- Email: [email protected]
Biomechanical analysis of walking
J. Biompchonics Vol. 14. No Pnnred in Great Britam.
IO. pp 671-670.
1981
BIOMECHANICAL
ANALYSIS
OF WALKING*
ANNA-LISA KAIRENTO and GORANHELLEN Department of Clinical Chemistry and Department of Physics, University of Helsinki, SF-00290 Helsinki 29, Finland Abstract-A biomechanical analysis of walking has been made for five healthy individuals and four invalids, each suffering from a differentdisease, alWing movement through defects in the nervous system. The results for each subject were reproducible from walk to walk. The motion wassymmetricalfor the healthy persons, in contrast to the asymmetry for the invalids. A highly significant diITerenoewas found in the relative mechanical energy of step pairs between the healthy and the ill groups.
INTRODUCTION The use of computers in biomechanical analysis of the motion of the human body has been increasing greatly
in recent years. The variety of applications grows all the time and covers different fields of bodily activity. Initially, the interest was in application to motion in sports. Plagenhoef (1966) demonstrated the primary importance of computers in procedures giving kinesiological data on motion of the whole body. Kinetic analysis was used earlier to study only one or two segments and the methods had not been applied to the whole body. Dempster (1955) presented a study setting out the biological data needed for analysing kinetic data. Ariel (1972, 1973) has since then applied kinesiological analysis to throwing the discus and shot putting. Kinetic analysis is performed on photographs of the motion taken with a high speed cinecamera. Kinesiological data can also be obtained with a telemetric system (Neukomm and Nigg, 1974) but compared to photography this method has a number of drawbacks, for example, analysis of each segment, separately, is not possible. In this work a kinetic analysis of the whole body in motion is applied to a study of walking. The walking of nine subjects was analyzed using the principles of kinesiology presented by Plagenhoef (1968). MEASURINGMETHOD The photographing of the walking was done with two cinecameras, Canon Scoopic 16 M-cameras, placed on opposite sides of the walking path, as shown in Fig. 1. Photography was performed in day light, with an additional three lights of 1000 W and the exposure was 18 frames/xc. Each individual was photographed 3-5 times to enable assessment of the reproducibility of the motion. The joint centres were marked with coloured tapes during the photographing and they were picked out by projecting the frames onto graph
paper. The values of coordinates representing the joint centres were used in a later computer analysis using a Honeywell Bull 66/20 computer. The length of each body segment was determined either by measurement of the subjects, directly, or of their photographs. The centre of gravity and radius of gyration were determined by the method of Plagenhoef. For determination of the mass of the segments, the volumes of different segments in the hand and foot were measured using water displacement. The masses were then calculated using the average density values of Demp ster. The directions of each of the segments between two joint centres were calculated and angle-time coordinates were then used throughout the study. A polynomial of the tenth-degree was fitted to the data : eAt)=e,(t)“+e,_l(t)n-l+
. . . + B,(t)+8()?
(1)
where s refers to a segment and n to the degree of the polynomial. The angular velocity o(t) and acceleration a(t) can be calculated by derivation of the equation of motion, d&t) o(t) = -&-’
(2)
d%(t) a(t) = F.
f3)
The effective force on each segment is due partly to its own motion and partly to the forces of other segments on it. Let US consider first the force acting on the forearm (Fig. 2). It consists of the muscle force component of the forearm itself and a total force component from other segments acting via the elbow : F, = ml#l-G,
= m, (r, +f,)
- G,,
(4)
where T, = 5 ti i=Z
*Received 4 Augusr 1979.
is the distance vector of the first joint centre to the origin, r, is the distance vector from the centre of mass 671
ANNA-LISA KAIRENTOand G&AN
612 x Second camera
HELLEN
F, = (mR),--G,+F,+,
= (ti),-G,+(my),+
F,,_i, (7)
right
where F,_, is the total force effect of the upper segments on the nth segment and (mT), is the total force effect of the lower segments on the nth segment. Since the total force on one segment acts via the joint centre of the adjacent segment, it is important to calculate the total moment, where total muscle forces are concerned. The moment acting on the joint centre of the uppermost segment in the case of the elbow is:
side
~. left
c
side
I
walking
direction
1 metre
Mr = (J,), +r, xF, = (Jc& x First Camera
Fig.
