change in the organization of degrees of freedom with learning

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This article was downloaded by: [DUT Library] On: 04 October 2014, At: 04:03 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Journal of Motor Behavior Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/vjmb20 Change in the Organization of Degrees of Freedom With Learning S. L. Hong a & K. M. Newell a a Department of Kinesiology, The Pennsylvania State University, University Park Published online: 07 Aug 2010. To cite this article: S. L. Hong & K. M. Newell (2006) Change in the Organization of Degrees of Freedom With Learning, Journal of Motor Behavior, 38:2, 88-100, DOI: 10.3200/JMBR.38.2.88-100 To link to this article: http://dx.doi.org/10.3200/JMBR.38.2.88-100 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

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This article was downloaded by: [DUT Library]On: 04 October 2014, At: 04:03Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Journal of Motor BehaviorPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/vjmb20

Change in the Organization of Degrees of FreedomWith LearningS. L. Hong a & K. M. Newell aa Department of Kinesiology, The Pennsylvania State University, University ParkPublished online: 07 Aug 2010.

To cite this article: S. L. Hong & K. M. Newell (2006) Change in the Organization of Degrees of Freedom With Learning,Journal of Motor Behavior, 38:2, 88-100, DOI: 10.3200/JMBR.38.2.88-100

To link to this article: http://dx.doi.org/10.3200/JMBR.38.2.88-100

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Change in the Organization of Degrees of Freedom With Learning

S. L. HongK. M. NewellDepartment of KinesiologyThe Pennsylvania State UniversityUniversity Park

ABSTRACT. The authors examined the effects of learning on thechange in the organization of the mechanical and dynamicaldegrees of freedom in 5 men who performed a ski-simulator task.A 3-dimensional analysis of the motion of the total-body center ofmass and the segmental centers of mass (head, torso, thighs, andshanks) over practice showed that the recruitment of mechanicaldegrees of freedom was strongly influenced by anatomical andtask constraints. Principal components analysis of the body seg-ments’ motions revealed that practice shifted their relative contri-butions but did not change the number of principal components.The present findings show that there can be independence in thepatterns of change in the mechanical and dynamical degrees offreedom that arise from practice.

Key words: dynamical systems, learning, multisegment move-ment, principal components analysis

ernstein (1967) presented the notion that coordinationrequires the mastery of redundant degrees of freedom.

The classic Bernsteinian example involved the kinematicanalysis of the hammer-striking patterns of a skilled black-smith. Although the motion at the individual joints of thearm remained highly variable, the trajectory of the hammerremained relatively invariant. Bernstein proposed that inmotor learning, early practice leads the learner to firstfreeze the degrees of freedom, eliminating any redundancy1

and creating a very rigid body movement. Further practicetends to release the restrictions placed on those degrees offreedom because they are gradually organized into a singleunit of coordinated action in which the reactive forcesembedded in the movement dynamics are exploited.

To date, there have been several examinations of certainaspects of Bernstein’s (1967) stages of learning (e.g.,McDonald, van Emmerik, & Newell, 1989; Newell & vanEmmerik, 1989; Schneider, Zernicke, Schmidt, & Hart,1989; Southard & Higgins, 1987; Steenbergen, Marteniuk,& Kalbfleisch, 1995; Vereijken, Whiting, & Beek, 1992;

Vereijken, Whiting, & Newell, 1992), but evidence in sup-port of the proposed sequence of qualitative states has notyet been obtained. Investigators have also questionedwhether Bernstein was referring to the collective spatial andtemporal organization of joints and body segments asreflected in the dynamical degrees of freedom or to motionsat individual joint angles, the mechanical degrees of free-dom. Indeed, the pattern of change with practice in themechanical and dynamical degrees of freedom seems to betask specific (see Newell, 1996; Newell & McDonald,1994; Newell & Vaillancourt, 2001) and essentially contin-uous rather than a reflection of distinct stages of learning(Ko, Challis, & Newell, 2003).

Bernstein’s (1967) degrees of freedom problem in humanmovement is multidimensional; it needs to be understoodon the multiple dimensions of change. Joint motions cap-ture the mechanical degrees of freedom at the behaviorallevel and were the focus of Bernstein’s framework, but it isthe spatiotemporal relations of the motions of the body seg-ments that reflect the dynamical degrees of freedom or thedimension of the behavior (Newell & Vaillancourt, 2001).The difficulty of determining the dimension of physicalactivities is probably one reason why so few attempts havebeen made at such analyses. Researchers have nowapproached that challenge by considering the linear multi-variate method of principal components analysis in investi-gations of whole-body actions (Haken, 1996; Kachigan,1986). The primary components revealed by principal com-ponents analysis are taken to represent multiple, indepen-

Correspondence address: S. L. Hong, Department of Kinesiol-ogy, 266 Recreation Building, The Pennsylvania State University,University Park, PA 16802-6501, USA. E-mail address:[email protected]

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Journal of Motor Behavior, 2006, Vol. 38, No. 2, 88–100Copyright © 2006 Heldref Publications

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dent modes of control defined by the variables that possesssignificant weightings within those components. The num-ber of components is taken as an index of the number ofdynamical degrees of freedom (dimension) and does notnecessarily directly relate to the number of mechanicaldegrees of freedom.

Vereijken, van Emmerik, et al. (1992) examined the direc-tion of freezing and freeing of the mechanical joint-spacedegrees of freedom in a ski-simulator task. They obtainedevidence for the freezing of the joints in the initial trials ofpractice and for the subsequently greater activity at mostjoints through continued practice. No evidence was foundfor the hypothesis that the change in joint involvement pro-gresses in a cephalocaudal direction. However, the failure toobtain that evidence may have reflected task specificity inthe change in joint-space degrees of freedom (Newell &McDonald, 1994). In a stabilometer study, Caillou, Nourrit,Deshamps, Lauriot, and Delignières (2002) found that theincrease in variability was statistically significant only in the(distal) ankle joints. Freeing occurred first on the right sideof the body; variability on the left side increased only towardthe final period of practice. Similarly, Ko et al. (2003) foundan increase only in ankle joint variability during the learningof a postural maintenance task on an oscillating platform.

