- Email: [email protected]
Three-dimensional motion of the center of gravity of the body during walking
ELSEVIER
Human Movement Science 16 (1997) 347-355
Three-dimensional motion of the center of gravity of the body during walking Michael W. Whittle a,b3* a Cline Chair of Rehabilitation Technology, The UnioersiQ of Tennessee at Chattanooga, Chattanooga, TN 37403, USA h H. Carey Hanlin Gait Analysis Laboratory, Siskin Hospital for Physical Rehabilitation, Chattanooga, TN 37403, USA
Abstract A kinematic gait analysis system was used to determine the 3-D motion of the center of the pelvis during walking, in 10 normal adults of both sexes. At the same time, force platform data were integrated twice to determine the 3-D motion of the center of gravity of the body. In general, the center of the pelvis showed greater excursions than the center of gravity of the body, so that within the pelvis, the center of gravity moved in the opposite direction to the motion of the trunk. In the medio-lateral and vertical directions, the phasing of motion was very similar between the center of gravity and the center of the pelvis. In the direction of progression, the motion of the center of the trunk led that of the center of gravity of the body with a phase difference of about 5”. Although the motion of the center of gravity within the pelvis during gait clearly relates to movements of the arms, legs and trunk, further studies would be needed to examine this motion in detail. PsyclNFO
classijication:
2330
Keywords: Human movement; Gait analysis; Center of gravity
1. Introduction The motion of the trunk during gait has long been known, thanks to a number of classical kinematic studies, summarized by Inman et al. (1981), and by
* E-mail: [email protected], Fax: + 1 423 785-2215, Tel.: + 1 423 755-4046. 0167-9457/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved PII SO167-9457(96)00052-S
348
M. W. Whittle/Human Movement Science 16 (I997) 347-355
Whittle (1996). The trunk rises and falls twice during the gait cycle, through a total range of about 46 mm (Perry, 19921, being lowest during double support and highest in the middle of the stance and swing phases. In the frontal plane, the trunk moves from side to side, once in each gait cycle, the trunk being over each leg during its stance phase, as might be expected from the need for support. The total range of side-to-side movement is also about 46 mm (Perry, 1992). As the upper body moves forwards, its speed varies a little, being fastest during the double support phases and slowest in the middle of the stance and swing phases (Whittle, 1996). Although as a first approximation the motion of the trunk and the motion of the center of gravity of the body are clearly similar, they are not exactly the same, since the center of gravity is affected by the positions of the arms and legs, which move independently of the trunk. Many of the classical studies which reported the motion of the center of gravity (e.g. Saunders et al., 1953) were actually kinematic studies of trunk motion. Only a few studies have described the actual motion of the center of gravity during gait, such as those by Shimba (1984) and Crowe et al, (1993). The author is not aware of any studies in which the 3-D motion of the trunk and of the center of gravity of the body have been measured simultaneously. The present study aimed to define the motion of the center of gravity within the trunk during walking, by comparing the motion of a reference point within the trunk with that of the center of gravity.
2. Methods The study was approved by the ethical committees of the University of Tennessee at Chattanooga and Siskin Hospital for Physical Rehabilitation, and the subjects gave informed consent. The motions of the trunk and of the center of gravity were studied in 10 normal healthy adult subjects, with no history of locomotor problems, consisting of one male and one female in each decade of age from the 20’s to the 60’s. They walked barefoot at self-selected speeds along the walkway of a gait analysis laboratory, with 50 mm diameter reflective targets stuck to the skin over the pelvis and lower limbs in standardized locations. The reference point for measuring the position of the trunk was the center of the pelvis, defined as the geometric center of the triangle formed by two markers over the anterior superior iliac spines and one over the midpoint between the two posterior superior iliac spines. The 3-D coordinates of these points in
M. W. Whittle/Human
Movement Science 16 (1997) 347-355
349
waking were determined using the Vicon gait analysis system (Oxford Metrics Ltd., Oxford, England). The motion of the center of gravity was determined using a pair of force platforms (Bertec Inc., Worthington, OH, USA). The gait cycle was defined as starting with initial contact by the left foot on the first force platform, and ending with a second initial contact by the left foot on the ground beyond the force platforms. The right foot landed on the second force platform about half way through the gait cycle. At the beginning of the cycle, the left foot contacted the first force platform, but although the right foot was still on the ground, no recording could be made from it, since it had not yet reached the force platforms. However, the right foot was still on the second force platform after the end of the cycle, so the data recorded from it could be moved to the beginning of the cycle (Fig. 1). This permitted an approximation to be made of the forces beneath both feet for the whole cycle. The data from both force platforms were combined to give the three orthogonal components of the overall ground reaction force vector. The average vertical force during the gait cycle was used to calculate the body weight, and hence the body mass. The three orthogonal components of the ground reaction force were then applied to the body mass, to determine its acceleration in three dimensions. The acceleration was integrated once to derive velocity, and a second time to derive position. RI ht
Left
1.8.
