Rosenbaum, 1980; Sidaway, 1991) in discreteaiming tasks. Indeed, Klapp (1975) and Mohagheghi and Anson(2002) using a reaction time-movement difficulty paradigm similarto Fitts and Peterson (1964) found an effect of target size on reactiontime such that very small targets paired with very short amplitudesmarkedly increased the preparation demand which resulted insubstantial increases in reaction time. These increased planning andprocessing times may contribute to the increased dwell times withthe complexity of these processes for the wrist adding to the timerequired to transition from one movement segment to the next.Interestingly, dwell times with durations similar to that found in thepresent experiment for wrist movements at high IDs have also beenfound prior to the primary saccades when participants are asked tovisually scan a set of stationary targets (Wu, Kwon, & Kowler, 2010).Wu et al. suggest that the increased dwell time was not related tosecondary saccades, but rather to the precision of the upcomingprimary saccade although increased dwell time did not appear to berelated to improved accuracy. Perhaps the wrist and eye movementsrequire more complicated planning than arms movements with thecost of this processing manifest in dwell time.
4.3. Why no robust general learning effects?
Following 20 days of practice, participants' movements under thevarious ID conditions changed in some subtle but important ways.First, endpoint variability (VE), also termed effective target width We
(e.g., Meyer et al., 1982; Schmidt et al., 1979; Zhai, Kong, & Ren,2004), was significantly reduced over practice for both the arm andwrist movements. That is, although, the amplitude, target width, andMT did not appreciably change participants reversed their move-ments more consistently over practice. Although more consistent intheir reversal point there were no significant changes in the linearMT–ID relationship (MT=a+b(log2(2A/W)) for arm movementsover practice. Note that reductions in the slope and intercept of thisrelationship have been reported in the literature (Schmidt & Lee,1999) and we hypothesized this type of change prior to theexperiment. This is somewhat puzzling especially in light of the factthat practice has an almost ubiquitous effect of improving perfor-mance although this difference tends to be greatly reduced later inpractice (e.g., Crossman, 1959; Newell & Rosenbloom, 1981). Inaddition, as noted in the introduction, Schmidt and Lee (1999) reportthat the slope of the Fitts' equation can be reduced to nearly zerofollowing extensive practice. Justification for this statement resides inan unpublished thesis at York University (Kelso, 1984). However, ourreview of this thesis indicates that movement times were notsystematically reduced over extensive practice. Kelso (1984) reportedthat when the slopes derived for each day of practice were plotted theslope of the slope-practice relationship was nearly zero. In this case azero slope indicated no change in slope over practice. Thus, the Kelso(1984) findings are compatible with the present findings. Perhaps thebase reason for observing relatively minor general improvements as aresult of extended practice is that a typical participant brings to theexperiment a great deal of previous experience using arm and wristaiming movements of various difficulties. Thus, performance
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improvements are going to be small assuming a typical learningcurve with a negatively accelerating slope (Fitts, 1964; Newell &Rosenbloom, 1981). That is, in mid to late practice one wouldexpect substantially smaller improvements relative to earlier inpractice.
Although the linear MT–ID relationship for arm movements didnot change over practice, the linear relationship weakened overpractice for wrist movements. This change appeared to be the resultof enhancements to open-loop control for movement under ID=3conditions such that the difference in MT between ID=1.5 and ID=3was reduced over practice and enhancement to closed-loop controlunder ID=6 conditions such that the difference between ID=4.5and ID=6 was also reduced. In addition, the MT–ID' relationship didresult in decreased slopes across days for the wrist and not the arm.However, this relationship was more the result of changes in the ID'resulting from reduced endpoint variability than from actual de-creases in movement time.
Of course, it is possible that features of the experimental protocolmay have played a role in limiting improvements over practice. First,a variable and distributed practice schedule was used across the20 days. That is, participants performed movements at four differentIDs with two different effectors in each session. There are numerousexamples where variable and distributed practice has been shown toenhance learning especially when the task variations are related as inthe present experiment (e.g., Shea & Kohl, 1990, 1991; Shea, Kohl, &Indermill, 1990; Shea & Morgan, 1979). However, it is possible thatparticipants would have demonstrated greater improvements if theyhad performed a single task (one ID with only one effector) (seeElliott et al., 2004). If this had been the case participants would havehad the opportunity to practice a single task many more times thanthey were able to in the variable and distributed practice sessionsused in the present experiment. It is also important to note that byasking participants to repeatedly perform movements to the four IDconditions, that they may have adopted a different control strategythan if they had practiced only one task. Wilde, Magnuson, and Shea(2005), for example, asked participants to practice three relativelysimple movement sequences. The task was to produce the sequencesas quickly and accurately as possible. One group was providedblocked practice and the other random practice. What was particu-larly interesting about the findings from this experiment was thatparticipants in the variable practice group organized all threesequences in the same manner while participants in the blockedpractice condition adopted a unique organization for each sequence.The unique organization resulted in faster movements for one of thesequences that were not realized under random practice. Perhaps bypracticing each ID in each practice session some improvements thatwould have been possible in more specific practice were not realized.However in the present experiment, we were interested in the MT–IDrelationship, which requires testing across ID conditions.
It is also possible that manipulating amplitude, while keeping thetarget width constant might yield different results. Note that in thepresent experiment amplitude was held constant while target widthwas manipulated to produce the various ID conditions. Increasingamplitudewhile holding the target width constant to create the variousIDs would create greater opportunities for the initial phase of themovement to be optimized while the endpoint accuracy requirementsremain the same as ID increases.
5. Summary
Over 20 days of practice with reciprocal Fitts' task end-pointvariability, but not movement time was reduced. Improvements arealso observed for high IDmovements of the wrist but not the arm. Theresult was a change in the linear MT–ID relationship for the wristmanifest in a reduction of R2 resulting from the reduction in MT forIDs=3 and 6 but not for IDs=1.5 and 4.5. This difference suggests
that Fitts' task should be viewed as really two fundamentally differenttypes of movement; lower ID movements characterized by cyclicalmovement and higher ID characterized by discrete movement withan IDc that separates the two styles of movement and the associatedmodes of control. More importantly, it may be prudent to determineseparate intercepts and slopes for these two types of movements inorder to more accurately characterize the movement time for highlypracticed aiming tasks.
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