Received April 23, 2021, accepted May 3, 2021, date of publication May 7, 2021, date of current version May 24, 2021.
Digital Object Identifier 10.1109/ACCESS.2021.3078202

Application of Supervised Principal Motion
Analysis to Evaluate Subjectively Easy
Sit-to-Stand Motion of Healthy People
CHONGYANG QIU1 , SHOGO OKAMOTO 1,2 , (Member, IEEE),YASUHIRO AKIYAMA 1 , (Member, IEEE), AND YOJI YAMADA1 , (Member, IEEE)
1 Department of Mechanical Systems Engineering, Nagoya University, Nagoya 464-8603, Japan
2 Department of Computer Sciences, Tokyo Metropolitan University, Hino 191-0065, Japan

Corresponding author: Shogo Okamoto (shogo.okamoto@mae.nagoya-u.ac.jp)
This work was supported in part by the MEXT Kakenhi under Grant 19K21584.

ABSTRACT Redundant human motions such as walking or sit-to-stand motions involve time-series dataof several variables. Principal motion analysis (PMA) can be adopted to decompose such motions into
independent motions, and their linear combinations can be used to approximate the motions. In contrast to theexisting PMA methods, which are unsupervised, we applied partial least-squares regression to perform PMA
such that the scores for the principal motions were correlated with a continuous objective variable. To validate
the practicality of this approach, we investigated the subjectively easy sit-to-stand movement of healthypeople. The participants were six healthy young individuals who performed the sit-to-stand movement
under 33 different conditions by changing the foot position, hand-grip position, and initial pitch angle ofthe upper body. The motion data and magnitude of the subjective burden reported for each movement wereanalyzed. Three principal motions correlated with the subjective burdens were determined and interpreted.
The correlation coefficients of the first, second, and third principal motions and the subjective burdens were0.60, 0.27, and 0.19, respectively. Moreover, the sit-to-stand conditions synthesized by the three principal
motions incurred a burden subjectively smaller than or comparable to the burdens in other conditions.
INDEX TERMS Motion synergy, foot position, handrail grip position, subjective burden, supervised
learning.
I. INTRODUCTION

By analyzing human motions, certain recommendations canbe suggested, for example, to ease motion-related pain andreduce the energy consumption. Human motion is dynamic
and involves multiple joints; hence, instead of the principal component analysis (PCA), principal motion analysis(PMA)1 is used to analyze this motion [1]–[5]. Similar to
PCA, PMA reduces the dimensions of the parameter spaces
without losing the information of the dynamically interlocked
multiple degrees of freedom of redundant systems. The setof the correlated time-series of these multiple degrees of
freedom is termed as the principal motion or motion synergy. Any sampled motion can be approximated by the linear
1 Several names have been used for the family of PMA techniques, including spectrum analysis, synergy analysis, motion primitives, and functional
PCA.
The associate editor coordinating the review of this manuscript andapproving it for publication was Mauro Gaggero
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combinations of several principal motions when the sample
set fits the space, with the scores of the principal motions
corresponding to the base. In other words, PMA represents
the time-extension of the PCA, and it is an unsupervised
method.
In contrast, generalized PMA is a supervised method basedon the categories of samples [6]. In this method, the principal
motions are identified by classifying samples according totheir categories. Specifically, this approach represents thetime-extension of the linear discriminant analysis method.
However, the generalized PMA does not allow the use ofcontinuous variables as objective variables to supervise theanalysis. To ensure the use of continuous objective variables,
we aimed to establish a PMA approach based on the partial
least-squares regression (PLS), which determines the principal motions whose scores are correlated with the continuous
objective variables. To the best of our knowledge, such an
extended PMA method has not yet been employed to analyze
human motions.

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

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We apply the PMA method extended by PLS on
sit-to-stand movements, with the subjectively reported magnitude of burden as the objective value. As summarized
in Section II, numerous studies have investigated methods
to reduce the physical burden on the lower limbs during
sit-to-stand movements [7]. These studies primarily discussed the influence of the environment and posture parameters on the lower-limb joint moments and biomechanicalindices but did not focus on the subjective burden pertaining
to sit-to-stand motions.
Furthermore, as discussed in Section II, many researchers
have focused on the moments of certain joints; however,the subjective burden of the complete body is determined by
the synergy of the burdens of multiple joints, not by a certain
lower-limb joint [8]. Few researchers have focused on therelationship between the magnitude of the subjective burden
and temporal evolution or motion of multiple joint angles andmoments during the sit-to-stand movement.
Therefore, in this study, we introduced a supervised
PMA that computes the principal motions such that theirscores are correlated with a continuous objective variable.
Then, its applicability in examining the human motions wasinvestigated considering the analysis of subjectively easy
sit-to-stand movements. As mentioned previously, the timeseries analyses of sit-to-stand motions have yet to be
performed from the viewpoint of subjective burdens. We
identified several principal motions correlated with the magnitude of subjective burden and investigated the sit-to-standmovements with a small subjective burden. This study wasapproved by the institutional review board of the School ofEngineering, Nagoya University (#18-2).
II. RELATED STUDIES