I.C.
Left I.C.
1 ooo- ----Yr-------. Lateral -1 oo;, 200-, \ - \
0
10 20 30 40 50 60 70 80 90 100 Gait cycle (%)
Fig. 1. Three orthogonal components of ground reaction force from both sides. The end of the data for the right side (after second left initial contact) has been moved to the beginning of the gait cycle. (I.C. = initial contact.)
350
M.W. Whittle/
Human Movement Science 16 (1997) 347-355
Since the integration constants were not known, this technique made it possible only to measure changes in position, superimposed on an unknown steady state. It was thus necessary to make the following simplifying assumption: that the position of the center of gravity was unchanged between the beginning of the gait cycle and its end. This was achieved by defining the position of the center of gravity as zero in all three dimensions at the beginning of the cycle, and by applying a linear correction so that it also ended the cycle with a value of zero. To permit comparisons to be made between the center of gravity and the position of the trunk, a similar correction was made to the location in three dimensions of the center of the pelvis. Assuming that the gait cycle is repeatable, this is a reasonable approximation for both the vertical and lateral directions, but it obviously neglects the forward motion of the body. Thus, in the direction of progression, this technique simply identified the variations in the fore-aft motion which were superimposed on an assumed uniform forward velocity. Each subject performed four walks, and the resulting trajectories of the center of gravity and the center of the pelvis in the three orthogonal axes were analyzed to determine the magnitudes of the peaks and troughs (relative to the mean for the whole cycle) and the points in the cycle at which they occurred. Mean values from all acceptable trials (see below) were used to reconstruct an ensemble average for the center of gravity and the center of the pelvis. The following sign convention was adopted for reporting: X: fore-aft (positive forwards); Y: lateral (positive to the left); 2: vertical (positive upwards).
3. Results Of the 120 measurements made (10 subjects, 4 walks, 3 dimensions), 6 were eliminated as they were clearly non-representative, with values beyond 3 standard deviations from the mean; the remainder were analyzed. The pattern of motion was approximately sinusoidal, with a frequency equal to the cycle frequency in the Y (lateral) direction, and double the cycle frequency in the X (fore-aft> and Z (vertical) directions. Table 1 gives the means and standard deviations for the magnitudes of the peaks and troughs for the 3-D motion of the center of gravity and the center of the pelvis. Table 2 gives the corresponding data for the timing of the peaks and troughs, in percentages of the gait cycle from left initial contact to the following left initial contact. Since each individual had a slightly different pattern, it was decided to illustrate the results using artificial waveforms, rather than to use actual subject
hf. W. Whittle/ Human Movement Science 16 (19971347-355
351
Table 1 Mean and standard deviation (SD) for the magnitude (mm) of peaks and troughs in 3-D excursions gravity (CG) and center of pelvis (CP) in fore-aft (X), lateral (Y) and vertical (2) directions First peak XCG Mean SD x CP Mean SD YCG Mean SD Y CP Mean SD ZCG Mean SD ZCP Mean SD
First trough
Second peak
Second trough
of center of
Total excursion
8.9 2.4
-1.1 2.7
8.1 2.9
-9.1 3.6
18.6
13.5 3.5
- 10.3 2.8
13.3 5.6
- 13.4 4.6
26.9
14.6 4.9
- 14.5 5.0
29.1
18.8 5.8
- 18.4 5.6
37.2
15.6 3.7
- 14.0 6.0
17.5 4.0
- 16.9 5.8
34.4
18.9 3.9
- 18.1 4.1
20.4 4.4
- 18.3 4.5
38.7
Table 2 Mean and standard deviation (SD) for the position in gait cycle (%) of peaks and troughs in 3-D excursions center of gravity (CG) and center of pelvis (CP) in fore-aft (X), lateral (Y) and vertical (Z) directions
XCG Mean SD x CP Mean SD YCG Mean SD Y CP Mean SD ZCG Mean SD ZCP Mean SD
First peak
First trough
Second peak
Second trough
16.9 2.3
46.3 1.8
66.3 2.4
96.4 2.0
12.9 2.7
41.6 2.8
61.5 2.0
91.6 3.1
34.5 3.7
88.5 5.8
35.2 5.3
85.8 5.3
29.1 2.1
4.9 2.8
79.5 1.8
53.6 2.1
29.1 1.9
4.7 1.9
79.0 1.7
53.5 1.9
of
352
M. W. Whittle/Human
-201 0
Movement Science 16 (19971347-355
IO 20 30 40 50 60 70 80 90 100 Gait cycle (%)
Fig. 2. Sinusoidal approximation of motion of center of pelvis (solid line) and center of gravity (dashed line) in fore-aft (X) direction during gait cycle. (Forwards positive.)
