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Perceived discomfort functions based on joint moment for various joint motion directions of the upper limb
Applied Ergonomics 45 (2014) 308e317
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Applied Ergonomics journal homepage: www.elsevier.com/locate/apergo
Perceived discomfort functions based on joint moment for various joint motion directions of the upper limb Takanori Chihara a, *, Taiki Izumi b, Akihiko Seo a a b
Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan Graduate School of Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 October 2012 Accepted 13 April 2013
The aim of the present study was to formulate the relationship between the perceived discomfort and the joint moment ratio for twelve joint motion directions of the upper limb by considering the betweensubject variability, and to investigate the effect of joint motion direction. Three approximation models (i.e., linear, exponential, and logistic function models) were compared in terms of the accuracy of predicting the perceived discomfort, and the logistic function was selected because its average error was lowest. The concept of L-R fuzzy number was used to consider the individual variability of perceived discomfort, and a simplified distribution of perceived discomfort was represented. Cluster analysis showed that the twelve discomfort functions formed two clusters: one for elbow flexion and a second for the remaining joint motions. The data show that elbow flexion is more sensitive than other joint motions to increases in the joint moment ratio. Ó 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.
Keywords: Biomechanics Function approximation Human diversity Perceived discomfort Fuzzy numbers
1. Introduction Biomechanical analysis and electromyogram (EMG) recordings are widely used to evaluate physical stress and fatigue; they are also applied to design problems of work environments and consumer products in order to reduce physical work load (Chaffin et al., 2006; Tsang and Vidulich, 2006). EMGs record the actual electrical activity of a muscle. However, EMG recordings require preliminary measurements, such as measurement of the maximum voluntary contraction for normalization (U.S. Department of Health and Human Services, 1992); hence, it is time consuming and imposes strain on subjects. In addition, measured EMG recordings evaluate muscle load on only the intended motion; thus, re-measurement of EMGs is necessary when the design variables of work environments and consumer products are changed. Physical load evaluation based on a biomechanical model with the joint angle and joint moment requires the measurements of only the joint angle and external force. Therefore, the experimental cost and strain on subjects may be lower for a biomechanical analysis than for EMG measurements. Biomechanical analysis does not necessarily require experimentation, because the analysis can
* Corresponding author. Tel.: þ81 42 585 8685; fax: þ81 42 583 5119. E-mail addresses: [email protected] (T. Chihara), [email protected] (T. Izumi), [email protected] (A. Seo).
be performed if the joint angles and external forces are given; hence, a biomechanical analysis can be used for the re-evaluation of the physical stress with a design change more effectively. The time that can be allocated to improving work environments or designing consumer products is decreasing with each passing year, in conjunction with the shortening of the development period. That is, an ergonomic physical load evaluation should be performed effectively in a short time. Thus, it is essential to develop an ergonomic design using a biomechanical analysis model that performs physical load evaluation more efficiently than EMG measurements (Lestrelin and Trasbot, 2005; LaFiandra, 2009). Research on postural discomfort imposed by varying joint angles has been reported (Kee and Lee, 2012). The relationships between the perceived discomfort and joint angle have been studied (Kee and Karwowski, 2001, 2004; Chung et al., 2003). Miedema et al. (1997) studied the effects of joint angle and duration on perceived discomfort, whereas Carey and Gallwey (2005) along with Khan et al. (2010) investigated the effects of joint angle and repetition. The ranking of perceived discomfort of joint motions have been investigated (Genaidy and Karwowski, 1993; Kee and Karwowski, 2003). The relationship between perceived discomfort and joint angle can be used to evaluate the discomfort of arbitrary human postures. However, in real situations of working or using a product, arbitrary external forces will act on the human body, and arbitrary moments will act on each joint. In addition, because perceived discomfort is affected more by the joint moment than the joint angle
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T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
(Carey and Gallwey, 2002; Dickerson et al., 2006), the relationship between perceived discomfort and joint moment should be quantified to improve the accuracy of perceived discomfort evaluation. The maximum joint moments that subjects can exert have been measured (Amundsen, 1990; Chaffin et al., 2006; National Institute of Technology and Evaluation, 2009). In these reports, the average maximum joint moment among subjects was measured, and the relationship between the maximum joint moment and joint angle was represented. Boussenna et al. (1982) investigated the relationships between the perceived discomfort and joint moments of the hip, knee, and ankle. Wang et al. (2004) investigated the relationship between the perceived discomfort and biomechanical parameters, including the joint moments when depressing a clutch pedal. Mukhopadhyay et al. (2007) investigated the effects of the joint moment of forearm pronation, forearm rotation angle, elbow angle, and exertion frequency on the perceived discomfort. However, they did not investigate the quantitative effect of the joint moment magnitude on perceived discomfort. Dickerson et al. (2006) investigated the effects of the shoulder joint moment, position of operation object, and stature of subjects on perceived discomfort in a simulated workstation. Perceived discomfort, which was measured by varying the direction and magnitude of external force, was mostly affected by, and represented as a linear function of, the shoulder joint moment. However, they did not investigate the effect of joint motion direction of the shoulder joint (i.e., extension, flexion, abduction, adduction, internal rotation, and external rotation). In addition, the perceived discomforts of the elbow and wrist joints were not considered, although the discomfort of other joints may be as important as that of the shoulder joint. Moreover, the abovementioned reports on the relationship between the perceived discomfort and joint moment or joint angle did not quantify individual differences. The perceived discomfort function for upper limb joints should be formulated by considering the variability so as to take into account human diversity during developing ergonomic design. The objective of the present study was to formulate the relationship between the perceived discomfort and joint moment by considering the variability of subjective evaluation, and to consider differences among the joint motion directions of the upper limb (i.e., shoulder extension, shoulder flexion, shoulder adduction, shoulder abduction, shoulder internal rotation, shoulder external rotation, elbow extension, elbow flexion, wrist extension, wrist flexion, wrist ulnar deviation, and wrist radial deviation). In this study, the perceived discomforts of subjects were measured when they exerted joint moments of arbitrary magnitude in each joint motion direction. The response surfaces of perceived discomfort were approximated by three different approximation models: linear, exponential, and logistic function models. The logistic function model was selected as the best approximation model because its accuracy was highest among the three models. The concept of fuzzy number was used to represent the variability of perceived discomfort among subjects. Finally, clustering the evaluation functions of perceived discomfort for each joint motion direction revealed that the function for the upper limb could be divided into two clusters. 2. Method 2.1. Measurement of perceived discomfort Ten healthy Japanese male subjects, aged between 21 and 25, participated in this experiment. All of them were university students, right handed, and none of the subjects had a musculoskeletal disorder. Their stature, weight, and gripping force are listed in Table 1. The target joint motion directions were the six directions of the shoulder joint (i.e., shoulder extension, shoulder flexion, shoulder
309
adduction, shoulder abduction, shoulder internal rotation, and shoulder external rotation), two directions of the elbow joint (i.e., elbow extension and elbow flexion), and four directions of the wrist joint (i.e., wrist extension, wrist flexion, wrist ulnar deviation, and wrist radial deviation). The subjects sat and exerted joint moments by holding a weight with the dominant hand in the instructed upper limb postures shown in Fig. 1. Note that the forearm is in the pronated position in Fig. 1(i) and in the supinated position in Fig. 1(j); the others are in neutral positions. The joint moment was calculated by magnitude of holding weight and the related segment length of each subject. The maximum joint moment for each subject was measured, after which joint moments with magnitudes of approximately 20, 40, and 60% of the premeasured maximum joint moment were added by adjusting the weight. The subjects kept the instructed postures for 10 s. The magnitude of joint moments was controlled by adjusting the weight. In addition, joint moments lower than the abovementioned magnitudes were added if a subject judged the magnitude as excessive. There was a 5-min rest period after each trial. The perceived discomfort was measured by the category partitioning scale 50 (CP-50) (Shen and Parsons, 1997). The CP-50 has a starting point (i.e., 0 ¼ no) and five categories (i.e., very slight discomfort, slight discomfort, discomfort, severe discomfort, and very severe discomfort). Thus, the ranges for each category are given as follows: “Very slight discomfort”: 1e10 “Slight discomfort”: 11e20 “Discomfort”: 21e30 “Severe discomfort”: 31e40 “Very severe discomfort”: 41e50 Each of the categories is further subdivided into 10 scale points. Subjects first choose the category to which a stimulus belongs, and then choose the degree among the 10 scale points. In this study, the subjects were instructed to rate their perceived discomfort for each magnitude of joint moment assuming the discomfort they perceive when exerting their maximum moment to be 50. The maximum discomfort level was set for all maximum joint moment in each subject and joint motion direction. It should be note that subject may not feel the same level of discomfort between the maximum joint moments at different joint motion directions. This experiment was approved by the Research Safety and Ethics Committee of Tokyo Metropolitan University. 2.2. Selection of approximation model The perceived discomfort probably increases as the magnitude of the joint moment increases. Therefore, the approximation model for the perceived discomfort function must be a monotonically Table 1 Stature, weight, and gripping force of subjects. Subject
Stature [cm]
Weight [kg]
Gripping force [kgf]
A B C D E F G H I J Average S. D.