Thus far, many researchers have applied unsupervised PMAs
on human gaits [1], [3], [4], [6], [9] and found their redundancies, synergies of multiple joints and muscles, and elementarycomponents. PMAs can be also used for other types of humanmotions [2], [5], [10]–[13]. For example, Yamada et al. analyzed the properties of therapeutic techniques of physicaltherapists based on their manual motions and forces applied
to the patients’ diseased body parts [13]. As mentioned previously, the present study used a supervised PMA whereas
these earlier studies leveraged unsupervised ones.
Many studies reported that the physical burden of sit-tostand motions can be reduced by ensuring more optimal
apparatus settings of parameters such as the height of a chair,and the shape, position, and type of handrails [14]–[26]. Some
researchers examined the effects of unilateral handrail useon the lower-limb joint moments [19], [20]. Katuhira et al.
investigated the influence of different handrail grip positions
on both upper- and lower-limb joint moments [23]. In general,
the initial knee flexion angle and foot position are criticalparameters influencing the lower-limb joint moments [24],[25]. Shepherd et al. reported that the initial tilt angle ofthe upper body affects the duration of occurrence of the
maximum moment [26]. Moreover, by using the momentum
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generated by the upper body, efficient sit-to-stand movements
can be performed [27], [28]. These studies focused on physical burdens comprising the lower-limb joint moments andbiomechanical indices whereas the present study discusses
the subjective burden of sit-to-stand motions.
For the analysis of sit-to-stand motions, the momentsof certain joints are particularly studied, which may bepartly because pain pertaining to joint diseases such as
knee osteoarthritis is linked with joint burdens such as themoments [29], [30]. Further, in the context of low-back pain,
the compressive force applied to the lumbar spine, which isusually computed based on the hip moments, is used as asafety standard for industrial workers [31], [32]. However,the subjective burden of the complete body is collectively
determined by the burdens of multiple joints. For example,
Chihara et al. investigated the optimal height and distanceof handrails by considering the surface electromyograms offour muscles during sit-to-stand movements [8]. The authors
noted that the combination of the electromyogram values ofmultiple muscles could more accurately predict the subjective
impressions compared to that obtained considering a single
muscle. In contrast, the present study computed the concurrent changes in multiple joint angles and moments.
Some researchers attempted to optimize the motions ofmultiple joints during the sit-to-stand motion through optimal
control and machine learning [33]–[35]. For example, Mombaur determined the lower-limb joint torques and motions
such that the sum of the squared joint torques was minimized [33]. Jamali et al. used reinforcement learning tominimize the energies of lower-limb joints required to perform stand-up motion [34]. Similarly, the motions involving
the least power consumption were identified using genetic
algorithms [35]. Furthermore, several studies indicated that
sit-to-stand motions are generated while ensuring reduced
muscle outputs. Specifically, the motions may be yielded toreduce the changes in muscle torques [36], [37] or the costvalues involving the magnitudes of the muscle torques andtheir changes [38]. Unlike these studies, we investigate therelationship between the magnitude of the subjective burden
and temporal evolution or motion of multiple joint angles andmoments.
III. PARTIAL LEAST-SQUARES (PLS) REGRESSION FOR
PRINCIPAL MOTION ANALYSIS (PMA)

In the PLS method, the covariance between multiple explanatory and objective variables that are continuous is analyzed
to determine their relevant linear linkages [39]. In this work,
the PLS is extended to the time-series data for one objective
variable. Suppose that a motion is represented by n0 typesof time-series variables with a data length of l. In this case,a single sit-to-stand motion can be discretized into l moments.
To express the motion at the k-th trial (k = 1, . . . , k 0 ) for(s)participant s (s = 1, . . . , s0 ), we establish vector xk (∈0
Rn l×1 ) as follows:
(s)

(s)T

(s)T

(s)T

xk = [x1k , . . . , xnk , . . . , xn0 k ]T(1)
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C. Qiu et al.: Application of Supervised PMA to Evaluate Subjectively Easy Sit-to-Stand Motion of Healthy People(s)where, xnk (∈ Rl×1 ) represents a column vector containing the time-series of the explanatory variable n (n =(s)1, . . . , n0 ) for participant s at trial k. For example, xnk can
be a time-series of a certain joint angle or moment. Each s0
participant undergoes k 0 trials. The motions of all the trials
0 0
0
are represented as matrix X (∈ Rs k ×n l ):(s)

X = [xk : k = 1, . . . , k 0 , s = 1, . . . , s0 ]T .