0
10 20
30 40 50 60 70
Gait cycle (%)
80 90100
Fig. 3. Sinusoidal approximation of motion of center of pelvis (solid line) and center of gravity (dashed line) in medio-lateral (Y) direction during gait cycle. (Left positive.)
0
10 20 30 40 50 60 70 80 90 100 Gait cycle (%)
Fig. 4. Sinusoidal approximation of motion of center of pelvis (solid line) and center of gravity (dashed line) in vertical (Z) direction during gait cycle. (Upwards positive.)
M. W. Whittle/Human Movement Science 16 (1997) 347-355
353
-d 10 20 3b 40 50 so 70 so 90100 Gait cycle (%) Fig. 5. Sinusoidal approximation left and upwards positive.)
of motion of center of gravity within the pelvis during gait cycle. (Forwards,
data. Figs. 2-4 show the approximate 3-D trajectories of the center of gravity and the center of the pelvis, obtained by applying the data from Tables 1 and 2 to sinusoidal waveforms. Subtracting the position of the center of the pelvis from the position of the center of gravity gave the motion of the center of gravity relative to the pelvis, which is shown in Fig. 5, based on the same sinusoidal reconstruction.
4. Discussion The 3-D trajectory of both the center of the pelvis and the center of gravity of the body are well described in the scientific literature. However, the trajectory of the center of gravity within the trunk during walking (Fig. 5) does not appear to have been described previously. The data in Tables 1 and 2, which were used to construct the approximations shown in Figs. 2-4, are in general agreement with previously published studies (Saunders et al., 1953; Inman et al., 1981; Perry, 1992; Crowe et al., 1993). The observed average total displacements in the present study were 39 mm in the vertical direction and 37 mm in the lateral direction (Table 1). These were somewhat less than the 46 mm in these two directions reported by Perry (1992), but the total displacement is known to be very sensitive to walking speed (Inman et al., 19811, which may well have differed between the two studies. It is worth noting that although Saunders et al. (1953) claimed to measure the motion of the center of gravity, they actually measured the motion of the center of the pelvis, using a kinematic system.