1. Schematic
+ ri x(m$A.
The moment of inertia of the arm (J,)i calculated using the Steiner rule ; hence:
diagram of the system used for photography.
fJ,h
(8)
can be
= m, (kg - r:),
(9)
where k is the radius of gyration. The total moment of the other segments can be calculated from the equation : Mn=mn(15f-r,2)a,+r,xF,+t,,xF,_,+M,_,,
(10)
where the last two terms are due to the moment effect of segment n - 1 on segment n. The total force F, on segment n includes the force of motion of the segment itself and the force of the lower segments on it. In studying body motion, valuable information can be gamed by analyzing the motion of the centre of gravity, which can be calculated using the equations : cos 0(t), + i mi(ri cos e(t), 1=2 i-1
C r,cosfNt),
+
a=,
(
y(t) = mlrl Fig. 2. Schematic diagram simulating the body. AB is the forearm, BC the upper arm, CD the trunk, DE the thigh, EF the leg, and FG the foot. AnglesB1-0, denote the angles of the segments with respect to a vertical plane. T, is the distance vector of the mass centre to the origin and rl is the distance vector from the antre of mass to the joint centre, r102 is the central and rla linear accekeration,mg is the force of gravity.
to the joint centre in the tirst segment and R, is the
distance vector of the mass centre of the first segment to the origin. The acceleration Rx,=
i
i=2
components
= iga ti (ai
C0S 8i -
r,(a, sin O1 + 0: cos O,), Of
(5)
sin 0,)
+ ri (al cos e1 - co: sin 8,).
e(t), +
(11)
5 m&isin8(r)i
i=2
i-l +
C
t,
sin
n=i
e(t),
i ?tl, (12) Y I=1
t, is the distance of the nth joint centre to the origin and ri is the distance from the centre of mass to the joint centre. The motion of the centre of gravity is harmonic and the energy it contains can be calculated from the equation : W = 2z2 mf2r2,
(13)
where f is frequency and r is the amplitude of the motion. This energy value includes the energy of the step pairs.
- ti (ai sin fIi + 0: cos Oi) -
%
of RI are:
sin
i m, )I I=1
(6)
The total force acting on the other segments can be calculated from the equation :
RESULlS The analysis of walking was performed on different subjects : in five healthy subjects and in four suffering from different defects derived from the central nervous system The subjects are labclled A to I. The letters C and I refer to the same person ; the former when she
Biomechanical analysis of walking Table 1. Significance of the differences between the results obtained for two walks by the same person, with an hour between the walks Amplitude
Velocity
AI-A, -
AiA, -
Acceleration
-
Moment
-
Longitude AI-A, -
Al-A,
-
Calculations are based on the two-way analysis of variance and the significance is calculated according to Fisher’s F-test (Hald, 1952). A, and A, denote photographing from the same side and A, and A, from the opposite side. - denotes P > 0.05.