(2)

The value of the objective variable at the k-th trial for(s)participant s is expressed as yk , and the values for all thetrials and participants can be defined as
(1)

(s0 )

(s)

y = [y1 , . . . , yk , . . . , yk 0 ]T .
The model formulas for PLS are as follows:aXX =t i pTi + Ex
y=

i=1
a
X

qi t i + ey

(3)

(4)
(5)

Similar to the first principal motions, pi and qi are calculated using t i , X i , and yi . The principal motions are independent of one another and do not statistically interfere.
tj ⊥ tk(j, k ∈ {1, . . . , a}, j 6= k).

(12)

IV. METHODS: APPLICATION TO SUBJECTIVELY EASY
SIT-TO-STAND MOTIONThis section describes the experimental methods and data
analyses performed to demonstrate the proposed PMA
extended by the PLS, considering subjectively easy sit-tostand motions.
A. PARTICIPANTS

Six healthy male university students (22.2 ± 0.8 years,
172.2 ± 4.4 cm, 59.6 ± 8.7 kg), who provided written
informed consent, participated in this experiment. The participants were not informed of the study objectives. None ofthe participants reported a history of diseases that affected
sit-to-stand movement.

i=1

where a is the number of principal motions adopted. X isdecomposed into two matrices with column vectors t i (∈0 0
0
Rs k ×1 ) and pi (∈ Rn l×1 ). t i is the vector of the principal
motion scores, which are the coordinates of the motion samples on the reduced space, and pi is the vector of the principal
motion loads. y is decomposed into a vectors, each of which
is described by qi t i , where qi is a scalar value. Ex and ey are
the residuals for X and y, respectively.
Based on these formulas, the scores and loads of the firstprincipal motion can be computed. First, t 1 is determinedsuch that the covariance of t 1 and y is maximized, as follows:
t1 =XX T y(6)

kX T yk

where k • k is the L2 norm. Next, p1 and q1 are respectively
calculated as
X T t1p1 =kt 1 kyT t 1q1 =kt 1 k(7)

B. APPARATUS

As shown in Fig. 1, a height-adjustable chair was used inthis experiment, with the height adjusted to the knee levelof each participant. A bilateral handrail was used, and the
distance between the two handrails was 0.7 m. The handrails
were adjusted to the height of the greater trochanter when
the participants were standing. When sitting on the chair,
the participants were instructed to match the middle of theirthigh and fore edge of the chair and maintain the distance
between the two feet as the distance between their acromia.
These configurations are summarized in Table 1. To control
the posture of the head, a mark was introduced at a heightof 1.7 m, 3 m in front of the chair. The participants were
instructed to look at the mark throughout the sit-to-standmovement.
TABLE 1. Configurations of sit-to-stand task and initial trunk tilt angle
and positions of the hands and feet.

(8)

such that the sums of the squared elements of Ex and ey areminimized.
To compute the i-th (i = 2, 3, . . .) principal motions,
we defineX i = X i−1 − t i−1 pTi−1
yi = yi−1 − qi−1 t i−1

(9)
(10)

where X 1 = X and y1 = y. X i and yi are the residuals
after removing the parts expressed by up to the (i − 1)-thprincipal motions from X and y, respectively. Therefore,t i is calculated asti =VOLUME 9, 2021

Xi Xi T yi
kXi T yi k

.

(11)

The forces applied to the handrails were measured using
force sensors (six-axial, PFS055YA251, Leptrino, Japan)
installed inside the handrails. One force sensor was installedon each of the two poles supporting a handrail. The groundreaction force applied to each foot was measured using a force
plate (M3D-FP-A, Tec Gihan Co. Ltd., Japan). A motion capture system (MAC 3D system, Motion Analysis Corporation,U.S.) was used to obtain the posture of the body to determine
the angles of the upper-limb and lower-limb joints. Markers
were set at the scapulae, elbow joints, wrist joints, greater
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FIGURE 1. Apparatus and experimental setup. The joint angles weremonitored using a motion capture system. The ground reaction forces andhandrail forces were measured.

FIGURE 2. Position of the feet, grip on the handrails, and tilt angles. The
three parameters were varied in the standing-up trials.

trochanters, knee joints (lateral femoral condyle), ankle joints(lateral malleolus), calcanei, distal phalanx of each foot, andthe seventh cervical segment. All the data were sampled
at 100 Hz.
C. TASKS