186 172 172 182 163 168 160 177 171 172 172 7.96
70.6 63.0 62.1 82.0 58.0 50.0 64.0 76.0 61.9 64.2 65.2 9.09
56 41 34 55 33 47 44 50 38 48 44.6 8.09
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(a) Shoulder extension
(b) Shoulder flexion
(c) Shoulder adduction
(e) Shoulder internal rotation (f) Shoulder external rotation Pronated position
Supinated position
(i) Wrist extension
(j) Wrist flexion
(d) Shoulder abduction
(g) Elbow extension
(k) Wrist ulnar deviation
(h) Elbow flexion
(l) Wrist radial deviation
Fig. 1. Instructed upper-limb postures for joint moment exertion.
increasing function. In addition, the perceived discomfort function is probably a linear or weakly nonlinear function. We assume that monotonically nonlinear functions are mainly divided into three types: those that increase during the early (Type 1), middle (Type 2), and late (Type 3) part of the function. In this study, the three function approximation models are set as follows:
y ¼ ax þ b
(1)
y ¼ a þ b$expðcxÞ
(2)
y ¼
a 1 þ expfbðx cÞg
(3)
where x and y denote the explanatory and objective variables, respectively, and a, b, and c are regression coefficients. Equation (1) represents the linear model. Eq. (2), which represents the exponential model, can express Type 1 and Type 3 functions. In addition, Eq. (3), which represents the logistic model, can express Type 2 functions. In this study, the perceived discomfort W (W ¼ [0, 50]), which is measured by the CP-50, is set as the objective variable, and the joint moment divided by the maximum joint moment (hereafter referred to as “the joint moment ratio r (r ¼ [0, 1])”) is set as the explanatory variable. The response surface of the perceived discomfort f(r) is approximated with the three models for each joint motion direction and subject. The regression coefficients are
obtained by minimizing the average absolute error (AAE). The AAE for i-th function model, j-th joint motion direction, and k-th subject was calculated as follows:
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 dijkl b y ijkl l¼1
Pn AAEijk ¼
n
(4)
where, dijkl and b y ijkl denote the measured and approximated perceived discomfort level for l-th joint moment ratio, and n is the number of the level of joint moment ratio. In addition, the AAE for ith function model was calculated by averaging AAEijk among the subjects. The AAEs of response surfaces are compared between the three approximation models, and the model with the lowest AAE is selected for the perceived discomfort function. One-way ANOVA was conducted at the 5% significance level, and post-hoc tests were carried out to compare the three models. ANOVA was conducted for each joint motion direction. 2.3. Formulation of perceived discomfort by considering human variability The variability of individual differences in perceived discomfort should be quantified. Personal factors such as stature, weight, and gripping force may be set as state variables of the perceived discomfort function so as to quantify individual differences, if the factors correlate with function parameters such as the regression
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
coefficient or maximum sensitivity. However, the personal factors may not always correlate with the function parameters. Therefore, if the personal factors do not correlate with the function parameters, the variability of individual differences should be quantified with a method that is different from taking the personal factors as the state variables. In such case, it is ideal to predict the detailed distribution of perceived discomfort by performing an experiment with a large number of conditions (i.e., the joint moment ratio) and subjects. However, it may be difficult to perform a sufficient number of experiments for predicting the detailed distribution. In this study, the concept of fuzzy number (Dubois and Prade, 1980) is used to represent the between-subject variability of perceived discomfort and thereby formulate the perceived discomfort function. The distribution of perceived discomfort may possibly become asymmetric. The asymmetric distribution is more general, and the symmetric distribution, which has the same degree of spread on each side, is one of special example of the asymmetric distribution. Therefore, in this study, the distribution of perceived discomfort is expressed by the L-R fuzzy number (Dubois and Prade, 1978), which has a different degree of spread on each side. It is note that the left and right extents of L-R fuzzy number become the same, if a data set is distributed symmetrically. In other words, the L-R fuzzy number can deal with both the symmetric and asymmetric distribution. In addition, the concept of fuzzy number was applied to express the human uncertainty and variability (Karwowski et al., 1984; Karwowski, 1992; Lee et al., 2003). Therefore, we consider that the fuzzy model can be applied to our study. Fig. 2 shows the triangular L-R fuzzy number used in this study to simplify the distribution of perceived discomfort. The horizontal and vertical axes in Fig. 2 represent the perceived discomfort and probability, respectively. Wmode denotes the mode of perceived discomfort to which the response surface of the perceived discomfort is applied. Here, the mode is the value that appears most often in a data set. a and b e the left and right extents, respectively, of the L-R fuzzy number e are defined as functions of the joint moment ratio. Pmax, which denotes the probability at the mode of perceived discomfort, is given by the following equation with the constraint that the sum of probabilities equals one:
Pmax ¼
2
(5)
aðrÞ þ bðrÞ
Here, a and b are represented by quadratic functions approximated on the basis of the minimum and maximum perceived discomforts for each joint moment ratio. In addition, a and b are branched in order to prevent the lower and upper bounds from falling below 0 and exceeding 50, respectively. a and b are respectively expressed as follows:
⎞ ⎛ P max⎜ 0, max (W + α − Wmode )⎟ α ⎠ ⎝
bðrÞ ¼
a1 r 2 þ a2 r þ a3 if Wmode ðrÞ a1 r 2 þ a2 r þ a3 0 2 if Wmode ðrÞ a1 r þ a2 r þ a3 0 Wmode ðrÞ
(6)
b1 r 2 þb2 r þb3 if Wmode ðrÞþ b1 r 2 þb2 r þb3 50 50Wmode ðrÞ if Wmode ðrÞþ b1 r 2 þb2 r þb3 50
(7)
where ai and bi (i ¼ 1, 2, 3) are the regression coefficients of a and b, respectively. The perceived discomfort function with human variability is thus defined by a triplet (Wmode, a, b). Fig. 3 shows the conceptual diagram of perceived discomfort function. It is note that the logistic model was taken as the example. As shown in Fig. 3, the variability of the subjects or the distribution of perceived discomfort is expressed roughly by the L-R fuzzy number in the given joint moment ratio. 2.4. Clustering of response surfaces The response surfaces of the mode of perceived discomfort for twelve joint motion directions are clustered so as to consider differences among the joint motion directions. The comparison between the discomfort functions may be performed without adopting the cluster analysis. However, it is difficult to define the discomfort functions are almost the same or completely different. Therefore, the clustering method was adopted to draw a line between the discomfort functions that have the different trends. The clustering steps are as follows: Step 1 The AAEs of the response surfaces for each joint motion direction Ei (i ¼ 1, 2, ., 12) are calculated. Step 2 The number of clusters, m, is set to 1. Step 3 The twelve response surfaces are divided into m clusters based on the parameters of the selected approximation function model. Step 4 The response surfaces for each divided cluster are predicted by using the experimental data belonging to each cluster. Step 5 The AAE of the j-th cluster’s response surface for the i-th joint motion direction ei,j is calculated. Step 6 T-tests between Ei and ei,j are carried out. If there is no significant difference for all i-th joint motion directions, the clustering sequence is terminated. Otherwise, m ¼ m þ 100 and return to step 3. In step 5, we note that the i-th joint motion direction belongs to the j-th cluster. For example, in the case of m ¼ 2, if the first and second clusters contain i ¼ 1, 2, 10, 11, 12 and i ¼ 3, 4, ., 9, respectively, the AAEs ei,1 (i ¼ 1, 2, 10, 11, 12) and ei,2 (i ¼ 3, 4, .,
W
⎞ ⎛ P max⎜⎜ 0, − max (W − β − Wmode )⎟⎟ β ⎠ ⎝
Pmax(α, β )
aðrÞ ¼
311
Wmode(r)
50 Wmode(r) + β (r)
Wmode(r) − α (r)
Wmode(r) W
α (r)
β (r)
Fig. 2. L-R fuzzy number.
0
0.2
0.4
0.6
1.0
r
Fig. 3. Conceptual diagram of perceived discomfort function considering human variability: The dots and the gray triangles represent the measured discomfort scores and the distribution in each joint moment ratio.
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9) are calculated. In step 6, the t-test is carried out at the 5% significance level. The divided clusters indicate the difference of history trend toward the transition of joint moment ratio. 3. Result
y=a y=
a 1 + exp{b(x − c )}
(a > 0, b < 0)
3.1. Comparison of approximation error
x = c,
dy ab d 2 y =− , =0 4 dx 2 dx
y=0 The result of ANOVA shows that all joint motion directions except the wrist radial deviation have the main effect of approximation model. Fig. 4 shows a comparison of the average AAE among subjects. The AAE of the linear model is significantly higher than that of the exponential or logistic function model, except in the case of wrist radial deviation. In addition, the logistic function model shows the lowest AAE among the three approximation models in all joint motion directions except the shoulder flexion. The average AAE of the logistic function model is around 2.0, which corresponds to approximately 4.0% of the scale of perceived discomfort. Therefore, the logistic function model is selected as the function approximation model of perceived discomfort. 3.2. Correlation between response surface parameters and participants’ features A correlation analysis between the personal factors of subjects (i.e., the stature, weight, and gripping force) and the parameters of the logistic function was carried out to consider the personal factors that can be set as state variables of the perceived discomfort function. Fig. 5 shows a conceptual diagram of the logistic function, which reaches a maximum sensitivity of eab/4 at x ¼ c (i.e., inflection point). This implies that the larger the eab/4 value, the more rapidly the function rises. In addition, the larger the c value, the earlier the function rises. Thus, in this study, the maximum sensitivity eab/4 and inflection point c are selected as the parameters of the logistic function. Fig. 6 shows the correlation coefficient between the personal factors and logistic function parameters. The maximum sensitivity is significantly correlated with the weight in the case of wrist ulnar deviation at the 5% significance level; however, no other correlation is significant. Similarly, no factors other than the stature and gripping force in the case of shoulder extension are significantly correlated with the inflection point.
12.0
Fig. 5. Conceptual diagram of logistic function.
3.3. Regression coefficient of response surface The perceived discomfort functions of each joint motion direction were predicted by using the experimental data of all subjects, because the abovementioned personal factors could not represent individual differences in perceived discomfort. Tables 2 and 3 depict the regression coefficients of the perceived discomfort function and L-R fuzzy number, respectively. Table 4 lists the AAE and maximum error of the perceived discomfort functions. As depicted in Table 4, the AAEs of the twelve functions range from 3.4 to 5.5, or 6.8e11% of the scale of perceived discomfort. In addition, the maximum errors range from 13 to 21. In addition, the perceived discomfort functions have scores with a range of 20e30 points based on between-subject variability. 3.4. Comparison and clustering of response surfaces Cluster analysis was performed on the twelve perceived discomfort functions and the number of clusters determined based on the procedure proposed in Section 2.4. The maximum sensitivity and inflection point, defined in Section 3.2, were taken as the variables of the cluster analysis. Table 5 shows the maximum sensitivity and the inflection point of the twelve perceived discomfort functions. Table 5 shows that the perceived discomfort function of elbow flexion has the highest maximum sensitivity and lowest inflection point among the twelve functions. The twelve functions were divided into two clusters based on the proposed procedure proposed in Section 2.4. The first cluster consists of eleven functions except that of elbow flexion; the second cluster consists of the perceived discomfort function of elbow flexion. The function for the first cluster is given as follows:
Linear model Exponential model Logistic function model
Average absolute error
10.0 8.0 6.0 4.0 2.0 0.0 Shoulder Shoulder Shoulder Shoulder Shoulder Shoulder Elbow Elbow Wrist Wrist Wrist Wrist extension flexion adduction abduction internal external extension flexion extension flexion ulnar radial rotation rotation deviation deviation Fig. 4. Comparison of average absolute error between the three approximation models: * p < 0.05, ** p < 0.01.