354
M. W. Whittle/
Human Movement Science 16 (1997) 347-355
In the fore-aft direction (X), it is necessary to relate the instantaneous position of both the center of gravity and the center of the pelvis to the position which they would have occupied had the forward velocity been entirely uniform. On this basis, both the center of gravity and the center of the pelvis moved forward during the first half of the stance phase on each side, peaking at about 15% and 65% of the cycle, during mid-stance. They then fell back, reaching a peak of posterior motion around 45% and 95% of the cycle, during terminal stance. These changes were due to variations in the forward velocity, which is greatest around the time of initial contact, and least during mid-stance (Whittle, 1996). There were small differences between the trajectory of the center of gravity and the center of the pelvis in the fore-aft direction; the magnitude of the displacements was about 4 mm greater for the center of the pelvis, and the peak excursions for the center of the pelvis took place about 5” earlier in the gait cycle. Within the pelvis, the center of gravity was moving posteriorly at the time of initial contact, reaching a peak of 8 mm behind its mean position at 9% and 59% of the cycle, around toe off on one side and foot flat on the other. It then moved anteriorly, reaching 6 mm in front of its mean position at 34% and 84% of the cycle, around heel rise on one side and during mid-swing on the other. In the lateral direction (Y) there was very little difference in the timing of motion between the center of gravity and the center of the pelvis, both reaching a peak in the direction of the supporting leg at about 36% and 86% of the cycle, around the time of heel rise. The magnitude of the lateral displacement of the center of the pelvis was 4 mm greater than that of the center of gravity. Within the pelvis, the center of gravity moved away from the supporting limb, with a maximal displacement of 4 mm at 32% and 82% of the cycle. In the vertical (Z) direction, the displacements of the center of gravity and the center of the pelvis were very nearly in phase. The total excursion of the center of the pelvis was about 6 mm greater than that of the center of gravity, with peaks of upward motion at 29% and 79%, during mid-stance on one side and mid-swing on the other, and troughs of downward motion at 4% and 54%, during loading response on one side and pre-swing on the other. Within the pelvis, the center of gravity was at its highest at 3% and 53%, and at its lowest at 28% and 78%. The total range of motion was 6 mm. The study achieved its primary goal, by establishing the feasibility of making simultaneous measurements of the center of gravity of the body and the center of the pelvis, and by using them to show how the center of gravity moves relative to the trunk during walking. However, further studies are still needed. The data in Tables 1 and 2 show that there are small differences in motion between the center of gravity of the body and the center of the trunk, in both
M. W. Whittle/Human
Mol,ement Science 16 f 19971347-355
355
magnitude and timing. These differences have not been examined to date. Using a sinusoidal curve in Figs. 2-5, rather than actual data, makes it easier to visualize the relative motions, but loses some of the information obtained. No attempt has been made to interpret the motion of the center of gravity within the pelvis, although it clearly relates to the motions of the arms, legs and trunk. These deficiencies will be addressed in future studies.
References Crowe, A., P. Schiereck, Re. de Boer and W. Keessen, 1993. Characterization of gait of young adult females by means of body centre of mass oscillations derived from ground reaction forces. Gait and Posture 1, 61-68. Inman, V.T., H.J. Ralston and F. Todd, 1981. Human walking. Baltimore, MD: Williams and Wilkins. Perry, J., 1992. Gait analysis: Normal and pathological function. Thorofare, NJ: SLACK Incorporated. Saunders, J.B.D.M., V.T. Inman and H.S. Eberhart, 1953. The major determinants in normal and pathological gait. Journal of Bone and Joint Surgery 35A, 543-558. Shimba, T., 1984. An estimation of center of gravity from force platform data. Journal of Biomechanics 17, 53-60. Whittle, M.W., 1996. Gait analysis: An introduction (2nd ed.). Oxford: Butterworth-Heinemann.
Human Movement Science 16 (1997) 347-355
Three-dimensional motion of the center of gravity of the body during walking Michael W. Whittle a,b3* a Cline Chair of Rehabilitation Technology, The UnioersiQ of Tennessee at Chattanooga, Chattanooga, TN 37403, USA h H. Carey Hanlin Gait Analysis Laboratory, Siskin Hospital for Physical Rehabilitation, Chattanooga, TN 37403, USA
Abstract A kinematic gait analysis system was used to determine the 3-D motion of the center of the pelvis during walking, in 10 normal adults of both sexes. At the same time, force platform data were integrated twice to determine the 3-D motion of the center of gravity of the body. In general, the center of the pelvis showed greater excursions than the center of gravity of the body, so that within the pelvis, the center of gravity moved in the opposite direction to the motion of the trunk. In the medio-lateral and vertical directions, the phasing of motion was very similar between the center of gravity and the center of the pelvis. In the direction of progression, the motion of the center of the trunk led that of the center of gravity of the body with a phase difference of about 5”. Although the motion of the center of gravity within the pelvis during gait clearly relates to movements of the arms, legs and trunk, further studies would be needed to examine this motion in detail. PsyclNFO
classijication:
2330
Keywords: Human movement; Gait analysis; Center of gravity
1. Introduction The motion of the trunk during gait has long been known, thanks to a number of classical kinematic studies, summarized by Inman et al. (1981), and by
* E-mail: [email protected], Fax: + 1 423 785-2215, Tel.: + 1 423 755-4046. 0167-9457/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved PII SO167-9457(96)00052-S
348
M. W. Whittle/Human Movement Science 16 (I997) 347-355
Whittle (1996). The trunk rises and falls twice during the gait cycle, through a total range of about 46 mm (Perry, 19921, being lowest during double support and highest in the middle of the stance and swing phases. In the frontal plane, the trunk moves from side to side, once in each gait cycle, the trunk being over each leg during its stance phase, as might be expected from the need for support. The total range of side-to-side movement is also about 46 mm (Perry, 1992). As the upper body moves forwards, its speed varies a little, being fastest during the double support phases and slowest in the middle of the stance and swing phases (Whittle, 1996). Although as a first approximation the motion of the trunk and the motion of the center of gravity of the body are clearly similar, they are not exactly the same, since the center of gravity is affected by the positions of the arms and legs, which move independently of the trunk. Many of the classical studies which reported the motion of the center of gravity (e.g. Saunders et al., 1953) were actually kinematic studies of trunk motion. Only a few studies have described the actual motion of the center of gravity during gait, such as those by Shimba (1984) and Crowe et al, (1993). The author is not aware of any studies in which the 3-D motion of the trunk and of the center of gravity of the body have been measured simultaneously. The present study aimed to define the motion of the center of gravity within the trunk during walking, by comparing the motion of a reference point within the trunk with that of the center of gravity.