The participants repeatedly stood up from a seated positionon the chair. For each trial, we varied or controlled the initial posture. The parameters to control the posture included
the trunk-tilt angle, grip position, and foot (ankle) position.
Three to five levels for each parameter were considered aslisted in Table 1. As shown in Fig. 2, three initial trunk-tilt
angles (15◦ , 30◦ , 45◦ ) were considered as the angle between
the trunk vector and gravity vector. The trunk vector was
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defined by the center of the greater trochanters and seventh
cervical segment. The participants were instructed not to flex
their trunk before they rose from the seat. In other words,
the participants did not leverage the angular momentum of
the trunk to stand up. Further, five grip positions (H1 , H2 ,H3 , H4 , H5 ) and three ankle positions (A1 , A2 , A3 ) wereconsidered. Positions H1 and A1 matched the middle of thethigh, whereas H3 and A3 matched the knee joint. H2 andA2 were positioned at the center of H1 and H3 and A1 and
A3 , respectively. The distances for H3 –H4 and H4 –H5 were
the same as that between H1 and H2 . The participants started
their stand-up motion with the initial conditions defined by
the three parameters. At the standing-up position, the participants’ trunks were upright while gripping the handrail.
The participants pushed the handrails downward, without any
pulling motion. The participants did not change the positionof the grip or feet during a single standing-up motion. Further,during the motions, the complete soles were in contact withthe ground. We determined the parameters through informal experiments in which the subjectively easiest motions
were likely to be included in the space established by theseparameters. For example, when the trunk-tilt angle is smaller
than 15◦ , it is relatively difficult or tiring to stand up; hence,
we excluded such small trunk-tilt angles. Similarly, when theankle is positioned in front of A3 or the grip is positioned
behind H1 , the standing-up motion involves a large subjective
burden, and thus, such parameters were excluded.
By varying the three types of parameters, 33 conditions
were implemented in a randomized order in a single set.
These 33 conditions did not exhaustively include all the
combinations of the three parameters because certain combinations resulted in virtually impossible motions. Under these
difficult conditions, only a few or none of the participants
could perform the standing-up motions. For example, noneof the participants could stand up when the initial trunk angle
was 15◦ and the grip and ankle positions were H1 and A3 ,respectively. Each participant performed two experimental
sets, and a total of 66 motions were recorded.
The level of subjective burden was investigated throughthe magnitude estimation method. First, the participants were
instructed to practice the sit-to-stand movement under thereference condition, wherein the trunk-tilt angle, grip position, and ankle position were 30◦ , H3 , and A2 , respectively.
The experienced subjective burden for the complete body inthis condition corresponded to a score of 100. Among thetested conditions, the reference condition incurred a moderateburden. After each trial of the sit-to-stand movement, the participants assigned a certain score to the subjective burden.
A higher score represented a heavier load. If a participant felt
a certain motion was two times more tiring than the reference
motion, the score was 200. The movement speed and force
applied to the handrails were determined by the participants
themselves such that they could perform the standing-up
motions naturally. The participants were instructed to avoid
the generation of laterally asymmetric motions as much as
possible.
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D. DATA ANALYSIS
1) COMPUTATION OF JOINT ANGLES AND MOMENTS

The ankle angle was the angle between the calf and gravity
vector. The knee angle represented the flexion of the knee
joint. The trunk-tilt angle was defined as the angle between
the gravity vector and trunk vector connecting the seventh
cervical segment and center of the greater trochanters. The
shoulder angle was computed as the inner product of the trunk
vector and upper-arm vector, whereas the elbow angle was
the flexion of the elbow joint. These angles were zero at the
upright standing position. The internal static joint moments
were computed and used for further analysis because theacceleration of the motion was small. Directions to support the body weight were defined positive. The mean values of the bilateral limbs were used to compute the angles
and moments of the joints assuming laterally symmetricmotions.
2) CYCLE OF SIT-TO-STAND MOTION AND NORMALIZATION

The period from the seating-off to the instant at which theangular velocity of the trunk became zero was normalized toa 100% cycle. The joint moments were normalized according
to the height and weight of each participant. The scoresof the subjective burden assigned by the participants werenormalized by the geometric mean of the scores of all thetrials.
3) PMA EXTENDED WITH PLS

In this study, the magnitude of the subjective burden was
the objective variable, whereas the time-series of the ankle,
knee, trunk, shoulder, and elbow joint angles, as well as
the ankle, knee, hip, shoulder, and elbow joint moments,
were considered as the explanatory variables (n0 = 10). The
time-series were discretized into 101 instants: l = 101. For
each instant, the explanatory variables, i.e., joint angles andmoments, were normalized as the z-scores for the individuals.
Because each of the six participants conducted 66 trials,
k 0 = 66 and s0 = 6.
V. RESULTS
A. CORRELATION BETWEEN THE PRINCIPAL MOTIONSAND SUBJECTIVE BURDEN