Haken (1996) and Ko et al. (2003) showed a shift towardlower component (dimensional) control with practice; amajority of the variability at the joint motions was repre-sented by one and two principal components, respectively.In those studies, however, only a two-dimensional (2D)analysis of the kinematic data of the torso and limbs wasperformed. Chen, Liu, Mayer-Kress, and Newell (2005)revisited the pedalo task with a three-dimensional (3D)analysis and found that they needed three to six componentsto capture 95% of the variance within the data, even afterparticipants had practiced extensively. The aforementionedstudies also differed in other ways, however, because Hakenperformed the principal components analysis on eachmovement cycle, whereas Ko et al. and Chen et al. used thatanalysis over multiple movement cycles. Nevertheless, inall of those studies a general decrease was found in thenumber of principal components that were required to cap-ture the movement variance following extensive practice.

A different theoretical view than Bernstein’s (1967)freezing–freeing hypothesis is the recruitment–suppressionhypothesis (Buchanan & Kelso, 1999; Buchanan, Kelso,DeGuzman, & Ding, 1997). Instead of a focus on changes injoint angle amplitude, that approach is centered on planes ofmotion supplementary to the primary planes of motion of themovement. Buchanan and his colleagues proposed that oneshould consider increases in motion in the supplementaryplanes as recruitment, whereas a decrease in motion can beconsidered to be suppression of those supplementary degreesof freedom. For example, the transition from a curvilinear toa rectilinear trajectory represents suppression of degrees offreedom, whereas the reverse constitutes recruitment. Fur-thermore, the recruitment and suppression of those mechani-

cal degrees of freedom have been found to be a means ofmaintaining coordinative stability (Buchanan et al.; Fink,Kelso, Jirsa, & DeGuzman, 2000). Buchanan et al. found thatincreased recruitment accompanied an increase in movementfrequency in a finger flexion–extension task in which motionof the vertical plane increased and suppressed motion on thehorizontal plane as the fingers began to travel in an ellipticalorbit. Fink et al. presented similar findings in a task in whichparticipants were required to coordinate two hand-held pen-dulums in an out-of-phase pattern restricted to the frontal orthe sagittal plane. Increased cycle frequency generatedincreased motion in the secondary plane of motion, which ledFink and colleagues to hypothesize that the occurrence ofrecruitment serves to prevent the coordination pattern fromtransitioning to the more stable in-phase pattern.

Buchanan and Kelso (1999) have proposed that therecruitment–suppression hypothesis is compatible withBernstein’s (1967) notion of freezing and freeing of degreesof freedom, that is, that increased joint activity leads togreater environmental adaptability. However, an oft-forgot-ten point of Bernstein’s blacksmith example and the resultsof Vereijken, Whiting, et al. (1992) is that in both studies, anincrease in movement velocity as a function of practice wasfound. It would be reasonable to hypothesize that recruit-ment, or freeing of degrees of freedom, would be related toan increase in movement velocity in situations in whichvelocity is acting as a control parameter in the dynamicalsystems framework. What remains elusive is the effect thatrecruitment and suppression of mechanical degrees of free-dom may have on the direction of change in the dynamicaldegrees of freedom during learning.

In this article, we pursue the proposition that an under-standing of the degrees of freedom problem requires (a) abasic analysis of the kinematics of the mechanical degrees offreedom of the motion of the limbs and torso, measuring theirrecruitment and suppression in 3D space, and (b) a clear dis-tinction in the analysis between the mechanical and dynami-cal degrees of freedom. Our general goal in this study was toreaddress the degrees of freedom question within the dynam-ical recruitment and suppression hypothesis by using a 3Danalysis of the well-researched ski-simulator task (e.g., Nour-rit, Delignières, Caillou, Deschamps, & Lauriot, 2003; Nour-rit, Deschamps, Lauriot, Caillou, & Delignières, 2000; vanEmmerik, den Brinker, Vereijken, & Whiting, 1989;Vereijken, van Emmerik, Bongaardt, Beek, & Newell, 1997;Vereijken, van Emmerik, et al., 1992; Vereijken, Whiting, etal., 1992). Vereijken, Whiting, et al. have proposed that thecritical relationship between the motion of the center of massof the performer and the forcing of the platform representsthe order parameter for that task. A shortcoming of many ofthe aforementioned studies, however, has been that the use ofonly 1- and 2D analyses of the movement has limited thepotential for full assessment of recruitment and suppressionof the degrees of freedom. Indeed, the interpretation that theentire task can be captured with a single coordination modewas based on only frontal plane motion and was probably

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compromised by the failure to consider the strong role of theanteroposterior motion in the ski-simulator task.

In this study, we examined the effects of practice on plat-form amplitude, velocity, and the recruitment and suppres-sion of the mechanical degrees of freedom. In addition, weinvestigated the proposed reduction in the dynamicaldegrees of freedom (Mitra, Amazeen, & Turvey, 1998), ordimensionality (Newell & Vaillancourt, 2001), or the orderparameters (Haken, 1996) as a function of practice. Previ-ous ski-simulator studies have led to the hypothesis thatthere will be an increase in the mechanical degrees of free-dom recruited as a function of both practice and increasedcycle frequency accompanied by a reduction in dimensionof the behavior. We performed an examination of thechange in the dimension of dynamical degrees of freedomthrough an analysis of the motion of the segmental centersof mass in three physical planes through the use of princi-pal components analysis (PCA). Our focus was on theeffects of practice on the number of active modes of coor-dination and the organization of the segmental variableswithin those modes during the learning and performance ofthe task.

Method

Participants

Five 16- to 24-year-old men with minimal experience asskiers (occasional recreational skiers) and with no experi-ence on the ski-simulator apparatus volunteered as partici-pants. Their average height was 176.1 ± 8.1 cm, and theiraverage weight was 64.6 ± 5.0 kg. We measured the heightsand weights of the participants while they were dressed intheir shorts and sneakers in order to minimize the possibil-ity of occlusion of any the joint markers during the experi-ment. All participants provided informed consent beforetesting. The Pennsylvania State University InstitutionalReview Board approved all experimental procedures.