2. Methods The study was approved by the ethical committees of the University of Tennessee at Chattanooga and Siskin Hospital for Physical Rehabilitation, and the subjects gave informed consent. The motions of the trunk and of the center of gravity were studied in 10 normal healthy adult subjects, with no history of locomotor problems, consisting of one male and one female in each decade of age from the 20’s to the 60’s. They walked barefoot at self-selected speeds along the walkway of a gait analysis laboratory, with 50 mm diameter reflective targets stuck to the skin over the pelvis and lower limbs in standardized locations. The reference point for measuring the position of the trunk was the center of the pelvis, defined as the geometric center of the triangle formed by two markers over the anterior superior iliac spines and one over the midpoint between the two posterior superior iliac spines. The 3-D coordinates of these points in
M. W. Whittle/Human
Movement Science 16 (1997) 347-355
349
waking were determined using the Vicon gait analysis system (Oxford Metrics Ltd., Oxford, England). The motion of the center of gravity was determined using a pair of force platforms (Bertec Inc., Worthington, OH, USA). The gait cycle was defined as starting with initial contact by the left foot on the first force platform, and ending with a second initial contact by the left foot on the ground beyond the force platforms. The right foot landed on the second force platform about half way through the gait cycle. At the beginning of the cycle, the left foot contacted the first force platform, but although the right foot was still on the ground, no recording could be made from it, since it had not yet reached the force platforms. However, the right foot was still on the second force platform after the end of the cycle, so the data recorded from it could be moved to the beginning of the cycle (Fig. 1). This permitted an approximation to be made of the forces beneath both feet for the whole cycle. The data from both force platforms were combined to give the three orthogonal components of the overall ground reaction force vector. The average vertical force during the gait cycle was used to calculate the body weight, and hence the body mass. The three orthogonal components of the ground reaction force were then applied to the body mass, to determine its acceleration in three dimensions. The acceleration was integrated once to derive velocity, and a second time to derive position. RI ht
Left
1.8.
I.C.
Left I.C.
1 ooo- ----Yr-------. Lateral -1 oo;, 200-, \ - \
0
10 20 30 40 50 60 70 80 90 100 Gait cycle (%)
Fig. 1. Three orthogonal components of ground reaction force from both sides. The end of the data for the right side (after second left initial contact) has been moved to the beginning of the gait cycle. (I.C. = initial contact.)
350
M.W. Whittle/
Human Movement Science 16 (1997) 347-355
Since the integration constants were not known, this technique made it possible only to measure changes in position, superimposed on an unknown steady state. It was thus necessary to make the following simplifying assumption: that the position of the center of gravity was unchanged between the beginning of the gait cycle and its end. This was achieved by defining the position of the center of gravity as zero in all three dimensions at the beginning of the cycle, and by applying a linear correction so that it also ended the cycle with a value of zero. To permit comparisons to be made between the center of gravity and the position of the trunk, a similar correction was made to the location in three dimensions of the center of the pelvis. Assuming that the gait cycle is repeatable, this is a reasonable approximation for both the vertical and lateral directions, but it obviously neglects the forward motion of the body. Thus, in the direction of progression, this technique simply identified the variations in the fore-aft motion which were superimposed on an assumed uniform forward velocity. Each subject performed four walks, and the resulting trajectories of the center of gravity and the center of the pelvis in the three orthogonal axes were analyzed to determine the magnitudes of the peaks and troughs (relative to the mean for the whole cycle) and the points in the cycle at which they occurred. Mean values from all acceptable trials (see below) were used to reconstruct an ensemble average for the center of gravity and the center of the pelvis. The following sign convention was adopted for reporting: X: fore-aft (positive forwards); Y: lateral (positive to the left); 2: vertical (positive upwards).