Table 2 lists the correlation coefficients between the scores ofthe four major principal motions and magnitude of the subjective burden. Based on the correlation coefficients, the first
three principal motions were considered in this work. The
linear combination of these three principal motions exhibiteda correlation coefficient of 0.74 with the reported subjective burdens. Even when the fourth principal motion was
included, the correlation coefficient exhibited only a slightincrease, reaching 0.77. Bartlett’s test can be used to determine the number of principal components for PCA. This
test was incorporated in the present analysis; however, thisapproach resulted in a larger number of significant principal
motions, i.e., nine, several of which exhibited extremely small
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FIGURE 3. Loads of the three principal motions. Zero of the vertical axis
represents the mean value of all the trials. A positive load indicates thatthe corresponding joint angle or moment is greater than that of the mean
sit-to-stand motion.

correlation coefficients with the subjective burdens. Hence,
we did not adopt Bartlett’s test as a criterion to determine thenumber of principal motions.
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FIGURE 4. Schematic of the initial positions and moments represented by the individual principal motions. The arc
arrows are the representative internal joint moments. (a)–(c) correspond to the first–third principal motions.

TABLE 2. Correlation coefficients between the scores of each principal
motion and magnitude of the subjective burden.

B. PRINCIPAL MOTIONSThis section describes each principal motion and its meaning
based on the corresponding loads of the joint angles andmoments (pi ). Fig. 3 shows the loads for each principal
motion. The zero of the vertical axis represents the meanvalue of all the trials at each motion cycle because all thevariables were normalized to z-scores before being applied to
the PMA-PLS, as described in Section IV-D3. Hence, at a certain motion cycle, a positive load of a joint angle or moment
indicates that the angle or moment is greater than the mean
joint angle or moment at the corresponding motion cycle. In
Section VI, these principal motions are discussed based on therelationships between the center of the body mass and base of
the support.
1) FIRST PRINCIPAL MOTION

The load of the first principal motion is shown in Fig. 3 (a). At
0% of the cycle, the ankle and knee angles are substantiallysmaller than the average, i.e., zero, indicating that the feetare in the anterior positions when seating-off. The momentof the knee joint is small in the first half of the motion.
Subsequently, the moment returns to the normal level atapproximately 50% of the cycle. The moment of the hip joint
exhibits an opposite trend to that of the knee. Specifically,
the moment of the hip joint is relatively larger than the
average in the first half cycle and gradually returns to theaverage level. The moment of the ankle joint is considerably
smaller than the average throughout the cycle, whereas the73256

shoulder and elbow joint moments are larger than the average.
Relatively large moments are applied to the upper limbs.
Collectively, the sit-to-stand movement represented by the
first principal motion is performed as follows. The feet areplaced in the anterior positions, and later, the hip and arms areleveraged to raise the body. In other words, the knee and ankle
joints are not efficiently used to stand up. A typical initial
posture represented by the first principal motion is shownin Fig. 4 (a). Note that the movements that are dominant in
the first principal motion incur a large subjective burden.
2) SECOND PRINCIPAL MOTIONAs shown in Fig. 3 (b), in this motion, the initial trunk-tilt
angle and angle of the elbow joint is considerably larger andsmaller than the average, respectively. In other words, the grip
position pertains to relatively anterior positions. In the lastphase of the cycle, the angles of the ankle and knee joints
are larger than the average, which indicates that the knees
are not entirely extended. This phenomenon occurs when theparticipants place their hands in anterior positions. In termsof the moments, the moment of the ankle joint is relatively
large throughout the cycle. The moment of the knee joint issmaller than the average at the central part (∼40%).
In this motion, the initial upper trunk is relatively flexed,
and the grip position is relatively anterior. The participants do
not or cannot utilize their arms to support their body weights
because the grip position is far from the center of the bodyowing to the relatively extended elbows. Instead, the weightof the body, which is leaned forward, is mainly balanced by
the ankle moments. A typical initial position represented by
the second principal motion is shown in Fig. 4 (b).
3) THIRD PRINCIPAL MOTIONAs shown in Fig. 3 (c), initially, the angles of the knee joints
are smaller than the average, indicating that the feet are positioned anteriorly. The initial trunk-tilt angle is larger than the
average and decreases sharply, indicating that the extension of
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TABLE 3. Criteria to judge the valid synthesized motions.

the upper trunk is relatively rapid. The angles of the shoulder
and elbow joints indicate that the grip position is close to theknee. In this motion, the hip joint bears less burden in thecentral phase. Large shoulder and elbow moments indicatethat a large force is applied to the handrail in the first halfphase, thereby assisting the extension of the upper body.
A typical initial position represented by the third principal
motion is shown in Fig. 4 (c).
VI. SYNTHESIS OF THE SIT-TO-STAND MOTION WITH A
SMALL SUBJECTIVE BURDEN
A. METHOD TO SYNTHESIZE SUBJECTIVELY EASY
SIT-TO-STAND MOTIONS

