Body Segment Parameters: A Survey of Measurement Techniques
Rudolfs Drillis, Ph. D. * Renato Contini, B.S. * Maurice Bluestein, M.M.E. *
Human motor activity is determined by the
response of the subject to constantly changing external and internal stimuli.
The motor response has a definite pattern which can be analyzed on the basis of
temporal, kinematic and kinetic factors.
Temporal factors are those related to time: cadence (tempo) or the number of movements per unit time (minute or
second), the variability of successive durations of motion, and temporal
pattern. The temporal pattern of each movement consists of two or more phases.
The relative duration of these phases and their interrelationships are
indicative characteristics of the movement under consideration. For example, in
walking, two basic time phases may be noted, the stance phase when the leg is in
contact with the ground and the swing phase. The ratio of swingphase time to
stancephase time is one of the basic characteristics of gait.
The kinematic analysis of movement can be
accomplished by studying the linear and angular displacements of the entire
body, the joints (neck, shoulder, elbow, wrist, hip, knee, ankle) and the
segments (head, upper arm, forearm, hand, thigh, shank, foot). For the purpose
of investigation, the most important
kinematic characteristics are: the paths of motion, linear and angular
displacement curves, amplitudes or ranges of motion, the instantaneous and
average velocities and their directions, and finally the linear and angular
accelerations of the body segments under investigation. Information on these
criteria can be obtained readily from objective (optical or electrical)
recordings of the movements of a subject.
The kinetic analysis is concerned with
the influence of different forces and moments acting on the body or a body
segment during the performance of a given activity. To determine these forces
and moments, accurate data on the mass (weight), location of mass centers
(centers of gravity), and the mass moments of inertia of the subject's body
segments are required.
At present there are limited data on body
segment parameters, especially those for American subjects. Such data available
are based on studies made on a limited number of dissected male cadavers. This
cannot be regarded as a representative sample for our normal population with its
wide range of age and difference of body build. There are no data available on
female subjects in the United States.
A precise knowledge of these body segment
parameters has many applications, such as in the design of work activities or
the improvement of athletic performances. It has particular value in
understanding orthopedic and prosthetic problems. It would result in a better
design of braces and prosthetic devices and more reliable methods for their
adjustment. From these data it would also be possible to develop more precise
and effective procedures for the evaluation of braces and artificial
limbs. These procedures would replace the use of subjective ratings on
performance by an amputee or a disabled person.
The information on body segment
parameters obtained by simple clinical methods can be very useful in general
medical practice. It would provide a tool for the determination of:
 body segment growth and decay in normal and abnormal conditions
 body segment density changes in normal and pathological cases;
 body mass distribution asymmetry;
 more precise body composition (fat, bones, muscles).
The aim of this article is to give a
brief review of the methods used by different investigators for the
determination of body segment parameters. Since some of the first treatises and
papers are no longer available, we include some tables and figures which
summarize the data obtained by some of the earlier researchers.
Early Efforts
Since ancient times there has existed an
intense curiosity about the mass distribution of the human body and the relative
proportions of its various segments. Those professions which had to select or
classify subjects of varying body build were particularly interested in the
problem. In spite of individual differences between particular subjects there
are many characteristics which are common to all normal human beings. Thus the
lower extremities are longer and heavier than the upper extremities, the upper
arm is larger than the forearm, the thigh is larger than the shank, and other
similar relationships.
Historically this interest was first
directed to the length relationships between the body segments. To characterize
these relationships certain rules and canons were promulgated. Each canon has
its own standard unit of measure or module. Sometimes the dimension of a body
segment or component parts of a body segment were used as modules and
occasionally the module was based on some abstract deduction.
The oldest known module is the distance
measured between the floor (sole) and the ankle joint. This module was used in
Egypt some time around the period 3000 b.c. On this basis, the height of the human figure was
set equal to 21.25 units. Several centuries later in Egypt a new module, the
length of the middle finger, was introduced. In this instance body height was
set equal to 19 units. This standard was in use up until the time of
Cleopatra.(Fig. 1)
In the fifth century B.C., Polyclitus, a
Greek sculptor, introduced as a module the width of the palm at the base of the
fingers. He established the height of the body from the sole of the foot to the
top of the head as 20 units, and on this basis the face was 1/10 of the total
body height, the head 1/8, and the head and neck together 1/6 of the
total body height. In the first century B.C., Vitruvius, a Roman architect, in
his research on body proportions found that body height was equal to the arm
spreadthe distance between the tips of the middle fingers with arms outstretched. The horizontal
lines tangent to the apex of the head and the sole of the foot and the two
vertical lines at the finger tips formed the "square of the ancients." This
square was adopted by Leonardo da Vinci. He later modified the square by
changing the position of the extremities and scribing a circle around the human
figure.