Apparatus

A ski-simulator (Skier’s Edge, Park City, UT) served asthe experimental apparatus. The apparatus is promotedcommercially both as a rehabilitation device and as a devicethat affords a simulation of slalom skiing. The ski-simulatoris a movable wheeled platform composed of two codepen-dent footplates, atop two parallel metal rails (see Figure 1).The bow-like shape of the rails allows sideways movementof the platform, but in a somewhat angular fashion. An elas-tic band harnesses the platform to the rails, and wheneverone moves the platform by force away from the center ofthe apparatus, it oscillates until its resting position isregained. To maintain those oscillations, the participantmust produce force. Vereijken, Whiting, et al. (1992) haveshown that the torque produced by angular motion of theparticipant’s center of mass causes much of the forcing.

We used a sampling frequency of 50 Hz during datarecording with a 3D motion-capture system (SELSPOT AB,

Molndal, Sweden). Two infrared cameras detected the posi-tions of infrared-light-emitting diodes (LEDs) in 3D space.We recorded the positions of 13 LEDs during each trial, 2were placed on the edges of the platform and the remainderon the participant’s body. To prevent occlusion of thoseLEDs during the trials, we placed the LEDs for the hips andankles slightly away from the actual joint centers. Beforeeach practice session, we measured the distance of the LEDplacement from the actual hip (greater trochanter) and ankle(lateral malleolus) joint centers. Linear transformation thenenabled us to account for the readjustment of that displace-ment from the actual joint centers. The remaining LEDswere placed on the feet (shoe tips), knees (the patella),shoulders (frontal aspect of the caput humeri), and head(center of the forehead). Hypoallergenic double-sided adhe-sive tape ensured that the LEDs remained adhered to theskin during the practice trials. We filtered the raw data byusing a ninth-order Butterworth low-pass filter with a cutofffrequency of 12.5 Hz.

Procedure

The only instruction provided to the participants was thatthey were to learn to produce large amplitude sidewaysmovements on the apparatus as fluently as possible. Toincrease the difficulty, we required the participants to per-form those movements with their arms held behind theirbacks (Vereijken, van Emmerik, et al., 1992). Neither feed-back nor additional instructions were given concerning per-formance and methods for successfully accomplishing thetask. Each participant completed 7 days of practice; eachpractice day included 20 trials, each 30 s in length, with arest period provided following 10 trials or at the partici-pant’s request. Pilot testing had shown that a trial durationof 1 min was excessively taxing, and we decided to use atrial time half that used in Vereijken et al. in order to preventthe effects of fatigue from affecting the outcomes of theexperiment.

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90 Journal of Motor Behavior

FIGURE 1. Schematic of the ski apparatus and the experi-mental setup.

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Dependent Measures

Positional data of the 13 LEDs collected over the courseof a trial served as raw data. To remove the effects of trialinitiation, we discarded data from the first 5 s of each trial.From the raw data, we determined the total-body center ofmass (CM) by using a segmental method based on theregression equations from Chandler, Clauser, McConville,Reynolds, and Young (1975), as provided in Enoka (1988).That method allowed us to represent each body segment asa rigid body, with all its mass acting at a single point inspace and with each point possessing three translationaldegrees of freedom. Because the positions of the upper andlower arms were fixed in relation to the body (arms heldbehind back), we combined their respective contributions tothe total mass of the body with that of the trunk for thosecalculations.

We derived the center of the platform as the mean of thetwo front upper corners of the platform in space. We com-pared the amplitudes of motion of the CM on the mediolater-al (x), anteroposterior (y), and superoinferior (z) axes in theanalysis of recruitment and suppression of the mechanicaldegrees of freedom (see Figure 1). The analysis first requiredthat we use a peak-detection program coded in MATLAB(The MathWorks, Natick, MA) to compare slopes over afour-point window (0.08 s). The program enabled us to markthe individual cycles of the platform center within a giventrial, as defined by the point at which a complete reversal ofthe slope was found (where all the points within the windowhad changed direction). We defined a cycle as a completemovement, that is, a return to the similar endpoint. Thus, acycle was calculated as motion initiated from the right end-point and a full return to that point. We calculated the totalabsolute displacement of a given variable during each cycle.Similar calculations were performed on the individual seg-mental CMs as a degrees of freedom analysis. Because of thenature of the motion of the platform, however, we subtractedits vertical motion from all segmental and total-body CMmotion on the superoinferior axis, thus ensuring that none ofthe vertical motion of the various body segments was gener-ated because of the motion of the platform.

Statistical Analyses

Using the Minitab (Minitab, Inc., State College, PA) sta-tistical package, we ran within-participant one-way repeat-

ed measures analyses of variance (ANOVAs) on severaldependent variables that captured the platform and segmen-tal motion. We selected five practice blocks for detailed rep-resentative analysis, and we created those blocks from fivetrial segments in Days 1, 2, 4, and 7 (see Table 1). BecauseVereijken, van Emmerik, et al. (1992; Vereijken et al., 1997)had noted that the most significant change with learningoccurs early in practice, we selected the first and last fivetrials from Day 1 as Blocks 1 and 2.

We ran PCA with 18 dependent variables, namely, thepositions of six segmental CMs (head, torso, right and leftthighs, and shanks) in all three axes of motion on the first 5trials of Day 1 (early practice) and on Trials 11–15 on Day7 (late practice).2 Because we derived the position of thetotal-body CM in three dimensions from the segmentalCMs by virtue of the estimation technique devised by Chan-dler et al. (1975), each segment represented a rigid struc-ture. Thus, the CM of each segment can be considered apoint at which the entire mass of the segment is concentrat-ed that possesses three degrees of freedom (translationsalong three independent axes of motion). We removed thefeet from the analysis because their motion would havebeen more reflective of the platform motion than of bodymotion. We derived the principal components by obtainingthe eigenvalues from the matrix of the correlation coeffi-cients obtained from the original matrix of time series,whereas the eigenvectors provided the weightings or rela-tive contributions of each segmental variable within eachcomponent. Use of the correlation matrix rather than thecovariance matrix obviated the need for initial normaliza-tion of the data to unit variance (Kachigan, 1986). Ourinterpretation of the PCA results is focused on the follow-ing two key points: (a) the number of components requiredto capture a significant proportion of the variance (90% forthis study, although the number varied depending on exper-imenter preferences) and (b) the significantly weightedvariables within each component. We compared changes inthe percentage of variance accounted for by each compo-nent through the use of paired t tests. Any increases in vari-ance accounted for within each component and also overallsuggest increasing stability of the various coordinationmodes,3 whereas the significantly weighted variables with-in each principal component are markers of the organizationof segmental variables, revealing the degree to which thesegments act within each component.

