'Walking-Mode Maps' Based on Slip/Non-Slip ... - Semantic Scholar

Original Article

Industrial Health 2008, 46, 23–31

‘Walking-Mode Maps’ Based on Slip/Non-Slip Criteria Takeshi YAMAGUCHI1* and Kazuo HOKKIRIGAWA1 1Graduate

School of Engineering, Tohoku University, 6–6–01 Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 9808579, Japan Received August 4, 2007 and accepted October 16, 2007

Abstract: ‘Walking-Mode Maps’, based on Slip/Non-Slip criteria, are proposed. Slip/Non-Slip criteria are expressed as follows: • for a slip to occur: |Fh/Fn|h ≥ µs or |Fh/Fn|t ≥ µs • for no slip to occur: |Fh/Fn|h < µs or |Fh/Fn|t < µs |Fh/Fn|h and |Fh/Fn|t are the maximum peak value of the traction coefficient at heel-strike and toe-off respectively, and µs is the static friction coefficient between shoe sole and walkway. The ‘Walking-Mode Map’ for the level-surface shows the possible regime of each walking mode as Slip, Slip possible or No slip. Our results, which are based upon a small population and strictly-specified test conditions, indicate that a static friction coefficient higher than 0.47 will prevent both forward and backward slips under our test conditions and under a range of step lengths of 0.55 to 0.95 m and walking speeds of 1.0 to 1.9 m/s. We also found that shorter steps reduce the chance of a slip. A ‘Walking-Mode Map’ for inclined-surface ambulation has also been developed. The inclined-surface results show the friction and inclination-angle-related regime of each walking mode: Slip, Forward slip at heel-strike phase in descending, Backward slip at toe-off phase in ascending, or No slip. Again, extreme caution must be taken in generalizing these small-sample results (n=1, for the inclined tests) to the general population. Key words: Slip, Fall, Walking-Mode Map, Traction Coefficient, Static friction coefficient

Introduction Falling accidents are a serious problem in Japan and in other countries1, 2). The number of fatalities caused by falling accidents is increasing in Japan, and has exceeded 4,000 fatalities/yr since 20013). The number of fatalities caused by falling accidents exceeds that of pedestrians killed in traffic accidents3). Prevention of slip between the shoe sole or foot sole and the walkway surface is an important element in reducing the toll from falling accidents because slipping is one of the most common causes of fall accidents4–8). Slip between shoe or foot sole and walkway surface during walking occurs when the friction required for ambulation, which we call the traction coefficient, defined as the ratio of horizontal force to normal force between the shoe or foot sole and the walkway surface, exceeds available fric*To whom correspondence should be addressed.

tion between them. We express the available friction using the static friction coefficient. Thus, to prevent slipping, a static friction coefficient higher than the traction coefficient is required at the contact interface between the shoe or foot sole and the walkway. Looked at another way, a gait which generates a traction coefficient lower than the static friction coefficient is desirable for safe walking. The static friction coefficient that would be required for safe ambulation can be estimated from the traction coefficient during walking without slips. However, the traction coefficient and, thus, the chance of slipping, is impacted both by gait9, 10), viz., step length, walking speed and ramp angle11, 12), and by walkway conditions. ‘Wear-Mode Maps’13–20) have been proposed in the field of tribology. Hokkirigawa13, 15–18) proposed several for metals and ceramics. ‘Wear-Mode Maps’ are effective for understanding the transition condition of wear modes, and also give information on how to reduce or

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Table 1.

Age, stature and weight information for each subject

Subject No.

Age (yr)

Stature (m)

Weight (kg)

1

23

1.71

57

2 3 4 5 6 7 8

28 24 23 22 23 22 22

1.81 1.75 1.72 1.72 1.69 1.69 1.75

85 67 66 59 57 75 56

9

45

1.87

86

Average (S.D.)

25.8 (7.4)

1.74 (0.06)

67.6 (11.9)

control the wear of materials. We propose ‘WalkingMode Maps’, analogous to ‘Wear-Mode Maps’, based on walking tests and theoretical considerations.* The purpose of this paper is to define walking-mode maps based on walking tests under a wide range of step lengths and walking speeds in level- and inclined-surface walking.

Fig. 1. Schematic diagram of experimental set-up for level-surface walking.