Diirer (14701528) and Zeising
(18101876) based their canons on mathematical abstracts which were not in
accordance with any actual relationships.
At the beginning of the twentieth
century, Kollmann tried to introduce a decimal standard by dividing the body height into ten
equal parts. Each of these in turn could be subdivided into ten subunits.
According to this standard, the head height is equal to 13 of these smaller
units: seated height, 5253; leg length, 47; and the whole arm, 44
units.(Fig. 2)
Previous Studies in Body
Parameters
Starting with the early investigators,
the idea has prevailed that volumetric methods are best for determining
relationships between body segments. There were basically two methods which were
used for the determination of the volume of the body segments: (1) body segment
immersion, and (2) segment zone measurement or component method. In these
methods it is assumed that the density or specific gravity of any one body
segment is homogeneous along its length. Hence the mass of the segment can be
found by multiplying its volume by its density.
Immersion Method
Harless in Germany first used the
immersion method. In 1858 he published a text book on Plastic Anatomy,
and in 1860 a treatise, The Static Moments of the Human Body Limbs.
In his investigations, Harless dissected five male cadavers and three female
cadavers. For his final report, however, he used only the data gathered on two
of the subjects.
The immersion method involves determining
how much water is displaced by the submerged segment. Previous researchers,
including Harless, have relied on the measurement of the overflow of a water
tank to find the volume of water displaced.
Harless started his studies with the
determination of the absolute and relative lengths of the body and its segments.
The absolute lengths were measured in centimeters. For determining the relative
lengths, Harless used the hand as a standard unit. The standard hand measurement
was equal to the distance from the wrist joint to the tip of the middle finger
of the right hand. Later Harless also used the total height of the body as a
relative unit of length. In the more recent studies on body parameters, this
unit is accepted as the basis for the proportions of the various segment
lengths. The results of Harless' studies are shown in Table 1.
For obtaining the absolute weights of the
body segments, Harless used the gram as the standard. As a unit for relative
weights, he first decided to use the weight of the right hand, but later
established as his unit the one thousandth part of the total body weight. His
results are given in Table 2.
In a very careful way Harless determined
the volume and density (specific gravity) of the body segments. The results of
these measurements are presented in Table 3.
To determine the location of mass centers
(centers of gravity), Harless used a wellbalanced board on which the segment
was moved until it was in balance. The line coincident with the fulcrum axis of
the board was marked on the segment and its distance
from proximal and distal joints determined. The location of the mass center was
then expressed as a ratio assuming the segment length to be equal to one.
Harless also tried to determine the location of segment mass center from the
apex of the head by assuming that the body height is equal to 1,000. The data
for one subject are shown in Table 4. From the table, the asymmetry of the
subject becomes evident.
To visualize the mass distribution of the
human body, Harless constructed the model shown in Fig. 3. The linear
dimensions of the links of the model are proportional to the segment lengths;
the volumes of the spheres are proportional to segment masses. The centers
of the spheres indicate the location of mass
centers (centers of gravity) of the segments.
Modified models of the mass distribution
of the human body and mass center location of the segments have been made by
several other investigators. It is unfortunate that up to now a unified and
universally accepted subdivision of the human body into segments does not
exist.
In 1884, C. Meeh investigated the body
segment volumes of ten living subjects (8 males and 2 females), ranging in age
from 12 to 56 years. In order to approximate the mass of the segments, he
determined the specific gravity of the whole body. This was measured
during quiet respiration and was found to vary
between 0.946 and 1.071 and showed no definite variation with age. The segment
subdivision used by Meeh is shown in Fig. 4 and the results of the segment volume
measurements are presented in Table 5.
C. Spivak, in 1915, in the
United States, measured the volumes of various segments and the whole body for
15 males. He found that the value of specific gravity of the whole body ranged
from 0.916 to 1.049.
D. Zook, in 1930, made a thorough
study of how body segment volume changes with age. In making this study, he used
the immersion method for determining segment volumes. These were expressed in
per cent of whole body volume. His sample consisted of youngsters between the
ages of 5 and 19 years. His immersion technique was unique, but his claim that
it permitted the direct determination of the specific gravity of any particular
body segment does not seem to have been established. Some of his results are
shown in Fig. 5 and Fig. 6.