was in good health and the latter when she had myalgia in her legs, due to training exercises. The reproducibility of the results was ascertained after an interval of at least 1 hr between walks. The results are presented in Table 1, and it can be seen that there were no significant differences between the results obtained between walks of any one individual. In Fig. 3(a) the curves describing the accelerations of different segments during the walking of A are presented. Figure 3(b) presents the corresponding moments acting on the segments. it can be seen from Fig. 3 that the curves describing acceleration and moment as a function of time are harmonic. The amplitude is the average difference between the largest and the smallest values and the longitude is the average time between two maxima or minima - that is, the duration of step pairs. Table 2a
0.6
673
presents the two-way analysis of variance for the maximum, minimum, longitude and amplitude values of the segmental parameters (velocity, acceleration, and moment), firstly between segments within the same subject and secondly between subjects (all segments pooled) - considering, first the whole material and then the healthy and ill groups separately. According to the variance analysis it can be said, as regards the maximum and minimum values, the differences between segments and between persons were significant for velocity, acceleration and moment in both the healthy and ill groups and for the whole material. The longitudes were not significantly different for the motion within the ill group but were significantly different in the healthy group. For the whole material the significance is variable due to the variation between the two subgroups. Differences of amplitudes in velocity, acceleration and moment were significant within both groups and between groups. Table 2a contains data photographed from the right hand side and Table 2b the results obtained from the left hand side of the subject examined. Some differences can be observed in the maximum and minimum values between subjects, when comparing the data from the right side. It is also noticeable that there are no significant differences in the motion between segments as regards their longitude. Differences were, however, significant, when amplitude alone was considered. For calculation of the energy; from equation (13); the amplitude was standardized by multiplication by the reciprocal of the height of the subject; since it was
1.2
1.8
2.L
Time (s)
Fig. 3. (a).
ANNA-LISA KARENTO
674
and
G&CAN HELLEN
1.2 (b) Fig.3(a). Angular accelerations of different segments during the walking of person A. (b) Corresponding
moments acting on the segments. Symbols used are l the trunk, x the upper arm, n the forearm, A the thigh, + the leg and 0 the foot.
evident that height had a direct effect on the amplitude. It was also noticed (Fig. 4b) that the y-component of the centre of gravity had two amplitudes, caused by the alternation of the feet during walking. Energy values were calculated, corresponding to the maximum and minimum amplitude values. Table 3 presents results obtained for the motion of the centre of gravity. It can be seen that the difference between the left and right sides were statistically insignificant. On the other hand, the differences between the healthy group and the ill group was highly significant (P < 0.001). DISCUSSION
The analysis of the data was performed in this study in one plane ; the sag&al plane ; with two cameras, ion opposite sides and perpendicular to the motion. From Table 1 it is clear that the results were reproducible even though there was an interval between tests. It was also noted that differences between the left and right sides were not statistically significant, but there was a greater difference than between walks at different times, viewed from the same side. In Figs. 3(a) and 3(b) it can be seen that the motion is symmetrical for a healthy person and the motion of the feet is in the same phase as the body and opposite to that of the feet. The advance of the body and the feet is the same. In the ill group the lack of symmetry in motion is evident. In Tables 2(a) and (b) it is brought out, by means of two-
way analysis of variance, that the differences in motion between segments were significant for the calculated maximum and minimum values and the amplitudes of velocity, acceleration and moment As differences in longitude were not significant, we can infer that there was no time variation in the motion of segments. The differences between subjects within the ill group were not significant, but in the healthy group, were pronounced. In Table 3 one notices the significant difference between the healthy and ill groups as regards the relative mechanical energy needed to move the centre of gravity of the body with one step pair. It can be concluded that the body tries to optimize the energy needed for moving. It is interesting to note the difference in the relative energy used by the subject who was initially healthy but who later developed myalgia in her legs (C and I). By means of biomechanical analysis it is thus possible to calculate values for velocity, acceleration and moment of segments. It is, however, a doubtful means of deciding whether or not a person is healthy, because the variation between individuals is so great. The relative mechanical energy for moving the centre of mass of the body was significantly different between the healthy and ill groups. It must, however, be conch&d that the most reliable results are to be gained in follow-up studies, because of the individual differences
Biomedmnical
analysis of waking
675
t
+
+
f
I
I
+
+
t
+
f
+
I
+
+
+
t
+
+
+
I
I
+
+
+
+
+
+
T
+
+
+
t
+
+
+
7
7
+
+
t
T
+
T
+
+
+
I
t
+
+
+
I
T
+
+
+
+
t
+
I
+
+
+
+
+
+
+
I
I
+
+
11 lw
&E
efi
dl?i
Between segments
Longitude
+ +
Between segments
Between persons t
+
+
+
+
+
Acceleration
+
+ t
+
+
+
Velocity
+
-
+
+
+
+
Moment
+ denotes P c 0.01, (+ ) denotes P < 0.05 and - denotes P > 0.05.