Correlation coefficient
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
313
1.0
Stature
0.8
Weight
0.6
Gripping force
0.4 0.2 0.0 -0.2 -0.4 -0.6
*
-0.8 -1.0 Shoulder Shoulder Shoulder Shoulder Shoulder extension flexion adduction abduction internal rotation
Shoulder Elbow external extension rotation
Elbow flexion
Wrist extension
Wrist flexion
Wrist Wrist ulnar radial deviation deviation
Correlation coefficient
(a) Maximum sensitivity –ab/4 1.0
Stature
0.8
Weight
0.6
Gripping force
0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0
**
*
Shoulder Shoulder Shoulder Shoulder Shoulder extension flexion adduction abduction internal rotation
Elbow Shoulder external extension rotation
Elbow flexion
Wrist extension
Wrist flexion
Wrist Wrist radial ulnar deviation deviation
(b) Inflection point c Fig. 6. Correlation coefficients between personal factors (stature, weight, and gripping force) and logistic function parameters: * p < 0.05, ** p < 0.01.
Wmode ¼
aðrÞ ¼
bðrÞ ¼
49:3 1 þ expf7:56ðr 0:354Þg
(8)
linear model. Therefore, the perceived discomfort caused by joint moment exertion is probably nonlinear. The response surfaces and measured data of shoulder flexion, elbow flexion, and wrist flexion
40:9r 2 þ 38:9r þ 2:38 Wmode ðrÞ
if Wmode ðrÞ 40:9r 2 þ 38:9r þ 2:38 0 if Wmode ðrÞ 40:9r 2 þ 38:9r þ 2:38 0
(9)
39:0r 2 þ 35:3r þ 3:60 50 Wmode ðrÞ
if Wmode ðrÞ þ 39:0r 2 þ 35:3r þ 3:60 50 if Wmode ðrÞ þ 39:0r 2 þ 35:3r þ 3:60 50
(10)
In addition, Figs. 7 and 8 show the perceived discomfort functions of the first cluster and second cluster, respectively. 4. Discussion 4.1. Selection of regression model for perceived discomfort According to Fig. 4, the AAEs of nonlinear models (i.e., the exponential and logistic function models) are lower than that of the
are depicted in Fig. 9 as examples. It is note that the measured data of all subjects are plotted. Fig. 9 also implies that the perceived discomfort is nonlinear. In addition, the logistic function model has the lowest AAE among the three models for nearly all joint motion directions. That is, the logistic function model provides the best fit to the history of perceived discomfort among the three approximation models. We conclude that the logistic function model may best predict the perceived discomfort across the entire range of joint moment ratios.
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T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
Table 2 Regression coefficients of perceived discomfort function.
Table 4 Average absolute error and maximum error of perceived discomfort function.
Joint
Motion direction
a
b
c
Joint
Motion direction
AAE
Maximum error
Shoulder
Extension Flexion Adduction Abduction Internal rotation External rotation Extension Flexion Extension Flexion Ulnar deviation Radial deviation
49.8 48.7 48.7 49.4 48.3 49.2 49.3 48.9 49.6 50.0 50.6 49.7
6.68 7.17 8.19 7.48 8.58 8.53 8.26 9.93 7.89 8.47 6.40 6.47
0.398 0.335 0.322 0.367 0.296 0.346 0.338 0.234 0.366 0.344 0.420 0.379
Shoulder
Extension Flexion Adduction Abduction Internal rotation External rotation Extension Flexion Extension Flexion Ulnar deviation Radial deviation
4.37 4.43 5.02 4.60 4.44 3.82 3.47 3.86 3.57 3.91 4.39 5.43
18.0 17.8 18.5 15.1 19.0 15.3 13.2 16.5 16.6 15.5 21.0 13.4
Elbow Wrist
4.2. Influence of personal factors Correlation coefficients between the personal factors of participants and logistic function parameters of the perceived discomfort functions predicted for each subject were obtained. Hardly any significant correlations were found between the personal factors and logistic function parameters. In addition, correlative trends between personal factors and logistic function parameters are difficult to discern for all joint motion directions. Thus, personal factors cannot be used as state variables of the perceived discomfort function. 4.3. Influence of variability and joint motion direction on perceived discomfort The perceived discomfort functions for the twelve joint motion directions were predicted as shown in Tables 2 and 3. From Table 4, the maximum errors of the predicted functions correspond to approximately 10e20% of the perceived discomfort scale used here. In addition, the perceived discomfort score is varies widely due to the between-subject variability, because the perceived discomfort scores are distributed with a range of 20e30 points, which corresponds to 40e60% of the perceived discomfort scale. This agrees with the proposal that the between-subject variability of perceived discomfort should be considered when perceived discomfort functions are estimated. The twelve perceived discomfort functions were divided into two clusters: one consisting of the functions of the eleven joint motion directions excluding that of elbow flexion, and a second consisting of the function of elbow flexion. Therefore, most of the perceived discomforts for the joint motion directions of the upper limbs are expressed by a single function described in Eqs. (7)e(9). In addition, the function of elbow flexion has the highest maximum sensitivity and lowest inflection point (see Table 5). This indicates
Elbow Wrist
that the perceived discomfort of elbow flexion is more sensitive than that of other motions to an increase in the joint moment ratio. This may be explained by the three main agonist muscles for elbow flexion: the brachialis, biceps brachii, and brachioradialis. Among these, the brachioradialis works only when the muscle is subjected to extreme force (Neumann, 2009). Thus, the brachioradialis may have hardly worked during the measurement of perceived discomfort while it worked during the measurement of maximum joint moment. The lack of muscle activity of brachioradialis may have invoked the change of function patterns for the elbow flexion. That is, the all three agonist muscles (i.e., the brachialis, biceps brachii, and brachioradialis) worked during the measurement of maximum joint moment (i.e., the joint moment ratio r ¼ 1.0), while the two muscles except the brachioradialis mainly worked during the measurement with relatively low magnitude of joint moment ratio (i.e., r ¼ 0.2 and 0.4). Therefore, the perceived discomfort at the low joint moment ratio level for the elbow flexion was higher than that of the other joint motion directions. Thus, the function of elbow flexion has higher sensitivity at low joint moment ratio compared with that of the other joint motions, and the model for the elbow flexion showed different patterns from other joint motions. Björkstén and Jonsson (1977) concluded that 8% of the maximum voluntary force of contraction was recommended for static exertion. Fig. 10 shows the probability distribution when the joint motion ratio equals 8%. The peaks of both clusters range from 1 to 10, which indicates “slight discomfort.” Although this may agree with the result of the earlier study (Björkstén and Jonsson, 1977), the populations of “slight discomfort” for the two clusters are different. In the case of the first cluster, 96% of the subjects belong to “slight discomfort,” whereas 80% belong in the case of the second cluster. Therefore, the joint moment ratio for elbow flexion may need to be lower than that for the other joint motion directions
Table 5 Maximum sensitivity and inflection point of perceived discomfort function.
Table 3 Regression coefficients of L-R fuzzy number. Joint
Motion direction
a1
a2
a3
b1
b2
b3
Joint
Motion direction
Maximum sensitivity
Inflection point
Shoulder
Extension Flexion Adduction Abduction Internal rotation External rotation Extension Flexion Extension Flexion Ulnar deviation Radial deviation
40.9 35.7 38.9 33.5 39.3 40.1 36.1 33.1 42.2 54.0 65.5 40.2
38.5 32.6 36.5 30.7 35.3 38.7 33.1 26.1 40.3 52.2 66.2 37.9
2.49 3.52 2.79 3.10 3.84 1.59 3.06 5.99 2.26 2.03 0.58 2.95
46.2 43.7 40.9 42.0 34.7 36.3 33.2 18.2 39.1 31.8 38.3 36.2
43.9 42.1 37.2 38.7 30.2 33.4 30.3 12.7 35.1 26.8 36.1 34.3
2.07 2.13 3.66 3.17 4.49 2.78 2.85 5.05 3.64 3.75 2.00 2.17
Shoulder
Extension Flexion Adduction Abduction Internal rotation External rotation Extension Flexion Extension Flexion Ulnar deviation Radial deviation
83.2 87.3 99.7 92.3 103.7 104.9 101.7 121.6 97.8 106.0 80.9 80.3
0.398 0.335 0.322 0.367 0.296 0.346 0.338 0.234 0.366 0.344 0.420 0.379
Elbow Wrist
Elbow Wrist
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
50
40 30 20 10 0 0.0
0.2
0.4 0.6 Joint moment ratio
0.8
1.0
Perceived discomfort
Perceived discomfort
50
315
Logistic model
40 30
Linear model
20
Exponential model
10 0
(a) Mode of perceived discomfort with upper and lower bounds: the solid red lines represent the mode of perceived discomfort function Wmode(r), and dashed black lines represent the upper and lower bounds.
0.0
0.2
0.4 0.6 Joint moment ratio
0.8
1.0
(a) Shoulder flexion
0.30 Probability
0.20 r = 0.2
0.15
r = 0.6
r = 0.4
0.10 0.05 0.00 0
10 20 30 40 Perceived discomfort score
50
Perceived discomfort
r = 0.8
0.25
50
Logistic model
40 Linear model
30 Exponential model
20 10 0
(b) Distribution of each joint moment ratio
0.0
0.2
0.4 0.6 Joint moment ratio
Fig. 7. Perceived discomfort function of the first cluster (eleven joint motion directions excluding elbow flexion).