Methods Subjects Nine healthy male subjects participated in the walking tests on a level walkway. All of them were university staff and students. Age, stature and weight information for each subject is shown in table 1. A single subject (Number 1) participated in the inclined-walkway tests. Prior to participation, informed consent was obtained from each subject. Experimental set-up Figures 1 and 2 show the experimental set-ups for walking tests on level- and inclined-surface walkways. Eight force plates (OR6-5, Advanced Mechanical Technology Inc.) placed at the center of a 5-meter-long walkway were used to measure the three orthogonal components of the ground reaction force (Fx, Fy, Fn) as shown in Fig. 3 (a). The coordinate system has a lateral x-axis, a sagittal y-axis and a normal z-axis (Fig. 3(a)). The horizontal component of ground reaction force Fh is

Fig. 2. Experimental set-up for walking on an inclined surface.

expressed by the following equation: (1)

* The word map, strictly speaking, refers to a pictorial or graphical representation having one or more spatial components. In this paper, while our results have no spatial dimensions, we describe our results as a ‘Walking-Mode Map’, as similar terminology is, as seen above, used in tribological studies. With that clarification in mind, we will drop the single quotes and capitalization in the sequel.

The level-walkway walking tests were carried out under dry- (non-slippery) and lubricated- (slippery) walkway conditions. For the slippery condition, glycerin (purity of 97.0 wt%, density of 1.248 g/ml) was applied uniformly to a wooden board mounted on the right side of the forceplate array.

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Fig. 3. Schematic diagram of (a) three orthogonal components of ground reaction force on level walkway and (b) three orthogonal components of ground reaction force (Fx, Fy, Fn) and those of ground reaction force on inclined floor (Fx,θ , Fy,θ , Fn,θ ) .

For inclined-walkway walking tests, a steel-framed, wood-surfaced ramp was set atop the force-plate array as shown in Fig. 2. The ramp angles used in this experiment were 0, 5, 10, 15 and 20 degrees. The coordinate system of three orthogonal components of ground reaction force on the ramp (Fx,θ, Fy,θ, Fn,θ) and three orthogonal components of ground reaction force on the force plate (Fx, Fy, Fn) are shown in Fig. 3(b). Ramp and forceplate forces are related by these two equations; (2) (3) where θ is ramp angle. Infrared-reflective markers were attached to the toe and heel of one shoe in order to collect foot-velocity data. The marker positions were detected by a three-dimensional motion capture system (Vicon 612, Vicon Motion Systems Ltd.) as shown in Fig. 1. The data acquisition system consisted of the force-plate array, infrared cameras, and an analog-to-digital (A/D) converter. A personal computer was used to synchronize and collect ground-reaction-force and foot-motion, reflective-marker data at 120 Hz. Commercially available men’s shoes (0.27 m length) were used, and flat NBR (nitrile butadiene rubber, shore hardness HS70) sheet affixed to the shoe bottom served as the shoe sole. Walking protocol For the walking tests on the level walkway, step lengths were set at 0.55, 0.75 and 0.95 m, and the walking speeds were set at 1.0, 1.4 and 1.9 m/s for each step length. The step length was standardized by stepping on marks on the

walkway, and the walking speed was standardized by using a metronome. Thus, subjects were asked to walk under a total of 9 walking conditions (3 step lengths × 3 walking speeds). Subjects were also asked to look straight ahead as they walked. For walking tests on the glycerincovered walkway (slippery condition), appropriate safety equipments including helmets and pads were used. None of the subjects fell in the walking tests on lubricated walkway. For the walking tests on inclined walkways, the step length was set at 0.75 m, and the walking speed was set at 1.4 m/s.

Results and Discussion Slip/non-slip criteria during walking Figure 4 depicts the normal (Fn) and horizontal components (Fh) of ground-reaction force, traction coefficient (|Fh/Fn|), and velocity of toe or heel marker for subject Number 9 walking on a dry, level walkway with step length of 0.75 m and walking speed of 1.4 m/s. The period from heel contact to whole shoe-sole contact is the heel-strike phase; the period from heel-off to toe-off is the toe-off phase. Several peaks in the traction-coefficient curve can be seen at heel-strike and toe-off (Fig. 4). The slip/non-slip criteria can be expressed as follows; |Fh/Fn|h ≥ µs for a heel slip (4) |Fh/Fn|t ≥ µs for a toe slip (5) |Fh/Fn|h < µs to prevent heel slip (6) |Fh/Fn|t < µs to prevent toe slip (7) where |Fh/Fn|h and |Fh/Fn|t are the maximum peak values of traction coefficient obtained at heel-strike and at toe-off, respectively, when walking without slip. µs is the static friction coefficient between the shoe sole and walk-

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way surface. Although very large peak values of traction coefficient are observed immediately after heel contact and just before the end of the toe-off phase in Fig. 4, these values are anomalous, and do not generate macroscopic slips,

Fig. 4. Representative ground reaction forces, traction coefficient and velocity of heel and toe markers during walking on dry floor. No slips occurred.