Results

CM and Platform

Amplitude

Representative time series of the horizontal platformmotion on the mediolateral plane from a participant for sin-gle trials both early and late in practice are shown in Figure2. The individual trend of increased mean amplitude andreduced variability of amplitude over practice was robust ona group basis (see Figure 3A). As shown in the repeated

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TABLE 1. Trial Block Samples Drawn From Various Points During the Course of Practice

Block Day Trials

1 1 1–5 2 1 16–203 2 11–154 4 11–155 7 11–15

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measures ANOVA, the effect of practice was significant,F(4, 120) = 32.35, p < .01, on the mean cycle amplitude ofthe ski-simulator platform. Tukey post hoc tests showed thatthe movement amplitudes of Blocks 2 through 5 were sig-nificantly higher than was that of Block 1. No other pair-wise comparisons were significant, suggesting that thegreatest amount of change occurred between the first andlast five trials on Day 1.

A significant practice effect was also found for the variabil-ity (SD) of the cycle amplitude of the platform, F(4, 120) =9.29, p < .01. Tukey post hoc tests showed intratrial variabilityto be lower during Blocks 2 through 5 than during Block 1.Thus, practice induced an increase in mean platform cycleamplitude while decreasing intratrial variability.

Platform Velocity

Peak platform velocity increased significantly, F(4, 120) =32.66, p < .01, over the course of practice, beginning at 2.24cm/s and increasing to 3.58 cm/s during late practice (seeFigure 3B). Tukey post hoc comparisons showed that therewas a significant increase from the first practice block to thesecond, but no further significant increases were noted fromDay 2 onward. The practice effect was also significant inreducing intratrial variability, F(4, 120) = 7.92, p < .01.Tukey post hoc comparisons yielded significant pairwise dif-ferences similar to that of mean peak platform velocity.

CM

Example time series of the whole-body CM early (top)and late (bottom) in practice for a single individual areshown in Figure 4. The effect of practice on CM motion wassignificant for the mediolateral, F(4, 120) = 28.26, p < .01,anteroposterior, F(4, 120) = 3.14, p = .02, and superoinferi-or, F(4, 120) = 3.20, p = .02, axes, but the direction ofchange differed greatly across the axes of motion. Thechanges in mean amplitude across the blocks of practice areshown in Table 2. The change on the mediolateral axis waslower but approximately proportional to the amplitude ofthe platform center (Figure 3A). Tukey post hoc pairwisecomparison procedures revealed that only Block 1 was sig-nificantly different from the other blocks. The Tukey testalso revealed that motion on the anteroposterior and supero-inferior axes was significantly greater during Block 2 thanduring Blocks 1 and 5.

The variability of total motion of the CM during a trialdecreased significantly on the mediolateral, anteroposterior,and superoinferior axes, Fs(4, 120) = 3.32, 3.32, and 5.64,respectively, ps < .01. Tukey post hoc tests showed thatintratrial variability on the mediolateral and anteroposterioraxes decreased significantly from Block 1 to Block 5,whereas intratrial variability on the superoinferior axis wassignificantly lower in Blocks 3 through 5 than in Block 1.

Segmental CMs

The analyses presented within this section are divided bythe upper and lower body segments. A summary of the F

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92 Journal of Motor Behavior

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FIGURE 2. Platform motion of a participant over the courseof a trial during early (Day 1) and late (Day 7) practice.

FIGURE 3. Histogram displaying the effect of practice onmean platform amplitude (A) and peak cycle velocity (B) andtheir respective intratrial variabilities over the course of a trial.Error bars are standard deviations reflective of intertrial andintersubject variability. Asterisk (*) = significantly differentfrom Block 1.

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and the p values of all the repeated measures ANOVAs per-formed on the dependent variables can be seen in Table 3.

Upper Body Variables

The effect of practice was significant for the head andtorso on the mediolateral and superoinferior axes. Practiceresulted in an increase and a subsequent decrease in motionfor both head and torso motion in the superoinferior axis,both of which peaked during Blocks 2 and 3 (see Table 4),although the Tukey post hoc analysis revealed no significantdifferences between blocks for the torso. Little change wasnoted on the anteroposterior axis for both variables. Thoseresults suggest that increased recruitment of the mechanicaldegrees of freedom occurred on the superoinferior axis, sup-plementary to the primary plane of motion, but the motion ofthe head became suppressed later on in practice. The

increased motion of the CM on the mediolateral axisoccurred for the head and torso but did not match the medi-olateral motion of the CM’s magnitude of change. Changesin variability, however, were significant only for superoinfe-rior motion of the head and torso and for the mediolateralmotion of the torso. Overall, practice influenced upper bodyvariability in a fashion similar to that of the platform and thetotal-body CM, decreasing by the end of the practice.

Lower Body Variables

The effects of practice proved to be significant for all thelower body segments, but not in all axes of motion, becausechanges in motion on the superoinferior axis were not sig-nificant for the right thigh and shank. Unlike the head andtorso, the effect of practice on the motion of the shanks andthighs on the mediolateral axis was similar to that of the

FIGURE 4. Three-dimensional representation of the total-body center of mass motion of aparticipant over the course of a trial during early (Day 1, upper chart) and late (Day 7, lowerchart) practice. Position 0 on the x-axis refers to the center of the platform, Position 0 on they-axis refers to the front edge of the platform, and increases in position represent rearwardmotion. Position 0 on the z-axis refers to the ground.

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S. L. Hong & K. M. Newell

94 Journal of Motor Behavior

platform. The effect was marked by an early increase by theend of Day 1, but no significant differences between any ofthe later practice blocks were found in the Tukey post hoctests (see Tables 5 and 6). On the anteroposterior axis, suchchanges resulting from practice were found for both thethighs and the shanks. Similar to the upper body variables,increased motion was followed by a decrease on the supero-inferior axis for all the segments. Unlike the upper bodysegments, however, increased recruitment of the degrees offreedom occurred predominantly on the anteroposteriordirection rather than on the superoinferior direction. Signif-icant decreases in variability were evident for all the vari-ables, with the exception of the intratrial variability of theleft and right thighs on the anteroposterior axis. All the sig-nificant effects demonstrated a decrease in variability,although the rates for each variable differed.