0.8
1.0
(b) Elbow flexion
4.4. Validation of proposed model To validate the accuracy of response surfaces by limited number of data, the cross-validation (leave-one-out) method can be used
50 Perceived discomfort
so as to reduce the perceived discomfort for sensitive individuals. In this way, the proposed method can perform quantitative evaluation of the variability of perceived discomfort based on human diversity.
Logistic model
40 Linear model
30
Exponential model
20 10
Perceived discomfort
0 50
0.0
0.4 0.6 Joint moment ratio
30
0.8
1.0
(c) Wrist flexion
20 Fig. 9. Response surfaces and measured data.
10 0 0.0
0.2
0.4 0.6 Joint moment ratio
0.8
1.0
(a) Mode of perceived discomfort with upper and lower bounds: the solid red lines represent the mode of perceived discomfort function Wmode(r), and dashed black lines represent the upper and lower bounds
(Miller and Miller, 2010; Boukouvala and Ierapetritou, 2012). As an example, the cross-validation method was applied to the response surface of the shoulder flexion; that is, the response surface was developed by the data of nine subjects out of ten (i.e., the training
0.20 First cluster (eleven joint motion directions excluding elbow flexion)
0.30
0.15
0.20
Probability
r = 0.8
0.25 Probability
0.2
40
r = 0.6 r = 0.2
0.15
r = 0.4
0.10
Second cluster (elbow flexion)
0.10 0.05
0.05 0.00 0
10
20
30
40
50
Perceived discomfort score
(b) Distribution of each joint moment ratio Fig. 8. Perceived discomfort function of the second cluster (elbow flexion).
0.00 0
10
20
30
40
Perceived discomfort score Fig. 10. Probability distribution for r ¼ 0.08.
50
316
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
Table 6 Result of cross-validation for shoulder flexion: it is note that the AAE and maximum error of response surface developed by 10 subjects are 4.43 and 17.8 respectively (see Table 4). Subject
AAE
Maximum error
A B C D E F G H I J Average
2.92 2.82 4.08 6.55 2.53 9.22 5.88 7.69 3.40 2.69 4.78
6.0 5.4 6.8 14.2 4.1 19.8 13.9 13.1 4.7 4.2 9.2
set), then the AAE and maximum error of the other subject (i.e., the testing set) were calculated. As shown in Table 6, the average AAEs of ten subjects are almost the same as RSME of response surface developed by the ten subjects’ data. Therefore, we consider that the logistic function model is appropriate for expressing the perceived discomfort. However, some subjects have relatively high AAE; especially the AAE of subject F is approximately twice as that of ten subjects. This is because, the subjects has variability as shown in Fig. 9. In this study, the L-R fuzzy number was applied to deal with the variability of individual differences; and the distribution of perceived discomfort was expressed. In addition, the similar results with the shoulder flexion were obtained for the other joint motion directions. Thus, we conclude that the proposed function approximation model with the L-R fuzzy number is appropriate to express the perceived discomfort with the variability of individual differences. 5. Conclusions In this study, an approximation method of the perceived discomfort function for upper limb joint motion directions is proposed. The major findings are as follows: 1. The perceived discomfort caused by joint moment exertion shows a nonlinear trend. In addition, the logistic function provides the best fit as the perceived discomfort function among the three function approximation models tested: the linear, exponential, and logistic function models. 2. The perceived discomfort scores vary widely because of individual differences between subjects. However, using the personal factors of stature, weight, and gripping force as the state variables of the perceived discomfort function is difficult. 3. The twelve perceived discomfort functions are divided into two clusters: one for elbow flexion and another for the remaining eleven joint motion directions. In addition, the perceived discomfort of elbow flexion is more sensitive than that of other motions to an increase in the joint moment ratio. The proposed model is useful for proactive work environment design when the perceived discomfort of the upper limb is the main determinant factor. The joint moment can be calculated by using a biomechanical model; for example, many commercial software can be used (LaFiandra, 2009). In addition, the maximum joint moments have been measured by many researchers (Amundsen, 1990; Chaffin et al., 2006; National Institute of Technology and Evaluation, 2009). Therefore, the joint moment ratio can be calculated for an intended task, and then the perceived discomfort is
evaluated by the proposed method. The combination use of the proposed model and the biomechanical model gives predicted value of perceived discomfort of workers without time-consuming experiment. It is expected that the proposed model may contribute to the efficient work environment design. Acknowledgments This work was supported by JSPS KAKENHI Grant Number 24760123. References Amundsen, L.R., 1990. Muscle Strength Testing: Instrumented and NonInstrumented Systems. Churchill Livingstone, Philadelphia. Björkstén, M., Jonsson, B., 1977. Endurance limit of force in long-term intermittent static contractions. Scand. J. Work. Environ. Health. 3 (1), 23e27. Boukouvala, F., Ierapetritou, M.G., 2012. Feasibility analysis of black-box processes using an adaptive sampling Kriging-based method. Comput. & Chem. Eng. 36, 358e368. Boussenna, M., Corlett, E.N., Pheasant, S.T., 1982. The relation between discomfort and postural loading at the joints. Ergonomics 25 (4), 315e322. Carey, E.J., Gallwey, T.J., 2002. Effects of wrist posture, pace and exertion on discomfort. Int. J. Ind. Ergon. 29 (2), 85e94. Carey, E.J., Gallwey, T.J., 2005. Wrist discomfort levels for combined movements at constant force and repetition rate. Ergonomics 48 (2), 171e186. Chaffin, D.B., Andersson, G.B.J., Martin, B.J., 2006. Occupational Biomechanics, fourth ed. Wiley, New York. Chung, M.K., Lee, I., Kee, D., 2003. Assessment of postural load for lower limb postures based on perceived discomfort. Int. J. Ind. Ergon. 31 (1), 17e32. Dickerson, C.R., Martin, B.J., Chaffin, D.B., 2006. The relationship between shoulder torques and the perception of muscular effort in loaded reaches. Ergonomics 49 (11), 1036e1051. Dubois, D., Prade, H., 1978. Operations on fuzzy numbers. Int. J. Syst. Sci. 9 (6), 613e626. Dubois, D., Prade, H., 1980. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York. Genaidy, A., Karwowski, W., 1993. The effects of neutral posture deviations on perceived joint discomfort ratings in sitting and standing postures,. Ergonomics 36 (7), 785e792. Karwowski, W., 1992. The human world of fuzziness, human entropy, and the need for general fuzzy systems theory. J. Jpn. Soc. for Fuzzy Theory Syst. 4 (5), 591e609. Karwowski, W., Ayoub, M.M., Alley, L.R., Smith, J.L., 1984. Fuzzy approach in psychophysical modeling of human operator-manual lifting system. Fuzzy Sets Syst. 14 (1), 65e76. Kee, D., Karwowski, W., 2001. The boundaries for joint angles of isocomfort for sitting and standing males based on perceived comfort of static joint postures. Ergonomics 44 (6), 614e648. Kee, D., Karwowski, W., 2003. Ranking systems for evaluation of joint and joint motion stressfulness based on perceived discomforts. Appl. Ergon. 34 (2), 167e176. Kee, D., Karwowski, W., 2004. Joint angles of isocomfort for females based on the psychophysical scaling of static joint postures. Ergonomics 47 (4), 427e445. Kee, D., Lee, I., 2012. Relationship between subjective and objective measures in assessing postural stress. Appl. Ergon. 43 (2), 277e282. Khan, A.A., O’Sullivan, L., Gallwey, T.J., 2010. Effect on discomfort of frequency of wrist exertions combined with wrist articulations and forearm rotation. Int. J. Ind. Ergon. 40 (5), 492e503. LaFiandra, M., 2009. Methods, models, and technology for lifting biomechanics. In: Duffy, V.G. (Ed.), Handbook of Digital Human Modeling. CRC Press, New York, pp. 8-1e8-27. Lee, W., Karwowski, W., Marras, W.S., Rodrick, D., 2003. A neuro-fuzzy modeling of myoelectrical activity of trunk muscles due to manual lifting tasks,. Ergonomics 15 (1e3), 285e309. Lestrelin, D., Trasbot, J., 2005. The REAL MAN project: objectives, results and possible follow-up. In: SAE International Conference and Exposition of Digital Human Modeling for Design and Engineering. Paper No. 2005-01-2682. Miedema, M.C., Douwes, M., Dul, J., 1997. Recommended maximum holding times for prevention of discomfort of static standing postures. Int. J. Ind. Ergon. 19 (1), 9e18. Miller, J.N., Miller, J.C., 2010. Statistics and Chemometrics for Analytical Chemistry, sixth ed. Pearson Education, Essex. Mukhopadhyay, P., O’Sullivan, L., Gallwey, T.J., 2007. Estimating upper limb discomfort level due to intermittent isometric pronation torque with various combinations of elbow angles, forearm rotation angles, force and frequency with upper arm at 90 abduction. Int. J. Ind. Ergon. 37 (4), 313e325. National Institute of Technology and Evaluation, 2009. http://www.tech.nite.go.jp/ human/jp/pdf/20FYdata/nite_humandatabook.pdf (in Japanese). Neumann, D.A., 2009. Kinesiology of the Musculoskeletal System: Foundations for Rehabilitation, second ed. Mosby, Missouri.
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317 Shen, W., Parsons, K.C., 1997. Validity and reliability of rating scales for seated pressure discomfort. Int. J. Ind. Ergon. 20 (6), 441e461. Tsang, P.S., Vidulich, M.A., 2006. Mental workload and situation awareness. In: Salvendy, G. (Ed.), Handbook of Human Factors and Ergonomics, third ed. Wiley, New York, pp. 243e268.
317
U.S. Department of Health and Human Services, 1992. Selected Topics in Surface Electromyography for Use in the Occupational Setting: Expert Perspectives. National Institute for Occupational Safety and Health, Atlanta. Wang, X., Breton-Gadegbeku, B.L., Bouzon, L., 2004. Biomechanical evaluation of the comfort of automobile clutch pedal operation. Int. J. Ind. Ergon. 34 (3), 209e221.