In the period from 1952 to 1954, W.
Dempster at the University of Michigan made a very thorough study of human body
segment measurements. His investigations were based on values obtained on eight
cadavers. Besides volumes, he obtained values for mass, density, location of
mass center, and mass moments of inertia. The immersion method was used to
determine volume. However, these data have limited application since all of
Dempster's subjects were over 50 years of age (5283) and their average weight
was only 131.4 lb. The immersion method was used in Russia by
Ivanitzkiy (1956) and Salzgeber (1949).
The immersion technique can be applied
for the determination of the total segment volume or any portion thereof in a
stepbystep sequence. It can be applied as well on living subjects as on
cadavers. In this respect it is a useful technique.
There is some evidence that for most
practical purposes the density may be considered constant along the full length
of a segment. According to O. Salzgeber (1949), this problem was studied by N.
Bernstein in the 1930's before he started his extensive investigations on body
segment parameters. By dividing the extremities of a frozen cadaver into zones
of 2 cm. height, it was established that the volume centers and mass centers of
the extremities were practically coincident. It would seem therefore that the
density along the segment was fairly constant for the case studied. Accepting
this, it follows that the extremity mass, center of mass, and mass moment of
inertia may be determined from the volume data
obtained by immersion. However, it should be noted that for the whole body,
according to an investigation by Ivanitzkiy (1956), the mass center does not
coincide with the volume center, due to the smaller density of the
trunk.
Computational Methods
Harless was the first to introduce
computational methods as alternatives to the immersion method for determining
body volume and mass. He suggested that this would be better for specific trunk
segments since no definite marks or anatomical limits need be
applied.
He considered the upper part of the trunk
down to the iliac crest as the frustum of a right circular cone. The volume
(V1) is then determined by the formula:Eq. 1
He assumed that the volume of the lower
(abdominopelvic) part of the trunk (V2) can be approximated as a body
between two parallel, nonsimilar elliptical bases with a distance h
between them. The volume V2 is determined by the
formula:Eq. 2
On the basis of dimensions taken on one
subject, using these formulas he arrived at a value for V1 of 21,000 cm
cubed and 5,769 cm subed for V2. Using a value of 1.066 gr/cm cubed as
the appropriate specific gravity of these parts, the total trunk weight was
computed to be 28.515 kg. The actual weight of the trunk was determined (by
weighing) to be 29.608 kg. The computed weight thus differed from the actual
weight by 1.093 kg, or 3.69 per cent.
Several subsequent investigators used
this method subdividing the body into segments of equal height. For increased
accuracy these zones should be as small as practically possible a height of 2
cm is the practical lower limit. The zone markings are measured
starting usually from the proximal joint of the
body segment. The circumference of the zone is measured and it is assumed that
the crosssection is circular. The volume may be computed and on the basis of
accepted specific gravity values the mass may be found. From these values one
may compute the center of mass and mass moment of inertia.
Amar (1914) in order to compute the mass
moment of inertia of various body segments made a number of assumptions. He
assumed the trunk to be a cylinder, and that the extremities have the form of a
frustum of a cone. The mass moment of inertia for the trunk about a lateral axis
through the neck is determined from the formula:Eq. 3
and for the extremities by the
formula:Eq. 4
Weinbach (1938) proposed a modified zone
method based on two assumptions: (1) that any crosssection of a human body
segment is elliptical, and (2) that the specific gravity of the human body is
uniform in all its segments and equal to 1.000 gr/cm cubed. The area (A)
at any cross section is expressed by the equation:Eq. 5
Plotting a graph showing how the
equidistant crosssectional areas change relative to their location from the
proximal joint, it is possible to determine the total volume of the segment and
hence its mass and location of center of mass. The mass moment of inertia (/)
may be obtained by summing the products of the distances from the proximal joint
to the zone center squared (r squred) and the corresponding zone
mass:Eq. 6
Unfortunately both of Weinbach's
assumptions are questionable since the cross sections of human body segments are
not elliptical and the specific gravities of the different segments are not
equal to 1.000 gr/cm cubed nor is density truly uniform in all
segments.
Bashkirew (1958) determined the specific
gravity of the human body for the Russian population to be 1.044 gr/cm cubed
with a standard deviation of ±0.0131 gr/cm cubed and the limits from 0.978
minimum to 1.109 maximum. Boyd (1933) determined further that specific gravity
generally increases with age. Dempster (1955) showed that Weinbach's method was
good for determining the volume of the head, neck, and trunk but not good for
other body parts.