PCA

PCA showed that the number of components required toaccount for 90% or more of the total variance was neverfewer than three, and on some rare occasions four. Thus, thefocus in the experimental findings was solely on the firstthree components. The average percentage variance

accounted for by each component as a function of practicefor each participant can be seen in Table 7.

In general, the total amount of variance accounted for bythe three components increased significantly for all the par-ticipants, t(24) = –6.49, p < .01. Such a global change wasnot reflected in the individual components because thedirection of change was not identical for all participants.Paired t tests showed that the increase in percentage vari-ance accounted for was significant for the first component,t(24) = –2.30, p = .03, and for the decrease in the third com-ponent, t(24) = 3.86, p = .01. The change in the percentagevariance accounted for by the second component was notsignificant, t(24) = –1.28, p = .21.

Because of the number of samples within the time seriesentered into the PCA, we considered weightings significant

TABLE 2. Summary of the Mean Cycle Amplitudeand Intratrial Variability of the Total Body Centerof Mass Over the Course of Practice

Mean Amplitudeamplitude variability

(cm) (cm)

Block M SD M SD

Mediolateral (x) axis

1 34.5 12.93 5.5 6.362 52.9a 5.25 4.0 1.413 53.8a 3.87 3.3 0.904 51.4a 5.39 3.4 2.185 50.6a 4.96 2.5a 0.67

Anteroposterior (y) axis

1 3.1 0.86 0.7 0.732 3.5a 0.43 0.5 0.113 3.4 0.32 0.5 0.114 3.3 0.50 0.5 0.185 3.1b 0.37 0.4a 0.14

Superoinferior (z) axis

1 12.4 9.50 2.6 2.212 16.7a 4.99 1.8 0.813 16.0 3.60 1.5a 0.554 14.2 4.19 1.4a 1.015 12.5b 2.94 1.1a 0.34

aSignificantly different from Block 1. bSignificantly different fromBlock 2.

TABLE 3. Summary of the Results of the RepeatedMeasures Analysis of Variance on the Mean Cycle Amplitude and Its Intratrial Variability for the Various Body Segments

Cycle mean amplitude Intratrial variability

Axis F(4, 120) p F(4, 120) p

Head segment

x 33.76 < .001** 1.95 .107y 0.96 .431 1.74 .145z 3.85 .006** 6.31 < .001**

Torso segment

x 29.88 < .001** 3.06 .019*y 0.82 .512 2.44 .050z 3.18 .016* 5.60 < .001**

Right thigh segment

x 18.93 < .001** 3.97 .005**y 11.99 < .001** 1.59 .180z 2.36 .057 4.13 .004**

Left thigh segment

x 20.70 < .001** 3.31 .013*y 8.12 < .001** 1.27 .287z 2.99 .022* 4.79 .001**

Right shank segment

x 20.02 < .001** 4.14 .004**y 9.10 < .001** 3.41 .011*z 1.65 .165 2.94 .023*

Left shank segment

x 23.84 < .001** 3.56 .009**y 9.16 .001** 2.55 .043*z 2.98 .022* 2.90 .025*

*p < .05. **p < .01.

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if they were 0.25 higher or lower than zero (Kachigan,1986). During the early practice trials, there was no dis-cernible structure, either on an individual or a group basis,to the distribution of the significant variables across the var-ious components. The absence of structure was also the caseacross participants. A clear and consistent structure to the

weightings emerged only during the last practice block(Day 7). The first component encompassed the mediolater-al axis variables for all the segments, whereas significantweightings were found for the anteroposterior axis for thethighs and shanks (see Table 8 for a summary and compar-ison of early and late practice). In the second component, allthe vertical, superoinferior axis variables proved to be sig-nificant for all the variables, whereas motion of the head

TABLE 4. Summary of the Mean Cycle Amplitudeand Intratrial Variability of the Head and TorsoOver the Course of Practice

Mean Amplitudeamplitude variability

(cm) (cm)

Axis/Block M SD M SD

Head

Mediolateral (x) 1 18.1 8.56 3.9 2.162 31.8a 4.80 4.1 1.093 35.8a 4.72 3.8 0.934 32.8a 6.31 3.6 1.125 27.4a,c,d 4.23 3.1 0.79

Anteroposterior (y)1 4.2 1.59 1.2 1.272 4.4 0.90 1.0 0.553 4.0 0.81 0.8 0.334 3.9 0.74 0.9 0.345 4.1 0.77 0.8 0.29

Superoinferior (z)1 16.8 13.09 3.9 3.232 21.5 6.47 2.6 1.203 22.0 5.61 2.4a 1.004 18.2 6.04 2.0a 1.165 15.0b,c 3.81 1.6a 0.54

Torso

Mediolateral (x) 1 26.7 11.05 4.7 4.412 41.8a 5.11 3.8 1.203 43.6a 3.43 3.3 0.884 42.4a 5.12 3.2 1.565 40.1a 3.77 2.6a 0.72

Anteroposterior (y)1 2.9 0.77 0.8 0.802 3.0 0.32 0.6 0.193 2.9 0.35 0.5 0.174 3.0 0.38 0.6 0.205 2.7 0.35 0.4 0.17

Superoinferior (z)1 14.8 11.19 3.1 2.562 19.7 5.79 2.2 0.993 19.1 4.23 1.8a 0.704 16.7 5.21 1.7a 1.235 14.6 3.67 1.3a 0.42

aSignificantly different from Block 1. bSignificantly different fromBlock 2. cSignificantly different from Block 3. dSignificantly dif-ferent from Block 4.