Contents lists available at SciVerse ScienceDirect
Applied Ergonomics journal homepage: www.elsevier.com/locate/apergo
Perceived discomfort functions based on joint moment for various joint motion directions of the upper limb Takanori Chihara a, *, Taiki Izumi b, Akihiko Seo a a b
Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan Graduate School of Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 October 2012 Accepted 13 April 2013
The aim of the present study was to formulate the relationship between the perceived discomfort and the joint moment ratio for twelve joint motion directions of the upper limb by considering the betweensubject variability, and to investigate the effect of joint motion direction. Three approximation models (i.e., linear, exponential, and logistic function models) were compared in terms of the accuracy of predicting the perceived discomfort, and the logistic function was selected because its average error was lowest. The concept of L-R fuzzy number was used to consider the individual variability of perceived discomfort, and a simplified distribution of perceived discomfort was represented. Cluster analysis showed that the twelve discomfort functions formed two clusters: one for elbow flexion and a second for the remaining joint motions. The data show that elbow flexion is more sensitive than other joint motions to increases in the joint moment ratio. Ó 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.
Keywords: Biomechanics Function approximation Human diversity Perceived discomfort Fuzzy numbers
1. Introduction Biomechanical analysis and electromyogram (EMG) recordings are widely used to evaluate physical stress and fatigue; they are also applied to design problems of work environments and consumer products in order to reduce physical work load (Chaffin et al., 2006; Tsang and Vidulich, 2006). EMGs record the actual electrical activity of a muscle. However, EMG recordings require preliminary measurements, such as measurement of the maximum voluntary contraction for normalization (U.S. Department of Health and Human Services, 1992); hence, it is time consuming and imposes strain on subjects. In addition, measured EMG recordings evaluate muscle load on only the intended motion; thus, re-measurement of EMGs is necessary when the design variables of work environments and consumer products are changed. Physical load evaluation based on a biomechanical model with the joint angle and joint moment requires the measurements of only the joint angle and external force. Therefore, the experimental cost and strain on subjects may be lower for a biomechanical analysis than for EMG measurements. Biomechanical analysis does not necessarily require experimentation, because the analysis can
* Corresponding author. Tel.: þ81 42 585 8685; fax: þ81 42 583 5119. E-mail addresses: [email protected] (T. Chihara), [email protected] (T. Izumi), [email protected] (A. Seo).
be performed if the joint angles and external forces are given; hence, a biomechanical analysis can be used for the re-evaluation of the physical stress with a design change more effectively. The time that can be allocated to improving work environments or designing consumer products is decreasing with each passing year, in conjunction with the shortening of the development period. That is, an ergonomic physical load evaluation should be performed effectively in a short time. Thus, it is essential to develop an ergonomic design using a biomechanical analysis model that performs physical load evaluation more efficiently than EMG measurements (Lestrelin and Trasbot, 2005; LaFiandra, 2009). Research on postural discomfort imposed by varying joint angles has been reported (Kee and Lee, 2012). The relationships between the perceived discomfort and joint angle have been studied (Kee and Karwowski, 2001, 2004; Chung et al., 2003). Miedema et al. (1997) studied the effects of joint angle and duration on perceived discomfort, whereas Carey and Gallwey (2005) along with Khan et al. (2010) investigated the effects of joint angle and repetition. The ranking of perceived discomfort of joint motions have been investigated (Genaidy and Karwowski, 1993; Kee and Karwowski, 2003). The relationship between perceived discomfort and joint angle can be used to evaluate the discomfort of arbitrary human postures. However, in real situations of working or using a product, arbitrary external forces will act on the human body, and arbitrary moments will act on each joint. In addition, because perceived discomfort is affected more by the joint moment than the joint angle
0003-6870/$ e see front matter Ó 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved. http://dx.doi.org/10.1016/j.apergo.2013.04.016
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
(Carey and Gallwey, 2002; Dickerson et al., 2006), the relationship between perceived discomfort and joint moment should be quantified to improve the accuracy of perceived discomfort evaluation. The maximum joint moments that subjects can exert have been measured (Amundsen, 1990; Chaffin et al., 2006; National Institute of Technology and Evaluation, 2009). In these reports, the average maximum joint moment among subjects was measured, and the relationship between the maximum joint moment and joint angle was represented. Boussenna et al. (1982) investigated the relationships between the perceived discomfort and joint moments of the hip, knee, and ankle. Wang et al. (2004) investigated the relationship between the perceived discomfort and biomechanical parameters, including the joint moments when depressing a clutch pedal. Mukhopadhyay et al. (2007) investigated the effects of the joint moment of forearm pronation, forearm rotation angle, elbow angle, and exertion frequency on the perceived discomfort. However, they did not investigate the quantitative effect of the joint moment magnitude on perceived discomfort. Dickerson et al. (2006) investigated the effects of the shoulder joint moment, position of operation object, and stature of subjects on perceived discomfort in a simulated workstation. Perceived discomfort, which was measured by varying the direction and magnitude of external force, was mostly affected by, and represented as a linear function of, the shoulder joint moment. However, they did not investigate the effect of joint motion direction of the shoulder joint (i.e., extension, flexion, abduction, adduction, internal rotation, and external rotation). In addition, the perceived discomforts of the elbow and wrist joints were not considered, although the discomfort of other joints may be as important as that of the shoulder joint. Moreover, the abovementioned reports on the relationship between the perceived discomfort and joint moment or joint angle did not quantify individual differences. The perceived discomfort function for upper limb joints should be formulated by considering the variability so as to take into account human diversity during developing ergonomic design. The objective of the present study was to formulate the relationship between the perceived discomfort and joint moment by considering the variability of subjective evaluation, and to consider differences among the joint motion directions of the upper limb (i.e., shoulder extension, shoulder flexion, shoulder adduction, shoulder abduction, shoulder internal rotation, shoulder external rotation, elbow extension, elbow flexion, wrist extension, wrist flexion, wrist ulnar deviation, and wrist radial deviation). In this study, the perceived discomforts of subjects were measured when they exerted joint moments of arbitrary magnitude in each joint motion direction. The response surfaces of perceived discomfort were approximated by three different approximation models: linear, exponential, and logistic function models. The logistic function model was selected as the best approximation model because its accuracy was highest among the three models. The concept of fuzzy number was used to represent the variability of perceived discomfort among subjects. Finally, clustering the evaluation functions of perceived discomfort for each joint motion direction revealed that the function for the upper limb could be divided into two clusters. 2. Method 2.1. Measurement of perceived discomfort Ten healthy Japanese male subjects, aged between 21 and 25, participated in this experiment. All of them were university students, right handed, and none of the subjects had a musculoskeletal disorder. Their stature, weight, and gripping force are listed in Table 1. The target joint motion directions were the six directions of the shoulder joint (i.e., shoulder extension, shoulder flexion, shoulder
309
adduction, shoulder abduction, shoulder internal rotation, and shoulder external rotation), two directions of the elbow joint (i.e., elbow extension and elbow flexion), and four directions of the wrist joint (i.e., wrist extension, wrist flexion, wrist ulnar deviation, and wrist radial deviation). The subjects sat and exerted joint moments by holding a weight with the dominant hand in the instructed upper limb postures shown in Fig. 1. Note that the forearm is in the pronated position in Fig. 1(i) and in the supinated position in Fig. 1(j); the others are in neutral positions. The joint moment was calculated by magnitude of holding weight and the related segment length of each subject. The maximum joint moment for each subject was measured, after which joint moments with magnitudes of approximately 20, 40, and 60% of the premeasured maximum joint moment were added by adjusting the weight. The subjects kept the instructed postures for 10 s. The magnitude of joint moments was controlled by adjusting the weight. In addition, joint moments lower than the abovementioned magnitudes were added if a subject judged the magnitude as excessive. There was a 5-min rest period after each trial. The perceived discomfort was measured by the category partitioning scale 50 (CP-50) (Shen and Parsons, 1997). The CP-50 has a starting point (i.e., 0 ¼ no) and five categories (i.e., very slight discomfort, slight discomfort, discomfort, severe discomfort, and very severe discomfort). Thus, the ranges for each category are given as follows: “Very slight discomfort”: 1e10 “Slight discomfort”: 11e20 “Discomfort”: 21e30 “Severe discomfort”: 31e40 “Very severe discomfort”: 41e50 Each of the categories is further subdivided into 10 scale points. Subjects first choose the category to which a stimulus belongs, and then choose the degree among the 10 scale points. In this study, the subjects were instructed to rate their perceived discomfort for each magnitude of joint moment assuming the discomfort they perceive when exerting their maximum moment to be 50. The maximum discomfort level was set for all maximum joint moment in each subject and joint motion direction. It should be note that subject may not feel the same level of discomfort between the maximum joint moments at different joint motion directions. This experiment was approved by the Research Safety and Ethics Committee of Tokyo Metropolitan University. 2.2. Selection of approximation model The perceived discomfort probably increases as the magnitude of the joint moment increases. Therefore, the approximation model for the perceived discomfort function must be a monotonically Table 1 Stature, weight, and gripping force of subjects. Subject
Stature [cm]
Weight [kg]
Gripping force [kgf]
A B C D E F G H I J Average S. D.