3. Results Of the 120 measurements made (10 subjects, 4 walks, 3 dimensions), 6 were eliminated as they were clearly non-representative, with values beyond 3 standard deviations from the mean; the remainder were analyzed. The pattern of motion was approximately sinusoidal, with a frequency equal to the cycle frequency in the Y (lateral) direction, and double the cycle frequency in the X (fore-aft> and Z (vertical) directions. Table 1 gives the means and standard deviations for the magnitudes of the peaks and troughs for the 3-D motion of the center of gravity and the center of the pelvis. Table 2 gives the corresponding data for the timing of the peaks and troughs, in percentages of the gait cycle from left initial contact to the following left initial contact. Since each individual had a slightly different pattern, it was decided to illustrate the results using artificial waveforms, rather than to use actual subject
hf. W. Whittle/ Human Movement Science 16 (19971347-355
351
Table 1 Mean and standard deviation (SD) for the magnitude (mm) of peaks and troughs in 3-D excursions gravity (CG) and center of pelvis (CP) in fore-aft (X), lateral (Y) and vertical (2) directions First peak XCG Mean SD x CP Mean SD YCG Mean SD Y CP Mean SD ZCG Mean SD ZCP Mean SD
First trough
Second peak
Second trough
of center of
Total excursion
8.9 2.4
-1.1 2.7
8.1 2.9
-9.1 3.6
18.6
13.5 3.5
- 10.3 2.8
13.3 5.6
- 13.4 4.6
26.9
14.6 4.9
- 14.5 5.0
29.1
18.8 5.8
- 18.4 5.6
37.2
15.6 3.7
- 14.0 6.0
17.5 4.0
- 16.9 5.8
34.4
18.9 3.9
- 18.1 4.1
20.4 4.4
- 18.3 4.5
38.7
Table 2 Mean and standard deviation (SD) for the position in gait cycle (%) of peaks and troughs in 3-D excursions center of gravity (CG) and center of pelvis (CP) in fore-aft (X), lateral (Y) and vertical (Z) directions
XCG Mean SD x CP Mean SD YCG Mean SD Y CP Mean SD ZCG Mean SD ZCP Mean SD
First peak
First trough
Second peak
Second trough
16.9 2.3
46.3 1.8
66.3 2.4
96.4 2.0
12.9 2.7
41.6 2.8
61.5 2.0
91.6 3.1
34.5 3.7
88.5 5.8
35.2 5.3
85.8 5.3
29.1 2.1
4.9 2.8
79.5 1.8
53.6 2.1
29.1 1.9
4.7 1.9
79.0 1.7
53.5 1.9
of
352
M. W. Whittle/Human
-201 0
Movement Science 16 (19971347-355
IO 20 30 40 50 60 70 80 90 100 Gait cycle (%)
Fig. 2. Sinusoidal approximation of motion of center of pelvis (solid line) and center of gravity (dashed line) in fore-aft (X) direction during gait cycle. (Forwards positive.)
0
10 20
30 40 50 60 70
Gait cycle (%)
80 90100
Fig. 3. Sinusoidal approximation of motion of center of pelvis (solid line) and center of gravity (dashed line) in medio-lateral (Y) direction during gait cycle. (Left positive.)
0
10 20 30 40 50 60 70 80 90 100 Gait cycle (%)
Fig. 4. Sinusoidal approximation of motion of center of pelvis (solid line) and center of gravity (dashed line) in vertical (Z) direction during gait cycle. (Upwards positive.)