TABLE 5. Summary of the Mean Cycle Amplitudeand Intratrial Variability of the Left and RightThighs Over the Course of Practice

Mean Amplitudeamplitude variability

(cm) (cm)

Axis/Block M SD M SD

Right thigh segment

Mediolateral (x) 1 44.6 15.79 7.2 9.182 63.4a 6.81 4.7 1.853 62.9a 6.44 3.5a 0.984 61.4a 6.57 3.6a 2.895 63.6a 7.82 2.7a 0.66

Anteroposterior (y)1 8.9 1.53 1.8 2.662 12.2a 2.97 1.1 0.253 12.9a 3.10 1.1 0.194 112.0a 2.49 1.1 0.455 13.4a 2.28 1.1 0.41

Superoinferior (z)1 10.5 7.36 2.2 2.212 13.9 4.68 1.5 0.583 12.8 3.21 1.2a 0.374 11.9 3.07 1.3a 0.815 10.8 2.28 1.0a 0.31

Left thigh segment

Mediolateral (x) 1 43.6 15.71 7.1 9.502 61.4a 6.01 4.5 1.613 61.2a 3.53 3.5a 0.964 60.3a 5.74 3.9 2.755 61.3a 6.31 2.8a 0.62

Anteroposterior (y)1 9.9 2.25 1.8 2.742 12.7a 2.36 1.3 0.283 12.9a 2.08 1.1 0.304 12.4a 2.34 1.1 0.265 12.5a 1.79 1.3 0.47

Superoinferior (z)1 10.4 6.49 2.2 1.982 13.7a 4.10 1.6 0.703 12.5 2.75 1.2a 0.434 11.4 2.85 1.2a 0.765 10.7 2.24 1.0a 0.29

aSignificantly different from Block 1.

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96 Journal of Motor Behavior

and torso on the anteroposterior axis was significant for thethird component, thus accounting for all the variables with-in the PCA.

Discussion

The present experiment revealed contrasting patterns ofchange to the mechanical and dynamical degrees of free-

dom as a function of practice in the ski-simulator task. Themechanical degrees of freedom were both recruited andsuppressed over the course of practice, whereas no changesin the number of dynamical degrees of freedom were noted.Those findings confirm the importance of clearly distin-guishing which degrees of freedom are examined in draw-ing inferences about Bernstein’s (1967) conjecture that skillreflects the mastery of redundant degrees of freedom. Weobtained differences from the foundational experiments ofVereijken et al. (1997; Vereijken, van Emmerik, et al., 1992;Vereijken, Whiting, et al. 1992) with regard to the learningof the ski-simulator task in the 3D analysis of the change inmovement kinematics over the course of practice.

There was a significant increase in platform amplitudeand peak velocity over the practice period, together with adecrease in within- and between-trial variability of thosevariables. Thus, with practice, there was greater amplitudeand more rapid and rhythmical motion of the platform—allperformance features reflective of learning to attain the taskgoal. The exemplar time series seen in Figure 2 revealedthat by the end of the last practice session, the participantwas performing close to the limits of the apparatus.

Recruitment–Suppression of Mechanical Degrees of Freedom

There was both recruitment and subsequent suppressionof the supplementary degrees of freedom. The suppressionof the supplementary degrees of freedom preceded the sta-

TABLE 6. Summary of the Mean Cycle Amplitudeand Intratrial Variability of the Left and RightShanks Over the Course of Practice

Mean Amplitudeamplitude variability

(cm) (cm)

Axis/Block M SD M SD

Right shank segment

Mediolateral (x) 1 63.1 20.83 9.3 12.822 89.0a 7.52 5.6 2.543 87.4a 7.61 3.8a 1.084 84.9a 9.05 4.4a 4.355 89.5a 12.09 2.8a 0.67

Anteroposterior (y)1 14.1 2.95 2.8 3.752 19.6a 4.38 1.6 0.433 19.1a 3.28 1.4a 0.264 17.8a 4.43 1.3a 0.745 19.0a 3.32 1.3a 0.46

Superoinferior (z)1 5.5 3.83 1.4 1.582 7.1 3.14 1.0 0.383 6.1 2.17 0.8a 0.284 6.1 1.50 0.9 0.325 5.5 0.68 0.7a 0.19

Left shank segment

Mediolateral (x) 1 61.3 19.85 9.0 13.192 86.1a 6.04 5.3 2.143 85.8a 4.39 3.9a 1.134 83.1a 8.29 4.7 4.145 86.7a 10.13 2.8a 0.65

Anteroposterior (y)1 15.3 3.26 2.5 3.032 20.5a 3.32 1.7 0.503 19.0a 2.42 1.5 0.454 18.0a,b 3.50 1.3a 0.515 18.0a,b 3.14 1.6 0.65

Superoinferior (z)1 5.9 3.30 1.5 1.822 7.3 2.34 1.1 0.563 6.0 2.17 0.8 0.264 5.9 1.35 0.9 0.345 5.2b 1.10 0.8a 0.21

aSignificantly different from Block 1. bSignificantly different fromBlock 2.

TABLE 7. Mean Percentage of Variance and TotalVariance in Each of the 3 Key ComponentsAccounted For From Early (Trials 1–5 of Day 1)and Late (Trials 11–15 of Day 7) Practice

PC1 PC2 PC3 Total accountedParticipant (%) (%) (%) (%)

Early

AV 57.4 23.0 11.6 92.2BR 45.4 32.2 12.0 89.4JT 56.2 22.4 10.2 89.3MT 44.2 33.2 11.8 89.1SN 63.0 18.2 10.2 91.4Average 53.2 25.8 11.2 90.2

Late

AV 56.6 29.2 10.2 96.1BR 55.0 26.8 11.4 92.8JT 62.4 26.6 8.6 97.5MT 54.0 25.6 10.4 90.0SN 55.4 31.4 9.2 95.8Average 56.7* 27.9 10.0** 94.6**

Note. PC = principal component.*p < .05. **p < .01.

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bilization of the new global pattern of coordination (reflect-ed by the invariance in the weighting structure of the PCAvariables across trials and participants, as is discussedlater). Differences in the pattern of recruitment and sup-pression of the mechanical degrees of freedom were foundbetween the upper and lower body segments, although, col-lectively, a coherent pattern of change emerged. Head andtorso motion on the mediolateral and superoinferior axesincreased and then decreased subsequently over the courseof practice. The upper body motion on the anteroposterioraxis did not reflect those changes. The absence of recruit-ment on the anteroposterior axis for the head and torsoreflects a task constraint because large increases in motion

on that plane would have prevented the participants frommaintaining their upright posture during task performanceand increased their likelihood of falling.