Amphtude
+
Between persons
values
Between persons
+
(+I
Between ptrsons
Between segments
+
Between segments
Calculated for
Calculated for maximum values
Velocity
All persons
+
+
+
+
Acceleration
Healthy group
+
+
+
f
+
+
+
+
+
+
+
+
Velocity
from the left
Moment
Table 2b. Two-way analysis of variance of the material studied, photographed
+
+
+
+
Acceleration
Ill group
+
+
(+l
+
+
+
+
Moment
Biomechanical
analysis
of walking
lO.O-
S.O-
0.6
1.2
1.8
2.L Time (5)
lb) Fig. 4. Motion of the centre of gravity during the walking of person A. l as photographed from the right and A from the kft of the person. Figure (a) presents the x-component of the motion and (b) the y-component.
ANNA-LIISAKAIRENTO and G&AN HELLEN
678
Table 3. Calculated energy values of the motion of the centre of gravity. Letters from A to E denote the healthy persons, while F to I are for the ill persons
Mass (kg) Length (cm) W, (Nm) WY,(Nm) W’, (Nm) WtO, (Nm) W,, (Nm)
W, (Nm) W, Oum) W,, (Nm) Wlotb(Nm) W, (Nm)
Photographed from the right El Fl Dl
Al
A3
Bi
Cl
63.3 186 62.6 8.95 0.99 63.3 62.6
63.3 186 61.6 5.27 0.85 61.8 61.8
41.2 168 48.2 4.47 0.22 48.4 48.2
41.1 168 35.5 2.06 0.85 35.5 35.5
A2
A4
B2
c2
65.3 8.01 7.12 65.8 65.3
64.2 6.13 5.00 64.5 64.3
41.5 3.57 3.07 41.7 41.5
40.9 3.79 3.25 41.1 40.9
51.7 171 62.6 5.82 0.64 62.9 62.6
Photographed D2 52.7 3.58 3.01 52.8 52.7
87.0 189 44.9 1.42 0.42 44.9 44.9
70.0 196 19.9 1.54 0.16 20.0 20.0
from the left F2 E2 65.9 0.90 0.72 65.9 65.7
21.0 2.97 2.85 21.2 21.0
Gl
Hl
11
47.8 169 4.27 9.30 0.00 10.2 4.27
60.5 187 11.3 0.28 0.28 11.3 11.3
41.1 168 26.6 0.86 0.71 26.6 26.6
G2
HZ
I2
6.58 0.06 0.01 6.58 6.58
9.02 0.33 0.27 9.03 9.02
32.2 2.33 1.49 32.2 323
Al and A3 denote the walking of the same person with an interval of 1 hr ; A2 and A4 are of the same person from the opposite side. W, = x-component of energy value, WY, = y-component of energy corresponding to the largest amplitude and W,, corresponds to the smallest amplitude. W,O, = (W, = (Wi +. W:)1’2.
REFERENCES
Ariel, G. (1972) Computer&d biomechanical analysis of track and field athletics utilized by the Olympic training camp for throwing events. Track and Field QuurterIy Review 72,9%103.
Ariel, G. (1973) Computerized biomechanical analysis of human performance. ASME Symp. Mechanics and Sports. Dempster, W. (1955) Space requirements of the seated operator. WADC Technical Report pp. 55-159, Wright Air Development Center. Hald, A. (1952) Statistical Theory with Engineering Appli-
cations. pp. 456-480, John Wiley & Sons, Canada. Neukomtn, P. A. and Nigg, B. (1974) A telemetry system for the measurement, transmission, and registration of biomechanical and physiological data, applied to skiing. Intern. Series on Sport Sciences V. 1, Biomechanics IV, pp. 231-235. Plagenhoef, S. C. (1966) Methods for obtaining kinetic data to analyze human motion. Research Quarterly 37,103 112 Plagenhoef, S. C. (1968) Computer programs for obtaining kinetic data on human movement. J. Biomechanics 1, 221-234.