M. W. Whittle/Human Movement Science 16 (1997) 347-355
353
-d 10 20 3b 40 50 so 70 so 90100 Gait cycle (%) Fig. 5. Sinusoidal approximation left and upwards positive.)
of motion of center of gravity within the pelvis during gait cycle. (Forwards,
data. Figs. 2-4 show the approximate 3-D trajectories of the center of gravity and the center of the pelvis, obtained by applying the data from Tables 1 and 2 to sinusoidal waveforms. Subtracting the position of the center of the pelvis from the position of the center of gravity gave the motion of the center of gravity relative to the pelvis, which is shown in Fig. 5, based on the same sinusoidal reconstruction.
4. Discussion The 3-D trajectory of both the center of the pelvis and the center of gravity of the body are well described in the scientific literature. However, the trajectory of the center of gravity within the trunk during walking (Fig. 5) does not appear to have been described previously. The data in Tables 1 and 2, which were used to construct the approximations shown in Figs. 2-4, are in general agreement with previously published studies (Saunders et al., 1953; Inman et al., 1981; Perry, 1992; Crowe et al., 1993). The observed average total displacements in the present study were 39 mm in the vertical direction and 37 mm in the lateral direction (Table 1). These were somewhat less than the 46 mm in these two directions reported by Perry (1992), but the total displacement is known to be very sensitive to walking speed (Inman et al., 19811, which may well have differed between the two studies. It is worth noting that although Saunders et al. (1953) claimed to measure the motion of the center of gravity, they actually measured the motion of the center of the pelvis, using a kinematic system.
354
M. W. Whittle/
Human Movement Science 16 (1997) 347-355
In the fore-aft direction (X), it is necessary to relate the instantaneous position of both the center of gravity and the center of the pelvis to the position which they would have occupied had the forward velocity been entirely uniform. On this basis, both the center of gravity and the center of the pelvis moved forward during the first half of the stance phase on each side, peaking at about 15% and 65% of the cycle, during mid-stance. They then fell back, reaching a peak of posterior motion around 45% and 95% of the cycle, during terminal stance. These changes were due to variations in the forward velocity, which is greatest around the time of initial contact, and least during mid-stance (Whittle, 1996). There were small differences between the trajectory of the center of gravity and the center of the pelvis in the fore-aft direction; the magnitude of the displacements was about 4 mm greater for the center of the pelvis, and the peak excursions for the center of the pelvis took place about 5” earlier in the gait cycle. Within the pelvis, the center of gravity was moving posteriorly at the time of initial contact, reaching a peak of 8 mm behind its mean position at 9% and 59% of the cycle, around toe off on one side and foot flat on the other. It then moved anteriorly, reaching 6 mm in front of its mean position at 34% and 84% of the cycle, around heel rise on one side and during mid-swing on the other. In the lateral direction (Y) there was very little difference in the timing of motion between the center of gravity and the center of the pelvis, both reaching a peak in the direction of the supporting leg at about 36% and 86% of the cycle, around the time of heel rise. The magnitude of the lateral displacement of the center of the pelvis was 4 mm greater than that of the center of gravity. Within the pelvis, the center of gravity moved away from the supporting limb, with a maximal displacement of 4 mm at 32% and 82% of the cycle. In the vertical (Z) direction, the displacements of the center of gravity and the center of the pelvis were very nearly in phase. The total excursion of the center of the pelvis was about 6 mm greater than that of the center of gravity, with peaks of upward motion at 29% and 79%, during mid-stance on one side and mid-swing on the other, and troughs of downward motion at 4% and 54%, during loading response on one side and pre-swing on the other. Within the pelvis, the center of gravity was at its highest at 3% and 53%, and at its lowest at 28% and 78%. The total range of motion was 6 mm. The study achieved its primary goal, by establishing the feasibility of making simultaneous measurements of the center of gravity of the body and the center of the pelvis, and by using them to show how the center of gravity moves relative to the trunk during walking. However, further studies are still needed. The data in Tables 1 and 2 show that there are small differences in motion between the center of gravity of the body and the center of the trunk, in both
M. W. Whittle/Human
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magnitude and timing. These differences have not been examined to date. Using a sinusoidal curve in Figs. 2-5, rather than actual data, makes it easier to visualize the relative motions, but loses some of the information obtained. No attempt has been made to interpret the motion of the center of gravity within the pelvis, although it clearly relates to the motions of the arms, legs and trunk. These deficiencies will be addressed in future studies.
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