Based on the relationships between the principal motions
and subjective burdens, to determine the sit-to-stand motions
with small subjective burdens, we investigated a number of
combinations of the three principal motions. Fig. 5 shows the
distribution of the motion trials in the space of the principal motion scores. As each score was positively correlatedwith the subjective burden, the scores in the bottom left
regions were considered to correspond to less tiring motions.
We exhaustively synthesized the motions in the regions covered by the scores of −30 to 0 for each principal motion,
covering 2700 (303 ) motions.
The sit-to-stand movements in this region comprised
impossible or unrealistic motions. Furthermore, certain
motions did not end in a complete standing-up posture. To
ensure that the synthesized motions were complete and realistic, a series of evaluation criteria, as listed in Table 3, wereadopted. The synthesized motions that did not satisfy theconditions in the table were judged invalid. At the beginning of a sit-to-stand motion (0% motion cycle), we set the
maximal ankle angle as 30◦ , knee angle as 110◦ , and trunk
angle as 50◦ . The initial postures with trunk-tilt angles greaterthan 50◦ were regarded unnatural. Moreover, the postureswith ankle angles greater than 30◦ are difficult to accomplish,
for most individuals, while ensuring that the complete soleis in contact with the ground. Furthermore, these three joint
angles were required to be sufficiently small at the end of
the motion to complete the standing-up motion. We regarded
the postures with the trunk-tilt, knee, and ankle angles
smaller than 5◦ , 10◦ , and 10◦ , respectively, at 100% of the
motion cycle as complete standing-up postures. Moreover,the moments of the elbow and shoulder joints could not be
negative.
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FIGURE 5. (a) Distribution of the sit-to-stand motions based on the firstand second principal motion scores. (b) Distribution based on the first
and third principal motion scores. Blue circles indicate the observed
motion samples, and the red box is the area in which easy sit-to-standconditions were identified. The cross represents the synthesized motion
whose subjective burden is predicted to be the smallest.

B. SYNTHESIZED SUBJECTIVELY EASY MOTION

The synthesized motion with the smallest subjective burden
appears at the coordinates (−14, −23, −11), represented bya cross in Fig. 5, in the three-dimensional principal motion
space. In addition, the second and third easiest conditions also
occur near this coordinate, as indicated in Table 4. Owing to
the similarity in the three conditions, only the easiest condition is described herein. Assuming the weight and height ofthe participant as 60 kg and 172 cm, respectively, the simulated angles and moments of joints are shown in Fig. 6.
TABLE 4. Principal motion scores for the three easiest motions
synthesized by the three major principal motions.

The initial tilt angle is nearly 20◦ , and the feet are placed ata relatively posterior position because the initial knee angle
is approximately 100◦ . The corresponding initial posture is73257

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FIGURE 7. Initial conditions of the subjectively easy sit-to-standmovement synthesized by the three principal motions.

FIGURE 6. Synthesis of the condition that results in the minimum
subjective burden. (a) and (b) pertain to the joint angles and moments,
respectively.

shown in Fig. 7. Considering the angles of shoulder and elbow
joints when seating off, the grip position is above the pointclose to the middle part of the thigh. The angles of the ankle
joint, knee joint, and trunk are nearly zero at 100% of thecycle, in accordance with the standing posture.
Handrails are not intensively used to support the bodyweight because the shoulder and elbow moments are relatively small. The knee and hip moments are maximized at
approximately 20% of the cycle and then gradually decrease.
In contrast, the ankle moment does not clearly exhibit alocal peak and starts to increase after 50% of the cycle.
These characteristics of moments are consistent with thosefor the natural or unrestricted sit-to-stand motions without
handrails [22], [37], [40], [41]. After approximately 80% of
the cycle, a negative knee moment occurs, indicating that thegravity of the upper body generates a reverse moment on
the knee joint, which has also been observed for the motions
without handrails [22], [35], [37], [41].
C. EXPERIMENTAL VALIDATION OF SYNTHESIZEDMOTION
1) PARTICIPANTS AND TASKS

We invited 15 participants (male students, age: 22.7 ±1.0 years, height: 173.5 ± 4.6 cm, weight: 61.5 ± 8.9 kg)
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including the six participants in the experiment describedin Section III to a simplified experiment to evaluate thesynthesized motion. The participants provided written
informed consent.
Three types of initial postures were ranked. Posture 1 corresponded to the initial posture of the synthesized subjectively easiest motion: (trunk-tilt, grip position, ankle position)= (20o , H1 , A1 ), as shown in Fig. 7. Posture 2 corresponded tothe conditions used as a reference in the experiment describedin Section III: (trunk-tilt, grip position, ankle position) =(30o , H3 , A2 ). Posture 3 corresponded to a relatively difficult condition: (trunk-tilt, grip position, ankle position) =(15o , H3 , A2 ). Each initial posture was evaluated only once by
the individual participants. The initial postures and motions
were monitored by experimenters and videotaped for postreview. The ground reaction forces and handrail forces were
not recorded. As in the task described in Section IV, the participants did not move their feet and grip positions from thedesignated initial positions during the sit-to-stand motion.
Subsequently, the participants ranked the three postures thatwere experienced in randomized order. The participants were
instructed to perform the ranking based on the burden experienced by the complete body. One rank could only be assigned
to a one posture.
2) RESULTS