IO. pp 671-670.
1981
BIOMECHANICAL
ANALYSIS
OF WALKING*
ANNA-LISA KAIRENTO and GORANHELLEN Department of Clinical Chemistry and Department of Physics, University of Helsinki, SF-00290 Helsinki 29, Finland Abstract-A biomechanical analysis of walking has been made for five healthy individuals and four invalids, each suffering from a differentdisease, alWing movement through defects in the nervous system. The results for each subject were reproducible from walk to walk. The motion wassymmetricalfor the healthy persons, in contrast to the asymmetry for the invalids. A highly significant diITerenoewas found in the relative mechanical energy of step pairs between the healthy and the ill groups.
INTRODUCTION The use of computers in biomechanical analysis of the motion of the human body has been increasing greatly
in recent years. The variety of applications grows all the time and covers different fields of bodily activity. Initially, the interest was in application to motion in sports. Plagenhoef (1966) demonstrated the primary importance of computers in procedures giving kinesiological data on motion of the whole body. Kinetic analysis was used earlier to study only one or two segments and the methods had not been applied to the whole body. Dempster (1955) presented a study setting out the biological data needed for analysing kinetic data. Ariel (1972, 1973) has since then applied kinesiological analysis to throwing the discus and shot putting. Kinetic analysis is performed on photographs of the motion taken with a high speed cinecamera. Kinesiological data can also be obtained with a telemetric system (Neukomm and Nigg, 1974) but compared to photography this method has a number of drawbacks, for example, analysis of each segment, separately, is not possible. In this work a kinetic analysis of the whole body in motion is applied to a study of walking. The walking of nine subjects was analyzed using the principles of kinesiology presented by Plagenhoef (1968). MEASURINGMETHOD The photographing of the walking was done with two cinecameras, Canon Scoopic 16 M-cameras, placed on opposite sides of the walking path, as shown in Fig. 1. Photography was performed in day light, with an additional three lights of 1000 W and the exposure was 18 frames/xc. Each individual was photographed 3-5 times to enable assessment of the reproducibility of the motion. The joint centres were marked with coloured tapes during the photographing and they were picked out by projecting the frames onto graph
paper. The values of coordinates representing the joint centres were used in a later computer analysis using a Honeywell Bull 66/20 computer. The length of each body segment was determined either by measurement of the subjects, directly, or of their photographs. The centre of gravity and radius of gyration were determined by the method of Plagenhoef. For determination of the mass of the segments, the volumes of different segments in the hand and foot were measured using water displacement. The masses were then calculated using the average density values of Demp ster. The directions of each of the segments between two joint centres were calculated and angle-time coordinates were then used throughout the study. A polynomial of the tenth-degree was fitted to the data : eAt)=e,(t)“+e,_l(t)n-l+
. . . + B,(t)+8()?
(1)
where s refers to a segment and n to the degree of the polynomial. The angular velocity o(t) and acceleration a(t) can be calculated by derivation of the equation of motion, d&t) o(t) = -&-’
(2)
d%(t) a(t) = F.
f3)
The effective force on each segment is due partly to its own motion and partly to the forces of other segments on it. Let US consider first the force acting on the forearm (Fig. 2). It consists of the muscle force component of the forearm itself and a total force component from other segments acting via the elbow : F, = ml#l-G,
= m, (r, +f,)
- G,,
(4)
where T, = 5 ti i=Z
*Received 4 Augusr 1979.
is the distance vector of the first joint centre to the origin, r, is the distance vector from the centre of mass 671
ANNA-LISA KAIRENTOand G&AN
612 x Second camera
HELLEN
F, = (mR),--G,+F,+,
= (ti),-G,+(my),+
F,,_i, (7)
right
where F,_, is the total force effect of the upper segments on the nth segment and (mT), is the total force effect of the lower segments on the nth segment. Since the total force on one segment acts via the joint centre of the adjacent segment, it is important to calculate the total moment, where total muscle forces are concerned. The moment acting on the joint centre of the uppermost segment in the case of the elbow is:
side
~. left
c
side
I
walking
direction
1 metre
Mr = (J,), +r, xF, = (Jc& x First Camera
Fig.