With the arms included as part of the mass of the torso,the cumulative mass of head and torso results in approxi-mately 69% of the total-body mass (Chandler et al., 1975).The head and torso motion on both the primary (mediolat-eral) and supplementary (superoinferior) axes peaked dur-ing the intermediate practice blocks, after which theamount of motion decreased as practice progressed. Thatchange in head and torso motion is consistent with resultsfrom studies of the pendulum models by Vereijken et al.(1997), who hypothesized that novice performance transi-tions from resembling an inverted pendulum early in prac-tice to resembling a hanging pendulum over the course ofpractice. The inverted pendulum is illustrative of platformforcing that is dominated by the motion of the head andtorso in the mediolateral and superoinferior directions,which can be equated to the torque generated on thefrontal plane. With practice, the motion of the head andtorso decreases, thereby the head and torso become theaxis of rotation and a greater amount of forcing is per-formed by the lower limbs, thus resembling a hangingpendulum.

The lower limb segments showed a much different pat-tern of change as a function of learning. Unlike the upperbody segments, recruitment of the supplementary degreesof freedom was greater on the anteroposterior axis, asopposed to the superoinferior axis. Motion of the thighs onboth the mediolateral and anteroposterior axes increasedsignificantly by the end of Day 1, and that increase wasmaintained until the end of practice. On the superoinferioraxis, however, there was a decrease in motion following anincrease early in practice, but the effect of practice was sig-nificant only for the left thigh. Changes in anteroposteriormotion were, however, not similar for both shanks. Leftshank motion on that axis decreased following an increaseearly in practice, whereas no such decrease was seen for theright shank. The asymmetry in the effects of practice on legmotion is consistent with the hypothesis of Caillou et al.(2002) that the right limb serves as a forcing limb, whereasthe left remains as a supporting limb, with its motion morerestricted than that of its contralateral counterpart.

Links to the Freezing–Freeing Problem

The suppression of mechanical degrees of freedom dur-ing late practice suggests that the recruitment–suppressionhypothesis can be extended beyond Bernstein’s (1967)notion of freezing and freeing. We base that statement onthe finding that intratrial variability of platform amplitudeand velocity continued to decrease (increased stability) inthe later practice period despite suppression of the supple-mentary mechanical degrees of freedom. Buchanan et al.(1997) and Fink et al. (2000) have proposed that recruit-ment of mechanical degrees of freedom is one means ofachieving or preserving stability of the required coordina-

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TABLE 8. Distribution of Significant WeightingsWithin the Three Principal Components (PCs)From Early and Late Practice for a Single Partici-pant (a Structure Seen Across All Trials and Par-ticipants)

Early Late

Axis PC1 PC2 PC3 PC1 PC2 PC3

Head

x * * *y * * *z * * *

Torso

x * *y * * * *z * * *

Right thigh

x * *y * *z * *

Left thigh

x * *y *z *

Right shank

x *y * *z * *

Left shank

x *y *z *

Note. Asterisk (*) denotes significant weighting.

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tion pattern in action. Vereijken et al. (1997) showed signif-icant changes in mean relative phase between the motion ofthe total-body CM and the platform, suggesting a change inthe preferred coordination pattern over the course of prac-tice. In the analysis of the mechanical degrees of freedomhere, we subtracted the vertical motion of the platform fromall the segmental variables. Thus, any increased verticalmotion did not result from an increase in platform ampli-tude because the trajectory of the platform motion wascurvilinear. As such, peak velocity and peak cycle ampli-tude were still achieved even as previously recruited sup-plementary mechanical degrees of freedom became sup-pressed with practice. Thus, beyond preserving the stabilityof inherently stable coordination patterns, the recruitmentof supplementary degrees of freedom could possibly serveto destabilize the originally stable coordination pattern andfacilitate the emergence of a new task-relevant coordinationpattern (Zanone & Kelso, 1992, 1997). It should be noted,however, that that change in coordination strategies may betask dependent (Buchanan, 2004).

Another important aspect of the segmental results per-tains to the direction or anatomical sequence of freezing andfreeing of the mechanical degrees of freedom. In the currentstudy, as in Vereijken, van Emmerik, et al. (1992), we foundno definite sequence (e.g., proximodistal or cephalocaudal)of recruitment of the mechanical degrees of freedom. In fur-ther agreement with Vereijken et al., we also found that thegreatest amount of change in all the body segmentsoccurred by the end of the first day of practice. Thesequence of recruitment of the mechanical degrees of free-dom appeared to extend beyond the structural and function-al organismic constraints alone. There was a difference inrecruitment of mechanical degrees of freedom between theupper and lower body. Whereas greater recruitmentoccurred on the superoinferior axis for the head and torso,recruitment of the lower body variables, namely, the thighsand shanks, occurred predominantly on the anteroposterioraxis. Constrained by the task requirements, large incre-ments in forward and rearward motion of the upper bodysegments were made virtually impossible, whereas the taskconcomitantly limited the vertical motion of the shanks.That pattern of findings reflected the interaction of task andanatomical constraints on the change in the behavior of themechanical degrees of freedom (Newell, 1996; Newell &McDonald, 1994).

Dynamical Degrees of Freedom

No evidence of a change in the number of dynamicaldegrees of freedom organizing the coordinative behavior as afunction of practice was found. We propose that the absenceof change resulted from the constraints of the task and fromour higher dimensional analysis of the task being performedthan has been reported in previous ski-simulator studies (e.g.,Vereijken et al., 1997; Vereijken, van Emmerik, et al., 1992;Vereijken, Whiting, et al., 1992). The PCA findings also

revealed that a single order parameter was not sufficient tocapture the dynamics of the entire pattern of coordinationduring the performance of the ski-simulator task. There wasan evolution of the mechanical degrees of freedom recruitedwithin each coordination mode over the course of practice; aconsistent structure emerged across trials and participants bythe last practice session.