186 172 172 182 163 168 160 177 171 172 172 7.96
70.6 63.0 62.1 82.0 58.0 50.0 64.0 76.0 61.9 64.2 65.2 9.09
56 41 34 55 33 47 44 50 38 48 44.6 8.09
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T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
(a) Shoulder extension
(b) Shoulder flexion
(c) Shoulder adduction
(e) Shoulder internal rotation (f) Shoulder external rotation Pronated position
Supinated position
(i) Wrist extension
(j) Wrist flexion
(d) Shoulder abduction
(g) Elbow extension
(k) Wrist ulnar deviation
(h) Elbow flexion
(l) Wrist radial deviation
Fig. 1. Instructed upper-limb postures for joint moment exertion.
increasing function. In addition, the perceived discomfort function is probably a linear or weakly nonlinear function. We assume that monotonically nonlinear functions are mainly divided into three types: those that increase during the early (Type 1), middle (Type 2), and late (Type 3) part of the function. In this study, the three function approximation models are set as follows:
y ¼ ax þ b
(1)
y ¼ a þ b$expðcxÞ
(2)
y ¼
a 1 þ expfbðx cÞg
(3)
where x and y denote the explanatory and objective variables, respectively, and a, b, and c are regression coefficients. Equation (1) represents the linear model. Eq. (2), which represents the exponential model, can express Type 1 and Type 3 functions. In addition, Eq. (3), which represents the logistic model, can express Type 2 functions. In this study, the perceived discomfort W (W ¼ [0, 50]), which is measured by the CP-50, is set as the objective variable, and the joint moment divided by the maximum joint moment (hereafter referred to as “the joint moment ratio r (r ¼ [0, 1])”) is set as the explanatory variable. The response surface of the perceived discomfort f(r) is approximated with the three models for each joint motion direction and subject. The regression coefficients are
obtained by minimizing the average absolute error (AAE). The AAE for i-th function model, j-th joint motion direction, and k-th subject was calculated as follows:
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 dijkl b y ijkl l¼1
Pn AAEijk ¼
n
(4)
where, dijkl and b y ijkl denote the measured and approximated perceived discomfort level for l-th joint moment ratio, and n is the number of the level of joint moment ratio. In addition, the AAE for ith function model was calculated by averaging AAEijk among the subjects. The AAEs of response surfaces are compared between the three approximation models, and the model with the lowest AAE is selected for the perceived discomfort function. One-way ANOVA was conducted at the 5% significance level, and post-hoc tests were carried out to compare the three models. ANOVA was conducted for each joint motion direction. 2.3. Formulation of perceived discomfort by considering human variability The variability of individual differences in perceived discomfort should be quantified. Personal factors such as stature, weight, and gripping force may be set as state variables of the perceived discomfort function so as to quantify individual differences, if the factors correlate with function parameters such as the regression
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
coefficient or maximum sensitivity. However, the personal factors may not always correlate with the function parameters. Therefore, if the personal factors do not correlate with the function parameters, the variability of individual differences should be quantified with a method that is different from taking the personal factors as the state variables. In such case, it is ideal to predict the detailed distribution of perceived discomfort by performing an experiment with a large number of conditions (i.e., the joint moment ratio) and subjects. However, it may be difficult to perform a sufficient number of experiments for predicting the detailed distribution. In this study, the concept of fuzzy number (Dubois and Prade, 1980) is used to represent the between-subject variability of perceived discomfort and thereby formulate the perceived discomfort function. The distribution of perceived discomfort may possibly become asymmetric. The asymmetric distribution is more general, and the symmetric distribution, which has the same degree of spread on each side, is one of special example of the asymmetric distribution. Therefore, in this study, the distribution of perceived discomfort is expressed by the L-R fuzzy number (Dubois and Prade, 1978), which has a different degree of spread on each side. It is note that the left and right extents of L-R fuzzy number become the same, if a data set is distributed symmetrically. In other words, the L-R fuzzy number can deal with both the symmetric and asymmetric distribution. In addition, the concept of fuzzy number was applied to express the human uncertainty and variability (Karwowski et al., 1984; Karwowski, 1992; Lee et al., 2003). Therefore, we consider that the fuzzy model can be applied to our study. Fig. 2 shows the triangular L-R fuzzy number used in this study to simplify the distribution of perceived discomfort. The horizontal and vertical axes in Fig. 2 represent the perceived discomfort and probability, respectively. Wmode denotes the mode of perceived discomfort to which the response surface of the perceived discomfort is applied. Here, the mode is the value that appears most often in a data set. a and b e the left and right extents, respectively, of the L-R fuzzy number e are defined as functions of the joint moment ratio. Pmax, which denotes the probability at the mode of perceived discomfort, is given by the following equation with the constraint that the sum of probabilities equals one:
Pmax ¼
2
(5)
aðrÞ þ bðrÞ
Here, a and b are represented by quadratic functions approximated on the basis of the minimum and maximum perceived discomforts for each joint moment ratio. In addition, a and b are branched in order to prevent the lower and upper bounds from falling below 0 and exceeding 50, respectively. a and b are respectively expressed as follows:
⎞ ⎛ P max⎜ 0, max (W + α − Wmode )⎟ α ⎠ ⎝
bðrÞ ¼
a1 r 2 þ a2 r þ a3 if Wmode ðrÞ a1 r 2 þ a2 r þ a3 0 2 if Wmode ðrÞ a1 r þ a2 r þ a3 0 Wmode ðrÞ
(6)
b1 r 2 þb2 r þb3 if Wmode ðrÞþ b1 r 2 þb2 r þb3 50 50Wmode ðrÞ if Wmode ðrÞþ b1 r 2 þb2 r þb3 50
(7)
where ai and bi (i ¼ 1, 2, 3) are the regression coefficients of a and b, respectively. The perceived discomfort function with human variability is thus defined by a triplet (Wmode, a, b). Fig. 3 shows the conceptual diagram of perceived discomfort function. It is note that the logistic model was taken as the example. As shown in Fig. 3, the variability of the subjects or the distribution of perceived discomfort is expressed roughly by the L-R fuzzy number in the given joint moment ratio. 2.4. Clustering of response surfaces The response surfaces of the mode of perceived discomfort for twelve joint motion directions are clustered so as to consider differences among the joint motion directions. The comparison between the discomfort functions may be performed without adopting the cluster analysis. However, it is difficult to define the discomfort functions are almost the same or completely different. Therefore, the clustering method was adopted to draw a line between the discomfort functions that have the different trends. The clustering steps are as follows: Step 1 The AAEs of the response surfaces for each joint motion direction Ei (i ¼ 1, 2, ., 12) are calculated. Step 2 The number of clusters, m, is set to 1. Step 3 The twelve response surfaces are divided into m clusters based on the parameters of the selected approximation function model. Step 4 The response surfaces for each divided cluster are predicted by using the experimental data belonging to each cluster. Step 5 The AAE of the j-th cluster’s response surface for the i-th joint motion direction ei,j is calculated. Step 6 T-tests between Ei and ei,j are carried out. If there is no significant difference for all i-th joint motion directions, the clustering sequence is terminated. Otherwise, m ¼ m þ 100 and return to step 3. In step 5, we note that the i-th joint motion direction belongs to the j-th cluster. For example, in the case of m ¼ 2, if the first and second clusters contain i ¼ 1, 2, 10, 11, 12 and i ¼ 3, 4, ., 9, respectively, the AAEs ei,1 (i ¼ 1, 2, 10, 11, 12) and ei,2 (i ¼ 3, 4, .,
W
⎞ ⎛ P max⎜⎜ 0, − max (W − β − Wmode )⎟⎟ β ⎠ ⎝
Pmax(α, β )
aðrÞ ¼
311
Wmode(r)
50 Wmode(r) + β (r)
Wmode(r) − α (r)
Wmode(r) W
α (r)
β (r)
Fig. 2. L-R fuzzy number.
0
0.2
0.4
0.6
1.0
r
Fig. 3. Conceptual diagram of perceived discomfort function considering human variability: The dots and the gray triangles represent the measured discomfort scores and the distribution in each joint moment ratio.
312
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
9) are calculated. In step 6, the t-test is carried out at the 5% significance level. The divided clusters indicate the difference of history trend toward the transition of joint moment ratio. 3. Result
y=a y=
a 1 + exp{b(x − c )}
(a > 0, b < 0)
3.1. Comparison of approximation error
x = c,
dy ab d 2 y =− , =0 4 dx 2 dx
y=0 The result of ANOVA shows that all joint motion directions except the wrist radial deviation have the main effect of approximation model. Fig. 4 shows a comparison of the average AAE among subjects. The AAE of the linear model is significantly higher than that of the exponential or logistic function model, except in the case of wrist radial deviation. In addition, the logistic function model shows the lowest AAE among the three approximation models in all joint motion directions except the shoulder flexion. The average AAE of the logistic function model is around 2.0, which corresponds to approximately 4.0% of the scale of perceived discomfort. Therefore, the logistic function model is selected as the function approximation model of perceived discomfort. 3.2. Correlation between response surface parameters and participants’ features A correlation analysis between the personal factors of subjects (i.e., the stature, weight, and gripping force) and the parameters of the logistic function was carried out to consider the personal factors that can be set as state variables of the perceived discomfort function. Fig. 5 shows a conceptual diagram of the logistic function, which reaches a maximum sensitivity of eab/4 at x ¼ c (i.e., inflection point). This implies that the larger the eab/4 value, the more rapidly the function rises. In addition, the larger the c value, the earlier the function rises. Thus, in this study, the maximum sensitivity eab/4 and inflection point c are selected as the parameters of the logistic function. Fig. 6 shows the correlation coefficient between the personal factors and logistic function parameters. The maximum sensitivity is significantly correlated with the weight in the case of wrist ulnar deviation at the 5% significance level; however, no other correlation is significant. Similarly, no factors other than the stature and gripping force in the case of shoulder extension are significantly correlated with the inflection point.
12.0
Fig. 5. Conceptual diagram of logistic function.
3.3. Regression coefficient of response surface The perceived discomfort functions of each joint motion direction were predicted by using the experimental data of all subjects, because the abovementioned personal factors could not represent individual differences in perceived discomfort. Tables 2 and 3 depict the regression coefficients of the perceived discomfort function and L-R fuzzy number, respectively. Table 4 lists the AAE and maximum error of the perceived discomfort functions. As depicted in Table 4, the AAEs of the twelve functions range from 3.4 to 5.5, or 6.8e11% of the scale of perceived discomfort. In addition, the maximum errors range from 13 to 21. In addition, the perceived discomfort functions have scores with a range of 20e30 points based on between-subject variability. 3.4. Comparison and clustering of response surfaces Cluster analysis was performed on the twelve perceived discomfort functions and the number of clusters determined based on the procedure proposed in Section 2.4. The maximum sensitivity and inflection point, defined in Section 3.2, were taken as the variables of the cluster analysis. Table 5 shows the maximum sensitivity and the inflection point of the twelve perceived discomfort functions. Table 5 shows that the perceived discomfort function of elbow flexion has the highest maximum sensitivity and lowest inflection point among the twelve functions. The twelve functions were divided into two clusters based on the proposed procedure proposed in Section 2.4. The first cluster consists of eleven functions except that of elbow flexion; the second cluster consists of the perceived discomfort function of elbow flexion. The function for the first cluster is given as follows:
Linear model Exponential model Logistic function model
Average absolute error
10.0 8.0 6.0 4.0 2.0 0.0 Shoulder Shoulder Shoulder Shoulder Shoulder Shoulder Elbow Elbow Wrist Wrist Wrist Wrist extension flexion adduction abduction internal external extension flexion extension flexion ulnar radial rotation rotation deviation deviation Fig. 4. Comparison of average absolute error between the three approximation models: * p < 0.05, ** p < 0.01.