contributing to falling because both normal and horizontal components of the ground reaction force take extremely low values. (Essentially, these anomalies are a result of calculations that have an essentially zero-value normal force in the denominator of this calculation.) Therefore, we ignored the anomalous |Fh/Fn|h and the |Fh/Fn|t in our determination of the maximum peak values of traction coefficient. Based on the slip/non-slip criteria described above, and at least on ramps, where it is desirable to prevent both heel and toe slips, higher static friction coefficient than either |Fh/Fn|h or |Fh/Fn|t is desirable. For level-surface ambulation, to prevent heel-strike slips (forward slips) which may cause falling backwards, occurring during weight acceptance, we suggest the maximum peak value of traction coefficient after heel contact: |Fh/Fn|h, as the critical value of friction coefficient to prevent hazardous slips21). The maximum peak value of traction coefficient at toe-off phase (|Fh/Fn|t in this study) can be considered for level-surface ambulation in order to prevent backward slips. However, backward slips occurring at toe-off phase on a level surface have far less potential for pedestrian injury than do forward slips occurring during the heelstrike phase, which causes falling backward. Figure 5 shows relationship between step length and |Fh/Fn|h (Fig. 5(a)) or |Fh/Fn|t (Fig. 5(b)) for level-surface walking at a walking speed of 1.4 m/s. It can be seen in Fig. 5 that both |Fh/Fn|h and |Fh/Fn|t increase with step length for all subjects. It can be also seen in Fig. 5 that the values of |Fh/Fn|h and |Fh/Fn|t is subject dependent.

Fig. 5. Relationship between step length and the maximum peak value of traction coefficient at heel-strike (|Fh/Fn|h) and toe-off (|Fh/Fn|t) phases during walking on dry, level walkway at a walking speed of 1.4 m/s.

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WALKING-MODE MAPS Figure 6 shows relationship between walking speed and both |Fh/Fn|h and |Fh/Fn|t for level walking at step length of 0.75 m. |Fh/Fn|h and |Fh/Fn|t each take on almost constant values with respect to walking speed. The values are subject dependant. Comparing the two independent variables, the effect of walking speed on |Fh/Fn|h and |Fh/Fn|t is small compared to that of step length.

27 In the walking tests on the lubricated walkway, forward slips during the heel-strike phase or backward slips during toe-off phase occurred for several step-length/walking-speed combinations. As described above, backward slips have less potential for pedestrian injury than forward slips. Figure 7 shows time-dependant change in traction coefficient |Fh/Fn| and velocity of heel marker (Fig. 7(a)) or

Fig. 6. Relationship between walking speed and the maximum peak value of traction coefficient at heel-strike (|Fh/Fn|h) and toe-off (|Fh/Fn|t) phases for walking on a dry, level walkway using a step length of 0.75 m.

Fig. 7. Time-series plot of |Fh/Fn| and heel (graph (a)) and toe (graph (b)) velocity when slip occurred during walking on a lubricated walkway for subject Number 1.

28 toe marker (Fig. 7(b)) when slip occurred at heel-strike phase or at toe-off phase for subject No.1. As shown in Fig. 7 (a), the velocity of the heel marker decreases after heel contact, then increases as the result of forward slip that occurs at the moment when the heel velocity starts to increase. The traction coefficient |Fh/Fn| peaks at the moment when the forward slip occurs. That peak value of |Fh/Fn|=0.15 corresponds to the static friction coefficient µs at the contact interface between the shoe sole and the glycerin-covered walkway, and the traction coefficient |Fh/Fn| after slip occurrence corresponds to the kinetic friction coefficient µk. The static friction coefficient of 0.15 is lower than |Fh/Fn|h of 0.33 obtained in walking tests on dry walkway for the same subject under the same walking condition. As shown in Fig. 7 (b), the velocity of toe is negative for t>0.225 s. Therefore, backward slip occurs at the moment when the toe velocity becomes negative. On the other hand, the traction coefficient |Fh/Fn| peaks at the moment when the backward slip begins. That peak value of |Fh/Fn|=0.11 corresponds to the static friction coefficient µs; the traction coefficient |Fh/Fn| after a backward slip starts, corresponds to the kinetic friction coefficient µk. The static friction coefficient of 0.11 is lower than |Fh/Fn|t of 0.29 obtained in the walking tests on dry walkway for the same subject under the same walking condition. These results indicate that forward and backward slips follow the slip criteria expressed in equations (4) through (7).