Nine among the 15 participants selected posture 1 as theeasiest, and the remaining six participants selected posture 2.
Thirteen and two among the 15 participants felt that postures
3 and 2, respectively, were the most difficult conditions tostand up. Wilcoxon signed-rank tests with the Bonferroni
correction were applied to the assigned ranks. We observed
a significant difference between postures 1 and 3 (V = 120,z = 3.41, p = 6.10 × 10−4 < 0.001/3) and between postures
2 and 3 (V = 110, z = 2.84, p = 0.00280 < 0.01/3), andno difference between postures 1 and 2 (V = 78, z = 1.02,
p = 0.297 > 0.05/3). Posture 1, which was the initial postureof the supposedly easiest motion, was judged to be easier thanposture 3; however, a clear difference between postures 1 and
2 was not observed in terms of the subjective burden.
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C. Qiu et al.: Application of Supervised PMA to Evaluate Subjectively Easy Sit-to-Stand Motion of Healthy People

VII. DISCUSSION

In this section, we discuss and interpret the cause of thesubjective difficulty for each principal motion in terms of thecenter of mass (COM) and base of support (BOS), because,in general, sit-to-stand motions are considered to be a transferof the COM to the region above the BOS or the center ofground reaction force [27], [42].
The initial posture represented by the first principal motion
is shown in Fig. 4 (a). The feature of this posture is thatthe feet are in an anterior position. Under this condition,at the instant of seating off, the position of the COM wasconsiderably behind the BOS. The COM was required to be
moved forward while lifting up to complete the sit-to-standmotion. To this end, the participants were required to strongly
push the handrails to move their body upward, which resulted
in large shoulder moments, as shown in Fig. 3 (a). In general,
the initial knee angle should be large, and the foot position
should not be far from the COM [24], [25]. The motions
represented by the first principal motion is inefficient. Moreover, the COM was shifted forward, above the BOS, by the
hip and elbow extension moments. In previous reports [25],[43], the hip moments were also comparatively large when thefeet were anterior. To compensate for the initial gap between
the COM and BOS, additional shoulder, elbow, and hip
torques were required, which likely led to a large subjective
burden.
The initial posture represented by the second principal
motion is shown in Fig 4 (b). The key features of thismotion were the large trunk-tilt angle and ankle moments
throughout the motion. Without the handrail use, an excessively large initial trunk-tilt angle results in a longer periodof large supportive joint moments and a less effective sitto-stand motion [26]. With the handrail use in the present
study, to lift up the overly tilted upper body, relatively
large shoulder, elbow, and hip moments were required during the initial 0–10% phase. Subsequently, to cancel the
moment of the body to lean forward, large ankle torques
were required to be implemented until the end of the
motion because the COM was located in the anterior position due to the large trunk-tilt angle. Furthermore, relatively
large hip moments were required, except in the 10–30%
phase, because the COM was far from the hip and themoment arm about the hip was large. Moreover, the initial height of the COM was small, and greater energy was
required to transfer the COM to correspond to the uprightposition.
The initial posture represented by the third principal
motion is shown in Fig. 4 (c). The main differences between
this motion and the second principal motion pertain to theposition of the handrail grip and trunk-tilt angle. In the
representative third principal motion, the foot position wasanterior, and the COM did not lay on the BOS. As mentioned previously, owing to the initial gap between the COM
and BOS, the use of handrails was required to accomplish
the sit-to-stand motion because such gap between the COM
and BOS leads to low stability during the motion [44].
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This principal motion relied considerably on the handrails,i.e., the elbow and shoulder moments.
In contrast, as shown in Figs. 6 (a) and 7, in the case of thesynthesized supposedly easy sit-to-stand motion at the initialknee angle of approximately 100o , the feet positions wereposterior. In fact, this knee angle was similar to that of natural
sit-to-stand motion [41]. In general, posterior feet positions
lead to effortless sit-to-stand motions [45]–[47]. Further,
the COM, BOS, and grip position were aligned nearly vertically. In this configuration, the horizontal transfer of theCOMs was eliminated under the settings of the present study,
in which the participants did not utilize the momentum causedby tilting the upper body. Furthermore, this alignment benefited the participants as the reaction force from the handrail
did not produce moments to lean forward or backward about
the COM. These aspects likely explain the reasonably low
burden in synthesized motion or initial condition.
As shown in Fig. 6 (b), the moments of the upper limbs
were small, with a maximum value of only 10 Nm. The
moment values of the lower limbs were similar to thoseobserved when healthy people stand up without handrails,
as reported in [22], [41]. Thus, in our experimental settings,
the healthy young participants likely did not substantiallydepend on the handrails. In general, in the case of healthy
young people, the decrease in the lower-limb moments isonly approximately 10% because of the use of handrails,potentially because such individuals do not rely on thehandrails [16]. This result is consistent with that reported ina study in which healthy people used handrails to ensure postural stability rather than to decrease the required moments of
the lower-limb joints [48].
As described in Section V, the synthesized motion (posture 1) and posture 2 could not be clearly discerned interms of the subjective burdens. This phenomenon likely
occurred owing to the small difference in the subjective burden between postures 1 and 2 for young university students. In
the experiment described in Section V, the participants’ standup motions were not controlled, whereas their initial positions
were controlled. Thus, the participants could select the mosteffortless motion, irrespective of the initial postures.
This study has certain limitations. First, the motions
synthesized by the principal motions may not necessarily be executable. Because we adopted certain criteria,
as described in Table 3, the motions pertaining to the linear combinations of the three principal motion appeared
to be executable in this study; however, general methods
to evaluate whether the synthesized motions are biomechanically possible must be established. Second, the forward trunk-tilting motion was controlled in our experiment,
although the angular momentum of the upper body is transferred to the lower limbs in effective and natural sit-to-standmotions [27], [40], [42], [49]. Hence, our investigation likely
did not target natural motions. Nonetheless, the consideredsituation is expected to be close to the sit-to-stand motion
assisted by a supportive machine [50], [51], in which theuser does not perform fast trunk-tilting motion. Furthermore,73259