Correlation coefficient
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
313
1.0
Stature
0.8
Weight
0.6
Gripping force
0.4 0.2 0.0 -0.2 -0.4 -0.6
*
-0.8 -1.0 Shoulder Shoulder Shoulder Shoulder Shoulder extension flexion adduction abduction internal rotation
Shoulder Elbow external extension rotation
Elbow flexion
Wrist extension
Wrist flexion
Wrist Wrist ulnar radial deviation deviation
Correlation coefficient
(a) Maximum sensitivity –ab/4 1.0
Stature
0.8
Weight
0.6
Gripping force
0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0
**
*
Shoulder Shoulder Shoulder Shoulder Shoulder extension flexion adduction abduction internal rotation
Elbow Shoulder external extension rotation
Elbow flexion
Wrist extension
Wrist flexion
Wrist Wrist radial ulnar deviation deviation
(b) Inflection point c Fig. 6. Correlation coefficients between personal factors (stature, weight, and gripping force) and logistic function parameters: * p < 0.05, ** p < 0.01.
Wmode ¼
aðrÞ ¼
bðrÞ ¼
49:3 1 þ expf7:56ðr 0:354Þg
(8)
linear model. Therefore, the perceived discomfort caused by joint moment exertion is probably nonlinear. The response surfaces and measured data of shoulder flexion, elbow flexion, and wrist flexion
40:9r 2 þ 38:9r þ 2:38 Wmode ðrÞ
if Wmode ðrÞ 40:9r 2 þ 38:9r þ 2:38 0 if Wmode ðrÞ 40:9r 2 þ 38:9r þ 2:38 0
(9)
39:0r 2 þ 35:3r þ 3:60 50 Wmode ðrÞ
if Wmode ðrÞ þ 39:0r 2 þ 35:3r þ 3:60 50 if Wmode ðrÞ þ 39:0r 2 þ 35:3r þ 3:60 50
(10)
In addition, Figs. 7 and 8 show the perceived discomfort functions of the first cluster and second cluster, respectively. 4. Discussion 4.1. Selection of regression model for perceived discomfort According to Fig. 4, the AAEs of nonlinear models (i.e., the exponential and logistic function models) are lower than that of the
are depicted in Fig. 9 as examples. It is note that the measured data of all subjects are plotted. Fig. 9 also implies that the perceived discomfort is nonlinear. In addition, the logistic function model has the lowest AAE among the three models for nearly all joint motion directions. That is, the logistic function model provides the best fit to the history of perceived discomfort among the three approximation models. We conclude that the logistic function model may best predict the perceived discomfort across the entire range of joint moment ratios.
314
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Table 2 Regression coefficients of perceived discomfort function.
Table 4 Average absolute error and maximum error of perceived discomfort function.
Joint
Motion direction
a
b
c
Joint
Motion direction
AAE
Maximum error
Shoulder
Extension Flexion Adduction Abduction Internal rotation External rotation Extension Flexion Extension Flexion Ulnar deviation Radial deviation
49.8 48.7 48.7 49.4 48.3 49.2 49.3 48.9 49.6 50.0 50.6 49.7
6.68 7.17 8.19 7.48 8.58 8.53 8.26 9.93 7.89 8.47 6.40 6.47
0.398 0.335 0.322 0.367 0.296 0.346 0.338 0.234 0.366 0.344 0.420 0.379
Shoulder
Extension Flexion Adduction Abduction Internal rotation External rotation Extension Flexion Extension Flexion Ulnar deviation Radial deviation
4.37 4.43 5.02 4.60 4.44 3.82 3.47 3.86 3.57 3.91 4.39 5.43
18.0 17.8 18.5 15.1 19.0 15.3 13.2 16.5 16.6 15.5 21.0 13.4
Elbow Wrist
4.2. Influence of personal factors Correlation coefficients between the personal factors of participants and logistic function parameters of the perceived discomfort functions predicted for each subject were obtained. Hardly any significant correlations were found between the personal factors and logistic function parameters. In addition, correlative trends between personal factors and logistic function parameters are difficult to discern for all joint motion directions. Thus, personal factors cannot be used as state variables of the perceived discomfort function. 4.3. Influence of variability and joint motion direction on perceived discomfort The perceived discomfort functions for the twelve joint motion directions were predicted as shown in Tables 2 and 3. From Table 4, the maximum errors of the predicted functions correspond to approximately 10e20% of the perceived discomfort scale used here. In addition, the perceived discomfort score is varies widely due to the between-subject variability, because the perceived discomfort scores are distributed with a range of 20e30 points, which corresponds to 40e60% of the perceived discomfort scale. This agrees with the proposal that the between-subject variability of perceived discomfort should be considered when perceived discomfort functions are estimated. The twelve perceived discomfort functions were divided into two clusters: one consisting of the functions of the eleven joint motion directions excluding that of elbow flexion, and a second consisting of the function of elbow flexion. Therefore, most of the perceived discomforts for the joint motion directions of the upper limbs are expressed by a single function described in Eqs. (7)e(9). In addition, the function of elbow flexion has the highest maximum sensitivity and lowest inflection point (see Table 5). This indicates
Elbow Wrist
that the perceived discomfort of elbow flexion is more sensitive than that of other motions to an increase in the joint moment ratio. This may be explained by the three main agonist muscles for elbow flexion: the brachialis, biceps brachii, and brachioradialis. Among these, the brachioradialis works only when the muscle is subjected to extreme force (Neumann, 2009). Thus, the brachioradialis may have hardly worked during the measurement of perceived discomfort while it worked during the measurement of maximum joint moment. The lack of muscle activity of brachioradialis may have invoked the change of function patterns for the elbow flexion. That is, the all three agonist muscles (i.e., the brachialis, biceps brachii, and brachioradialis) worked during the measurement of maximum joint moment (i.e., the joint moment ratio r ¼ 1.0), while the two muscles except the brachioradialis mainly worked during the measurement with relatively low magnitude of joint moment ratio (i.e., r ¼ 0.2 and 0.4). Therefore, the perceived discomfort at the low joint moment ratio level for the elbow flexion was higher than that of the other joint motion directions. Thus, the function of elbow flexion has higher sensitivity at low joint moment ratio compared with that of the other joint motions, and the model for the elbow flexion showed different patterns from other joint motions. Björkstén and Jonsson (1977) concluded that 8% of the maximum voluntary force of contraction was recommended for static exertion. Fig. 10 shows the probability distribution when the joint motion ratio equals 8%. The peaks of both clusters range from 1 to 10, which indicates “slight discomfort.” Although this may agree with the result of the earlier study (Björkstén and Jonsson, 1977), the populations of “slight discomfort” for the two clusters are different. In the case of the first cluster, 96% of the subjects belong to “slight discomfort,” whereas 80% belong in the case of the second cluster. Therefore, the joint moment ratio for elbow flexion may need to be lower than that for the other joint motion directions
Table 5 Maximum sensitivity and inflection point of perceived discomfort function.
Table 3 Regression coefficients of L-R fuzzy number. Joint
Motion direction
a1
a2
a3
b1
b2
b3
Joint
Motion direction
Maximum sensitivity
Inflection point
Shoulder
Extension Flexion Adduction Abduction Internal rotation External rotation Extension Flexion Extension Flexion Ulnar deviation Radial deviation
40.9 35.7 38.9 33.5 39.3 40.1 36.1 33.1 42.2 54.0 65.5 40.2
38.5 32.6 36.5 30.7 35.3 38.7 33.1 26.1 40.3 52.2 66.2 37.9
2.49 3.52 2.79 3.10 3.84 1.59 3.06 5.99 2.26 2.03 0.58 2.95
46.2 43.7 40.9 42.0 34.7 36.3 33.2 18.2 39.1 31.8 38.3 36.2
43.9 42.1 37.2 38.7 30.2 33.4 30.3 12.7 35.1 26.8 36.1 34.3
2.07 2.13 3.66 3.17 4.49 2.78 2.85 5.05 3.64 3.75 2.00 2.17
Shoulder
Extension Flexion Adduction Abduction Internal rotation External rotation Extension Flexion Extension Flexion Ulnar deviation Radial deviation
83.2 87.3 99.7 92.3 103.7 104.9 101.7 121.6 97.8 106.0 80.9 80.3
0.398 0.335 0.322 0.367 0.296 0.346 0.338 0.234 0.366 0.344 0.420 0.379
Elbow Wrist
Elbow Wrist
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317
50
40 30 20 10 0 0.0
0.2
0.4 0.6 Joint moment ratio
0.8
1.0
Perceived discomfort
Perceived discomfort
50
315
Logistic model
40 30
Linear model
20
Exponential model
10 0
(a) Mode of perceived discomfort with upper and lower bounds: the solid red lines represent the mode of perceived discomfort function Wmode(r), and dashed black lines represent the upper and lower bounds.
0.0
0.2
0.4 0.6 Joint moment ratio
0.8
1.0
(a) Shoulder flexion
0.30 Probability
0.20 r = 0.2
0.15
r = 0.6
r = 0.4
0.10 0.05 0.00 0
10 20 30 40 Perceived discomfort score
50
Perceived discomfort
r = 0.8
0.25
50
Logistic model
40 Linear model
30 Exponential model
20 10 0
(b) Distribution of each joint moment ratio
0.0
0.2
0.4 0.6 Joint moment ratio
Fig. 7. Perceived discomfort function of the first cluster (eleven joint motion directions excluding elbow flexion).