The PCA revealed a pattern of findings different fromthose found by Haken (1996), Ko et al. (2003), and Chen etal. (2005), because practice had little effect on the numberof components required to capture 90% of the total varianceof all the variables. The first component captured about60% of the total variance—a far smaller contribution thanHaken reported for the learning of the pedalo. However, inour experiment, we entered fewer variables into the PCAthan did Chen et al., whereas Haken used the anglesbetween segmental links and the horizontal and verticalaxes as variables for the PCA. It is possible that Haken’s useof a 2D analysis reduced the estimate of the dimensions ofthe spatiotemporal patterns of the movement to a singleprincipal component.

The weighting structure of the PCA pointed to three dis-tinct coordination modes (illustrated in Figure 5). The firstmode, represented by the largest component within thePCA, reflected the mediolateral torque generated by thetotal-body CM on the platform, which has been previouslysuggested as the order parameter (Vereijken, Whiting, et al.,1992). The weighting structure of the first componentencompassed the mediolateral motion of the upper bodyand lower body as well as the anteroposterior motion of thelower body segments because all the aforementioned vari-ables are required for the generation of the mediolateraltorque. The inclusion of the anteroposterior segments mostlikely results from the fact that sideways motion of the bodyrequires knee flexion; thus, forward and rearward motion ofthe thighs and shanks are needed. The second coordinationmode captured the vertical motion of all the body segmentsthat was required for the maintenance of upright postureand also accommodated the vertical motion of the platform.The third coordination mode represented the generation oftorque required to counter the forward motion of the lowerbody segments during the generation of the horizontaltorque, a component dominated by the anteroposteriormotion of the upper body segments. That coherent and con-sistent structure of the coordination modes became stableacross trials and participants. We cannot yet rule out thepossibility, however, that the number of dynamical degreesof freedom and modes of coordination would be reducedwith further practice through the integration of segmentalvariables into the higher order components (Haken, 1996;Mitra et al., 1998), for example, from the third to the first orsecond component.

There were interesting individual differences in the vari-ance accounted for by the principal components (Table 7).All participants showed a decrease in the variance account-ed for by the third component. For 4 of the 5 participants,

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the increase in the variance accounted for by the first com-ponent was accompanied by a decrease in variance withinthe second component. A single participant (JT), however,demonstrated an increase in the variance accounted for byboth Principal Components 1 and 2. Participant JT also hadthe most variance captured by the three coordinationmodes. The individual patterns of change in coordinationpattern showed that there are individual differences in thestability of the various modes over practice that may includestability tradeoffs between the modes or dimensions of thebehavioral pattern, essentially passing along variancebetween modes in a complementary fashion. An open ques-tion is the order in which the modes are integrated overpractice time so that the learner can achieve a reduction inmodes or dimensions.

PCA revealed three components of the task, namely, a hor-izontal torque, a vertical normal force, and an anteroposteri-or torque. The first component is essential to task perfor-mance, whereas the second and third components serve tomaintain posture during the task. Those findings are compat-ible with the muscle modes (m-modes) found during themaintenance of posture by Krishnamoorthy, Goodman, Zat-siorsky, and Latash (2003)—who, on the basis of PCA,grouped m-modes into push-back, push-forward, and mixedmodes of control. The changes in significant variables withineach principal component, despite little change in platformamplitude from Block 3 to Block 4, is supportive of the ideaof a null space or uncontrolled manifold (Latash, Scholz, &Schöner, 2002; Scholz & Schöner, 1999; Schöner, 1995) inwhich changes to the joint-space degrees of freedom canoccur without any destabilization of task performance. Thechanges in variability also provide support for the principle ofdegeneracy; that is, the motor system may recruit differentstructures to achieve a single goal (Edelman & Gally, 2001).

Concluding Comments

In summary, the present 3D analysis of the learning ofthe ski-simulator task has revealed different patterns ofchange in the dynamical and mechanical degrees of free-dom (Newell & Vaillancourt, 2001). In this ski-simulatortask, the recruitment and suppression of the mechanicaldegrees of freedom as a function of practice seem to bedone within the same number of dynamical degrees of free-dom. Perhaps the confluence of constraints to performingthis task ensures that the three dimensions are required ifmotion on the platform is to occur (Newell, 1986). Thatinterpretation is the same as, for example, the notion thatjuggling has a particular form or component structure if theparticipant is to be observed or defined as juggling (Beek,1989). It also points out that more than a single coordina-tion mode is required to capture the richness of the collec-tive behavior of all the available limb segments performingthe task. Thus, the task constraints, in conjunction withthose of the organism and environment, significantly drivethe organization of movement and the nature of its chang-ing pattern of coordination and control over time.

The interaction of task, organismic, and environmentalconstraints affects not only the recruitment and suppressionof the mechanical degrees of freedom but also their spa-tiotemporal organization within the dynamical degrees offreedom. It is possible that linear analysis and the assumptionof orthogonality of the PCA may not adequately capture thedimensions of the ski-simulator behavior because both thedimensions themselves and their change over time are notnecessarily integer wholes. Those dimensions could be sub-tle and fractal so that the behavior of a mechanical degree offreedom is fractioned and is, in fact, shared between thedimensions of the coordinated behavior. A convention forperforming such an analysis has yet to be defined, however.Nevertheless, the findings of our experiment clearly showeddifferent patterns of change in the mechanical and dynamicaldegrees of freedom as a function of practice. The mastery ofdegenerate degrees of freedom seems to be considerablymore complex than was articulated by Bernstein (1967) in hisseminal writings, and the present data have provided furtherevidence that a more detailed consideration of the concomi-tant changes in the mechanical and dynamical degrees offreedom in learning is required.

NOTES

1. We use the term redundancy within this text to remain with-in the original theoretical framework of Bernstein (1967). In lightof more recent work by Edelman and Gally (2001), we find moretenable the use of the term degeneracy.

2. We also ran the PCA on the respective joint angles and rawjoint positions in three dimensions. All those analyses yielded sim-ilar numbers of components (between three and four) accountingfor the majority of the variance. The PCA was run on all theblocks, but, as a means of data reduction, we compared the com-ponents only between the first and last block.

3. We have used the term mode of coordination or coordinationmode so as to maintain similarity with the m-modes that Krish-namoorthy et al. (2003) found by using PCA.

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