1. Schematic
+ ri x(m$A.
The moment of inertia of the arm (J,)i calculated using the Steiner rule ; hence:
diagram of the system used for photography.
fJ,h
(8)
can be
= m, (kg - r:),
(9)
where k is the radius of gyration. The total moment of the other segments can be calculated from the equation : Mn=mn(15f-r,2)a,+r,xF,+t,,xF,_,+M,_,,
(10)
where the last two terms are due to the moment effect of segment n - 1 on segment n. The total force F, on segment n includes the force of motion of the segment itself and the force of the lower segments on it. In studying body motion, valuable information can be gamed by analyzing the motion of the centre of gravity, which can be calculated using the equations : cos 0(t), + i mi(ri cos e(t), 1=2 i-1
C r,cosfNt),
+
a=,
(
y(t) = mlrl Fig. 2. Schematic diagram simulating the body. AB is the forearm, BC the upper arm, CD the trunk, DE the thigh, EF the leg, and FG the foot. AnglesB1-0, denote the angles of the segments with respect to a vertical plane. T, is the distance vector of the mass centre to the origin and rl is the distance vector from the antre of mass to the joint centre, r102 is the central and rla linear accekeration,mg is the force of gravity.
to the joint centre in the tirst segment and R, is the
distance vector of the mass centre of the first segment to the origin. The acceleration Rx,=
i
i=2
components
= iga ti (ai
C0S 8i -
r,(a, sin O1 + 0: cos O,), Of
(5)
sin 0,)
+ ri (al cos e1 - co: sin 8,).
e(t), +
(11)
5 m&isin8(r)i
i=2
i-l +
C
t,
sin
n=i
e(t),
i ?tl, (12) Y I=1
t, is the distance of the nth joint centre to the origin and ri is the distance from the centre of mass to the joint centre. The motion of the centre of gravity is harmonic and the energy it contains can be calculated from the equation : W = 2z2 mf2r2,
(13)
where f is frequency and r is the amplitude of the motion. This energy value includes the energy of the step pairs.
- ti (ai sin fIi + 0: cos Oi) -
%
of RI are:
sin
i m, )I I=1
(6)
The total force acting on the other segments can be calculated from the equation :
RESULlS The analysis of walking was performed on different subjects : in five healthy subjects and in four suffering from different defects derived from the central nervous system The subjects are labclled A to I. The letters C and I refer to the same person ; the former when she
Biomechanical analysis of walking Table 1. Significance of the differences between the results obtained for two walks by the same person, with an hour between the walks Amplitude
Velocity
AI-A, -
AiA, -
Acceleration
-
Moment
-
Longitude AI-A, -
Al-A,
-
Calculations are based on the two-way analysis of variance and the significance is calculated according to Fisher’s F-test (Hald, 1952). A, and A, denote photographing from the same side and A, and A, from the opposite side. - denotes P > 0.05.
was in good health and the latter when she had myalgia in her legs, due to training exercises. The reproducibility of the results was ascertained after an interval of at least 1 hr between walks. The results are presented in Table 1, and it can be seen that there were no significant differences between the results obtained between walks of any one individual. In Fig. 3(a) the curves describing the accelerations of different segments during the walking of A are presented. Figure 3(b) presents the corresponding moments acting on the segments. it can be seen from Fig. 3 that the curves describing acceleration and moment as a function of time are harmonic. The amplitude is the average difference between the largest and the smallest values and the longitude is the average time between two maxima or minima - that is, the duration of step pairs. Table 2a
0.6
673
presents the two-way analysis of variance for the maximum, minimum, longitude and amplitude values of the segmental parameters (velocity, acceleration, and moment), firstly between segments within the same subject and secondly between subjects (all segments pooled) - considering, first the whole material and then the healthy and ill groups separately. According to the variance analysis it can be said, as regards the maximum and minimum values, the differences between segments and between persons were significant for velocity, acceleration and moment in both the healthy and ill groups and for the whole material. The longitudes were not significantly different for the motion within the ill group but were significantly different in the healthy group. For the whole material the significance is variable due to the variation between the two subgroups. Differences of amplitudes in velocity, acceleration and moment were significant within both groups and between groups. Table 2a contains data photographed from the right hand side and Table 2b the results obtained from the left hand side of the subject examined. Some differences can be observed in the maximum and minimum values between subjects, when comparing the data from the right side. It is also noticeable that there are no significant differences in the motion between segments as regards their longitude. Differences were, however, significant, when amplitude alone was considered. For calculation of the energy; from equation (13); the amplitude was standardized by multiplication by the reciprocal of the height of the subject; since it was
1.2
1.8
2.L
Time (s)
Fig. 3. (a).
