Synchronisation and Differentiation: Two Stages of Coordinative Structure



For each subject, we ensured the marker cables did not
interfere his motion. No subject reported a difficulty for
his performance.

Based on the marker setting, the body model was con-
structed. Our body model consists of 8 joints and 13 seg-
ments. Thejoints were defined as a planar angle between
two segments, which were defined by two sensor points
or virtual points (i.e., derived points from two sensors).
The joints are: neck (J1), lumbar (J2), left elbow (J3),
right elbow (J4), left hip (J5), left knee (J6), right hip
(J7) and right knee (J8). For samba shaking, the sen-
sors on the left wrist were moved to the shaker and the
joint was moved from right elbow to left wrist. While
the joint angles were evaluated by calculating the plane
angle between two segments, we regarded this angle as
an approximated hinge angle since both motions could
be regarded as a planar movement on the sagittal plane.

Experimental methods and protocols were as follows.
For kneading motion, five subjects participated in the
experiments: one professional (subject A, the expert),
three experienced (subject B, C, and D) and one novice
person (subject E). They were ordered by the years of
experience.

The subjects were requested to knead the clay for 60
seconds on a wooden table. Five trials were performed
on the same day, with short intervals between each trial.
Novice subjects were instructed the method by an expe-
rienced person (one of the experienced subjects).

For samba shaking, two subjects (subjects X and Y)
participated, both of who were advanced beginners. For
this experiment, we removed the table from the stage
and the subjects performed dance without obstacles. No
music was provided but a metronome signal was given
to them. Five trials were performed on different tempos,
90, 100, and 110 bpm (Beat Per Minute). Each perfor-
mance continued for 180 seconds. Subjects were asked
later which tempo had been most natural to them. Both
subjects reported that 100 bpm was favored. One beat
consists of four shaker sounds and one period of wrist os-
cillation makes two sounds. Then, 200 periods of wrist
oscillation (usually 100 period of the rest of the body)
per minute were recorded.

3.2 data processing

After measurement was done, time series data were pro-
cessed as described below. Relative phase was evaluated
by calculating instantaneous phase using Hilbert trans-
formation (Panter, 1965) (Pikovsky et al., 2001). With
this method, the instantaneous phase and amplitude are
obtained for arbitrary signals. After calculating the rel-
ative (instantaneous) phase between joint angles, the
magnitude of coordinations was evaluated.

After joint angles were calculated, time series data was
processed as follows.

filtering

First, smoothing by fourth-order Butterworth filter
(cutoff frequency is 10 Hz) was applied. Second, to
evaluate coordination within a single period of mo-
tion, low-frequency trends were subtracted. Low fre-
quency trend was obtained by long-term moving av-
erage (101 in our case, the result did not strongly
depend on the length of lag). The latter filtering was
required to obtain unambiguous origin on the phase
plane (i.e., for the instantaneous phase). We did not
use other parameters in the rest of process.

Hilbert transformation

Instantaneous phase and amplitude were obtained
by applying Hilbert transformation (Panter, 1965)
(Pikovsky et al., 2001). By this transformation,
phase portrait was reconstructed for each joint an-
gle. The phase was obtained by defining the origin
within the phase plane.

calculation of relative phase

Reference angle (i.e., time series of) was defined for
each subject. For kneading, the reference angle was
the hip of anterior stance side (left hip in Figure 2).
For samba shaking, left knee was chosen. Both an-
gles had sinusoidal-like time series and were regarded
as regularly moving parts. In kneading, the hip joint
defines the attitude of the torso and can be used as a
pivoting point for pushing down the clay. In samba
shaking, the knee and the wrist showed the most reg-
ular movement. Because the wrist’s period was twice
shorter than other joints, the knee was chosen. Cal-
culation of relative phase is based on the method de-
scribed in (Pikovsky et al., 2001).

After the relative phase was calculated, distribution
was evaluated by making histograms. The results are
shown in the next section.

4 Results

4.1 overview of kneading

The movement of kneading was decomposed into two
motions. One is the rocking motion of the torso and the
other is the circular motion of the hands and arms. See
Figure 2 for schematic representation. The two motions
were combined to efficiently stretch and fold the clay.
One may think that it is more efficient to push down
the clay at the swing down (i.e., forward) phase, but
we found pushing the clay in the swing backward phase
to be more efficient: the arms also help to move the
torso backward. However, it turned out to be nontrivial
feature. Only subject A (expert) showed this motion.

One reason for the phenomenon may be sought in the
complexity of motion. If one pushes the clay in the for-
ward phase, the motion is essentially simple cycle with-
out phase difference. On the other hand, when he pushes

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