C. Qiu et al.: Application of Supervised PMA to Evaluate Subjectively Easy Sit-to-Stand Motion of Healthy People

our experiment was designed to investigate the feasibility of
the PMA to evaluate subjectively easy sit-to-stand motion
involving healthy participants. Hence, the experimental condition was simplified and only a few of many determinantsof sit-to-stand motions [7] were considered. A truly subjectively easy motion may be achieved by considering a numberof these determinants collectively. Such motions should be
investigated for disabled people in future. Finally, the principal motions found in the present study involved only six
healthy young participants. Although the principal motions
are semantically valid, they might have been biased by thesmall group of participants.
VIII. CONCLUSION

A combination of PMA and PLS was adopted to analyze andsynthesize human motions, enabling the determination of theprincipal motions that are independent of one another, correlated with a continuous objective variable. To validate theperformance of the proposed approach, subjectively easy sitto-stand motions with handrail use were examined. Based on
the various motions performed by six healthy young people,
we computed the principal motions of sit-to-stand motions
correlated with the magnitude of the subjective difficulty
experienced throughout the motion. Three independent principal motions, whose meanings could be reasonably interpreted, were considered to synthesize the subjectively easy
motion. Finally, reasonably subjectively easy motions or initial postures were determined; however, the young participants could not significantly discern the synthesized andreference motions in terms of the subjective easiness. The
proposed method can be used to investigate the principal
motions of redundant time-series systems with continuous
objective variable to supervise the motions. Potential applications comprise the combination with online motion recognition techniques using wearable sensors [52] or cameras [53]to navigate people to motions with less burdens.
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CHONGYANG QIU was born in Ningbo,
Zhejiang, China, in 1994. He received the
B.S. degree from Zhejiang University, Zhejiang,
in 2017, and the M.S. degree in engineering from
Nagoya University, Nagoya, Japan, in 2020.

SHOGO OKAMOTO (Member, IEEE) received
the Ph.D. degree in information sciences fromTohoku University, in 2010. From 2010 to 2021,
he had been with Nagoya University. He is currently an Associate Professor with the Departmentof Computer Science, Tokyo Metropolitan University. His research interests include haptics, assistive robotics, human-centered informatics, andaffective engineering.
YASUHIRO AKIYAMA (Member, IEEE) received
the B.E. degree in engineering from the Tokyo
Institute of Technology, Tokyo, Japan, in 2006, andthe M.S. and Ph.D. degrees in engineering fromThe University of Tokyo, Tokyo, in 2008 and 2011,
respectively. Since 2016, he has been an Assistant Professor with Nagoya University, Japan. His
main research interests include mechanical safety,
human–robot interaction, and biomechanics.
YOJI YAMADA (Member, IEEE) received the
Ph.D. degree from the Tokyo Institute of Technology. Since 1983, he has been with Toyota Technological Institute, Nagoya, Japan. In 2004, he joined
the National Institute of Advanced Industrial Science and Technology (AIST), as a Leader of
the Safety Intelligence Research Group. In 2009,
he joined the Department of Mechanical Scienceand Engineering, Graduate School of Engineering,
Nagoya University, as a Professor.

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