ANNA-LISA KARENTO
674
and
G&CAN HELLEN
1.2 (b) Fig.3(a). Angular accelerations of different segments during the walking of person A. (b) Corresponding
moments acting on the segments. Symbols used are l the trunk, x the upper arm, n the forearm, A the thigh, + the leg and 0 the foot.
evident that height had a direct effect on the amplitude. It was also noticed (Fig. 4b) that the y-component of the centre of gravity had two amplitudes, caused by the alternation of the feet during walking. Energy values were calculated, corresponding to the maximum and minimum amplitude values. Table 3 presents results obtained for the motion of the centre of gravity. It can be seen that the difference between the left and right sides were statistically insignificant. On the other hand, the differences between the healthy group and the ill group was highly significant (P < 0.001). DISCUSSION
The analysis of the data was performed in this study in one plane ; the sag&al plane ; with two cameras, ion opposite sides and perpendicular to the motion. From Table 1 it is clear that the results were reproducible even though there was an interval between tests. It was also noted that differences between the left and right sides were not statistically significant, but there was a greater difference than between walks at different times, viewed from the same side. In Figs. 3(a) and 3(b) it can be seen that the motion is symmetrical for a healthy person and the motion of the feet is in the same phase as the body and opposite to that of the feet. The advance of the body and the feet is the same. In the ill group the lack of symmetry in motion is evident. In Tables 2(a) and (b) it is brought out, by means of two-
way analysis of variance, that the differences in motion between segments were significant for the calculated maximum and minimum values and the amplitudes of velocity, acceleration and moment As differences in longitude were not significant, we can infer that there was no time variation in the motion of segments. The differences between subjects within the ill group were not significant, but in the healthy group, were pronounced. In Table 3 one notices the significant difference between the healthy and ill groups as regards the relative mechanical energy needed to move the centre of gravity of the body with one step pair. It can be concluded that the body tries to optimize the energy needed for moving. It is interesting to note the difference in the relative energy used by the subject who was initially healthy but who later developed myalgia in her legs (C and I). By means of biomechanical analysis it is thus possible to calculate values for velocity, acceleration and moment of segments. It is, however, a doubtful means of deciding whether or not a person is healthy, because the variation between individuals is so great. The relative mechanical energy for moving the centre of mass of the body was significantly different between the healthy and ill groups. It must, however, be conch&d that the most reliable results are to be gained in follow-up studies, because of the individual differences
Biomedmnical
analysis of waking
675
t
+
+
f
I
I
+
+
t
+
f
+
I
+
+
+
t
+
+
+
I
I
+
+
+
+
+
+
T
+
+
+
t
+
+
+
7
7
+
+
t
T
+
T
+
+
+
I
t
+
+
+
I
T
+
+
+
+
t
+
I
+
+
+
+
+
+
+
I
I
+
+
11 lw
&E
efi
dl?i
Between segments
Longitude
+ +
Between segments
Between persons t
+
+
+
+
+
Acceleration
+
+ t
+
+
+
Velocity
+
-
+
+
+
+
Moment
+ denotes P c 0.01, (+ ) denotes P < 0.05 and - denotes P > 0.05.