0.8
1.0
(b) Elbow flexion
4.4. Validation of proposed model To validate the accuracy of response surfaces by limited number of data, the cross-validation (leave-one-out) method can be used
50 Perceived discomfort
so as to reduce the perceived discomfort for sensitive individuals. In this way, the proposed method can perform quantitative evaluation of the variability of perceived discomfort based on human diversity.
Logistic model
40 Linear model
30
Exponential model
20 10
Perceived discomfort
0 50
0.0
0.4 0.6 Joint moment ratio
30
0.8
1.0
(c) Wrist flexion
20 Fig. 9. Response surfaces and measured data.
10 0 0.0
0.2
0.4 0.6 Joint moment ratio
0.8
1.0
(a) Mode of perceived discomfort with upper and lower bounds: the solid red lines represent the mode of perceived discomfort function Wmode(r), and dashed black lines represent the upper and lower bounds
(Miller and Miller, 2010; Boukouvala and Ierapetritou, 2012). As an example, the cross-validation method was applied to the response surface of the shoulder flexion; that is, the response surface was developed by the data of nine subjects out of ten (i.e., the training
0.20 First cluster (eleven joint motion directions excluding elbow flexion)
0.30
0.15
0.20
Probability
r = 0.8
0.25 Probability
0.2
40
r = 0.6 r = 0.2
0.15
r = 0.4
0.10
Second cluster (elbow flexion)
0.10 0.05
0.05 0.00 0
10
20
30
40
50
Perceived discomfort score
(b) Distribution of each joint moment ratio Fig. 8. Perceived discomfort function of the second cluster (elbow flexion).
0.00 0
10
20
30
40
Perceived discomfort score Fig. 10. Probability distribution for r ¼ 0.08.
50
316
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Table 6 Result of cross-validation for shoulder flexion: it is note that the AAE and maximum error of response surface developed by 10 subjects are 4.43 and 17.8 respectively (see Table 4). Subject
AAE
Maximum error
A B C D E F G H I J Average
2.92 2.82 4.08 6.55 2.53 9.22 5.88 7.69 3.40 2.69 4.78
6.0 5.4 6.8 14.2 4.1 19.8 13.9 13.1 4.7 4.2 9.2
set), then the AAE and maximum error of the other subject (i.e., the testing set) were calculated. As shown in Table 6, the average AAEs of ten subjects are almost the same as RSME of response surface developed by the ten subjects’ data. Therefore, we consider that the logistic function model is appropriate for expressing the perceived discomfort. However, some subjects have relatively high AAE; especially the AAE of subject F is approximately twice as that of ten subjects. This is because, the subjects has variability as shown in Fig. 9. In this study, the L-R fuzzy number was applied to deal with the variability of individual differences; and the distribution of perceived discomfort was expressed. In addition, the similar results with the shoulder flexion were obtained for the other joint motion directions. Thus, we conclude that the proposed function approximation model with the L-R fuzzy number is appropriate to express the perceived discomfort with the variability of individual differences. 5. Conclusions In this study, an approximation method of the perceived discomfort function for upper limb joint motion directions is proposed. The major findings are as follows: 1. The perceived discomfort caused by joint moment exertion shows a nonlinear trend. In addition, the logistic function provides the best fit as the perceived discomfort function among the three function approximation models tested: the linear, exponential, and logistic function models. 2. The perceived discomfort scores vary widely because of individual differences between subjects. However, using the personal factors of stature, weight, and gripping force as the state variables of the perceived discomfort function is difficult. 3. The twelve perceived discomfort functions are divided into two clusters: one for elbow flexion and another for the remaining eleven joint motion directions. In addition, the perceived discomfort of elbow flexion is more sensitive than that of other motions to an increase in the joint moment ratio. The proposed model is useful for proactive work environment design when the perceived discomfort of the upper limb is the main determinant factor. The joint moment can be calculated by using a biomechanical model; for example, many commercial software can be used (LaFiandra, 2009). In addition, the maximum joint moments have been measured by many researchers (Amundsen, 1990; Chaffin et al., 2006; National Institute of Technology and Evaluation, 2009). Therefore, the joint moment ratio can be calculated for an intended task, and then the perceived discomfort is
evaluated by the proposed method. The combination use of the proposed model and the biomechanical model gives predicted value of perceived discomfort of workers without time-consuming experiment. It is expected that the proposed model may contribute to the efficient work environment design. Acknowledgments This work was supported by JSPS KAKENHI Grant Number 24760123. References Amundsen, L.R., 1990. Muscle Strength Testing: Instrumented and NonInstrumented Systems. Churchill Livingstone, Philadelphia. Björkstén, M., Jonsson, B., 1977. Endurance limit of force in long-term intermittent static contractions. Scand. J. Work. Environ. Health. 3 (1), 23e27. Boukouvala, F., Ierapetritou, M.G., 2012. Feasibility analysis of black-box processes using an adaptive sampling Kriging-based method. Comput. & Chem. Eng. 36, 358e368. Boussenna, M., Corlett, E.N., Pheasant, S.T., 1982. The relation between discomfort and postural loading at the joints. Ergonomics 25 (4), 315e322. Carey, E.J., Gallwey, T.J., 2002. Effects of wrist posture, pace and exertion on discomfort. Int. J. Ind. Ergon. 29 (2), 85e94. Carey, E.J., Gallwey, T.J., 2005. Wrist discomfort levels for combined movements at constant force and repetition rate. Ergonomics 48 (2), 171e186. Chaffin, D.B., Andersson, G.B.J., Martin, B.J., 2006. Occupational Biomechanics, fourth ed. Wiley, New York. Chung, M.K., Lee, I., Kee, D., 2003. Assessment of postural load for lower limb postures based on perceived discomfort. Int. J. Ind. Ergon. 31 (1), 17e32. Dickerson, C.R., Martin, B.J., Chaffin, D.B., 2006. The relationship between shoulder torques and the perception of muscular effort in loaded reaches. Ergonomics 49 (11), 1036e1051. Dubois, D., Prade, H., 1978. Operations on fuzzy numbers. Int. J. Syst. Sci. 9 (6), 613e626. Dubois, D., Prade, H., 1980. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York. Genaidy, A., Karwowski, W., 1993. The effects of neutral posture deviations on perceived joint discomfort ratings in sitting and standing postures,. Ergonomics 36 (7), 785e792. Karwowski, W., 1992. The human world of fuzziness, human entropy, and the need for general fuzzy systems theory. J. Jpn. Soc. for Fuzzy Theory Syst. 4 (5), 591e609. Karwowski, W., Ayoub, M.M., Alley, L.R., Smith, J.L., 1984. Fuzzy approach in psychophysical modeling of human operator-manual lifting system. Fuzzy Sets Syst. 14 (1), 65e76. Kee, D., Karwowski, W., 2001. The boundaries for joint angles of isocomfort for sitting and standing males based on perceived comfort of static joint postures. Ergonomics 44 (6), 614e648. Kee, D., Karwowski, W., 2003. Ranking systems for evaluation of joint and joint motion stressfulness based on perceived discomforts. Appl. Ergon. 34 (2), 167e176. Kee, D., Karwowski, W., 2004. Joint angles of isocomfort for females based on the psychophysical scaling of static joint postures. Ergonomics 47 (4), 427e445. Kee, D., Lee, I., 2012. Relationship between subjective and objective measures in assessing postural stress. Appl. Ergon. 43 (2), 277e282. Khan, A.A., O’Sullivan, L., Gallwey, T.J., 2010. Effect on discomfort of frequency of wrist exertions combined with wrist articulations and forearm rotation. Int. J. Ind. Ergon. 40 (5), 492e503. LaFiandra, M., 2009. Methods, models, and technology for lifting biomechanics. In: Duffy, V.G. (Ed.), Handbook of Digital Human Modeling. CRC Press, New York, pp. 8-1e8-27. Lee, W., Karwowski, W., Marras, W.S., Rodrick, D., 2003. A neuro-fuzzy modeling of myoelectrical activity of trunk muscles due to manual lifting tasks,. Ergonomics 15 (1e3), 285e309. Lestrelin, D., Trasbot, J., 2005. The REAL MAN project: objectives, results and possible follow-up. In: SAE International Conference and Exposition of Digital Human Modeling for Design and Engineering. Paper No. 2005-01-2682. Miedema, M.C., Douwes, M., Dul, J., 1997. Recommended maximum holding times for prevention of discomfort of static standing postures. Int. J. Ind. Ergon. 19 (1), 9e18. Miller, J.N., Miller, J.C., 2010. Statistics and Chemometrics for Analytical Chemistry, sixth ed. Pearson Education, Essex. Mukhopadhyay, P., O’Sullivan, L., Gallwey, T.J., 2007. Estimating upper limb discomfort level due to intermittent isometric pronation torque with various combinations of elbow angles, forearm rotation angles, force and frequency with upper arm at 90 abduction. Int. J. Ind. Ergon. 37 (4), 313e325. National Institute of Technology and Evaluation, 2009. http://www.tech.nite.go.jp/ human/jp/pdf/20FYdata/nite_humandatabook.pdf (in Japanese). Neumann, D.A., 2009. Kinesiology of the Musculoskeletal System: Foundations for Rehabilitation, second ed. Mosby, Missouri.
T. Chihara et al. / Applied Ergonomics 45 (2014) 308e317 Shen, W., Parsons, K.C., 1997. Validity and reliability of rating scales for seated pressure discomfort. Int. J. Ind. Ergon. 20 (6), 441e461. Tsang, P.S., Vidulich, M.A., 2006. Mental workload and situation awareness. In: Salvendy, G. (Ed.), Handbook of Human Factors and Ergonomics, third ed. Wiley, New York, pp. 243e268.
317
U.S. Department of Health and Human Services, 1992. Selected Topics in Surface Electromyography for Use in the Occupational Setting: Expert Perspectives. National Institute for Occupational Safety and Health, Atlanta. Wang, X., Breton-Gadegbeku, B.L., Bouzon, L., 2004. Biomechanical evaluation of the comfort of automobile clutch pedal operation. Int. J. Ind. Ergon. 34 (3), 209e221.