T YAMAGUCHI et al. Walking mode map for level-walkway Figure 8 shows the effect of step length and the maximum and the minimum values of |Fh/Fn|h, |Fh/Fn|t obtained in all walking tests on the dry, level walkway. The shaded area represents the envelope of the dataset. Based on the slip/non-slip criteria, slip will not occur when the static friction coefficient between shoe sole and walkway is greater than the maximum |Fh/Fn|h and |Fh/Fn|t for each step length. On the other hand, slip will occur for all subjects when the static friction coefficient takes lower values than that of the minimum |Fh/Fn|h and |Fh/Fn|t for each step length. Figure 9 is our walking-mode map for heel-strike (a) and toe-off (b) for level-surface walking as a function of the static friction coefficient and step length. Walking modes during the heel-strike phase can be divided into three regimes: Forward slip will occur, Forward slip may occur, and Forward slip will not occur (Fig. 9 (a)). Walking modes at toe-off phase can also be divided into three regimes: Backward slip will occur, Backward slip may occur, and Backward slip will not occur (Fig. 9 (b)). With the step lengths and walking speeds specific to this study, a static friction coefficient between shoe sole and floor higher than 0.47 would prevent both forward and backward slips during level-surface walking. Conversely, forward or backward slips will definitely occur when a static friction coefficient is lower than 0.11. In general, walking with a longer step length requires a higher available static friction coefficient. Application of these spe-

Fig. 8. The effect of step length on the maximum and the minimum values of |Fh/Fn|h and |Fh/Fn|t obtained in all walking tests for all subjects on the dry, level walkway.

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Fig. 9. Level-surface walking-mode maps at the heel-strike phase (a) and at the toe-off phase (b).

cific values cannot presently be generalized. Application of these results to standards development or litigation is not recommended because these results are based on only 9 male subjects. Walking Mode Map for inclined walkways Figure 10 shows change in traction coefficient |Ft,θ /Fn,θ | over time for subject Number 1 walking on an inclined walkway set at different ramp angles. The maximum peak value of traction coefficient at heel-strike phase |Ft,θ /Fn,θ |h and at toe-off phase |Ft,θ /Fn,θ |t can be observed in Fig. 10. It can also be seen that values of |Ft,θ /Fn,θ |h and |Ft,θ /Fn,θ |t are clearly and significantly affected by ramp angle. Figure 11 shows, for subject Number 1, relationship between ramp angle and |Ft,θ /Fn,θ |h or |Ft,θ /Fn,θ |t. |Ft,θ /Fn,θ |h decreases with increase of ramp angle as shown in Fig. 11(a). On the other hand, |Ft,θ /Fn,θ |t increases with increase of ramp angle as shown in Fig. 11(b). Figure 12 shows, for subject Number 1, a walkingmode map for walking on an inclined walkway as a function of static friction coefficient and ramp angle. Walking modes for inclined-surface ambulation can be divided into four regimes: No slip, Forward slip at heel-strike phase in descending, backward slip at toe-off phase in ascending, and slip. As compared with level-surface ambulation, backward slips on a ramp, which contribute to falling forward, have real potential for pedestrian injury. The

walking-mode map for inclined surfaces indicates that the needed static friction coefficient for safe walking without slipping increases with ramp angle in both pedestrian ascent and descent. That indicates walking on inclinedsurface has more slip-accident potential than walking on a level surface. Under the range of ramp angles (± 20˚), we determined that a static friction coefficient higher than 0.61 was desirable for preventing forward slips and backward slips in ascent and descent, based upon our singlesubject study, using a step length of 0.75 m and a walking speed of 1.4 m/s.

Conclusions Based on our walking tests for walking on level- and inclined-surface walkways, and the slip/non-slip criteria utilized, walking-mode maps were developed. Our results are as follows; (1) Walking modes for walking on a level walkway can be divided into three regimens: Slip, Possible slip, and No slip. (2) Our limited data indicates that a static friction coefficient higher than 0.47 may be desirable for walking without slipping under a wide range of step lengths of 0.55 to 0.95 m and walking speeds of 1.0 to 1.9 m/s, to prevent both backward and forward slips. (3) On a level walkway, a shorter step length will lower the chance of slipping. (4) Walking modes for walking on inclined walkways can

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Fig. 10. Traction coefficient |Fh,θ /Fn,θ | time series for subject No.1 walking on an inclined walkway with a step length of 0.75 m and a walking speed of 1.4 m/s.

Fig. 11. The relationship between ramp angle and |Ft,θ /Fn,θ |h (plot (a)) and |Ft,θ /Fn,θ |t (Plot (b)) .

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6)

7)

8)

9) 10) Fig. 12. Walking-mode map for ascending or descending an inclined walkway.

11)

be divided into four regimes: Slip, Forward slip at heel-strike phase in descending, Backward slip at toeoff phase in ascending, and No slip. (5) The required static friction coefficient for walking without slipping increases with ramp angle for both ascent and descent.

Acknowledgements The authors wish to thank to Mr. Y. Ohta at Industrial Technology Institute, Miyagi Prefectural Government (Japan) for his great help in the walking tests.

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