Amphtude
+
Between persons
values
Between persons
+
(+I
Between ptrsons
Between segments
+
Between segments
Calculated for
Calculated for maximum values
Velocity
All persons
+
+
+
+
Acceleration
Healthy group
+
+
+
f
+
+
+
+
+
+
+
+
Velocity
from the left
Moment
Table 2b. Two-way analysis of variance of the material studied, photographed
+
+
+
+
Acceleration
Ill group
+
+
(+l
+
+
+
+
Moment
Biomechanical
analysis
of walking
lO.O-
S.O-
0.6
1.2
1.8
2.L Time (5)
lb) Fig. 4. Motion of the centre of gravity during the walking of person A. l as photographed from the right and A from the kft of the person. Figure (a) presents the x-component of the motion and (b) the y-component.
ANNA-LIISAKAIRENTO and G&AN HELLEN
678
Table 3. Calculated energy values of the motion of the centre of gravity. Letters from A to E denote the healthy persons, while F to I are for the ill persons
Mass (kg) Length (cm) W, (Nm) WY,(Nm) W’, (Nm) WtO, (Nm) W,, (Nm)
W, (Nm) W, Oum) W,, (Nm) Wlotb(Nm) W, (Nm)
Photographed from the right El Fl Dl
Al
A3
Bi
Cl
63.3 186 62.6 8.95 0.99 63.3 62.6
63.3 186 61.6 5.27 0.85 61.8 61.8
41.2 168 48.2 4.47 0.22 48.4 48.2
41.1 168 35.5 2.06 0.85 35.5 35.5
A2
A4
B2
c2
65.3 8.01 7.12 65.8 65.3
64.2 6.13 5.00 64.5 64.3
41.5 3.57 3.07 41.7 41.5
40.9 3.79 3.25 41.1 40.9
51.7 171 62.6 5.82 0.64 62.9 62.6
Photographed D2 52.7 3.58 3.01 52.8 52.7
87.0 189 44.9 1.42 0.42 44.9 44.9
70.0 196 19.9 1.54 0.16 20.0 20.0
from the left F2 E2 65.9 0.90 0.72 65.9 65.7
21.0 2.97 2.85 21.2 21.0
Gl
Hl
11
47.8 169 4.27 9.30 0.00 10.2 4.27
60.5 187 11.3 0.28 0.28 11.3 11.3
41.1 168 26.6 0.86 0.71 26.6 26.6
G2
HZ
I2
6.58 0.06 0.01 6.58 6.58
9.02 0.33 0.27 9.03 9.02
32.2 2.33 1.49 32.2 323
Al and A3 denote the walking of the same person with an interval of 1 hr ; A2 and A4 are of the same person from the opposite side. W, = x-component of energy value, WY, = y-component of energy corresponding to the largest amplitude and W,, corresponds to the smallest amplitude. W,O, = (W, = (Wi +. W:)1’2.
REFERENCES
Ariel, G. (1972) Computer&d biomechanical analysis of track and field athletics utilized by the Olympic training camp for throwing events. Track and Field QuurterIy Review 72,9%103.
Ariel, G. (1973) Computerized biomechanical analysis of human performance. ASME Symp. Mechanics and Sports. Dempster, W. (1955) Space requirements of the seated operator. WADC Technical Report pp. 55-159, Wright Air Development Center. Hald, A. (1952) Statistical Theory with Engineering Appli-
cations. pp. 456-480, John Wiley & Sons, Canada. Neukomtn, P. A. and Nigg, B. (1974) A telemetry system for the measurement, transmission, and registration of biomechanical and physiological data, applied to skiing. Intern. Series on Sport Sciences V. 1, Biomechanics IV, pp. 231-235. Plagenhoef, S. C. (1966) Methods for obtaining kinetic data to analyze human motion. Research Quarterly 37,103 112 Plagenhoef, S. C. (1968) Computer programs for obtaining kinetic data on human movement. J. Biomechanics 1, 221-234.