It is evident that the determination of
body segment parameters, based on the assumption that the segments can be
represented by geometric solids, should not be used when great accuracy is
desired. This method is useful only when an approximate value is
adequate.
Fischer introduced another approximate
method of determining human body parameters by computation known as the
"coefficient method." According to this procedure, it is assumed that fixed
relations exist between body weight, segment length, and the segment parameters
which we intend to find. There are three such relationships or ratios expressed
as coefficients. For the body segment mass, the coefficient is identified as
C1 and represents the ratio of the segment mass to the total body mass.
The second coefficient C2 is the ratio of the distance of the mass center
from the proximal joint to the total length of the segment. The third
coefficient C3 is the ratio of the radius of gyration of the segment
about the mediolateral centroidal axis to the total segment length. Thus to
determine the mass of a given segment for a new subject, it would be sufficient
to multiply his total body mass by coefficient C1 corresponding segment
mass. Similarly the location of mass center and radius of gyration can be
determined by multiplying the segment length by the coefficients C2 and
C3 respectively.
Table 6 compares the values of
coefficient C1obtained by different
investigators.
Table 6 shows that the differences
between the coefficients obtained by different investigators for particular
segment masses are great. The difference is highest for the trunk and head mass
where the coefficients vary from 49.68 to 56.50 per cent of body mass. Next
highest difference is in the thigh coefficients from 19.30 to 24.43 per cent of
body mass. Since the number of subjects used in the studies, with the exception
of that of Bernstein, is small and no anthropological information on body build
is given, it is difficult to draw any definite conclusions about the scientific
and practical value of these coefficients for body segment mass
determination.
As already mentioned, the data obtained
by Harless are based on two decapitated male cadavers, and since the blood had
been removed some errors are possible. The data of Meeh are based on volume
measurements of eight living subjects. The large coefficient for the trunk is
influenced by the assumption that all body segments have the same average
density, where actually it is less for the trunk.
Braune and Fischer (1889) made a very
careful study of several cadavers. Their coefficients are based on data taken on
three male cadavers whose weight and height were close to the data for the
average German soldier. The relative masses (coefficients) of the segments were
expressed in thousandths of the whole body mass. The positions of the mass
center and radius of gyration (for determination of the segment mass moments of
inertia) were expressed as proportional parts of the segment's total
length. Fischer's coefficients have been accepted and used in most subsequent
investigations to date.
N. Bernstein and his coworkers (1936) at
the Russian AllUnion Institute of Experimental Medicine in Moscow carried out
an extensive investigation on body segment parameters of living subjects. The
study took care of anthropological typology of body build. The results of this
investigation were published in a monograph, Determination of Location of the
Centers of Gravity and Mass (weight) of the Limbs of the Living Human Body
(in Russian). At present the monograph is not available in the United
States. Excerpts of this investigation, which cover 76 male and 76 female
subjects, 12 to 75 years old, were published by N. Bernstein in 1935 in his
chapters on movement in the book, Physiology of Work (in Russian), by G.
P. Konradi, A. D. Slonim, and V. C. Farfel.
Table 7 shows data for the comparison of
segment masses of living male and female subjects as established by Bernstein's
investigation. The data are selfexplanatory.
Determination of Mass Center
Location
In the biomechanical analysis of
movements it is necessary to know the location of the segment mass center which
represents the point of application of the resultant force of gravity acting on
the segment. The mass center location of a segment system such as an arm or a
leg or the whole body determines the characteristics of the motion.
Table 8 shows the relative location of
the mass center for different segments. It is evident that the assumption that
mass center of all segments is located 45 per cent from the proximal and 55 per
cent from the distal end of the segment is not valid. Since the mass
distribution of the body is related to body build it seems that the mass center
location also depends on it.
Bernstein claims that he was able to
locate the mass centers with an accuracy of ±1 mm. Hence the data of Table 9
represent the result of very careful measurements. An analysis of these data
shows that there is no definite trend of the coefficients differing with age or
sex. The variance of the coefficients is very high and reaches nine per cent as
maximum. Thus the use of the same coefficients for subjects with a wide range of
body build is highly questionable.
Fig. 7 and Fig. 8 represent, in
modification, Fischer's schemes for the indication of the mass center location
of the extremities. The letters of the alphabet indicate the location levels of
the mass centers on the human figure. The corresponding cross sections through the
segments are shown separately. The letters designate the following:
Amass center of upper
arm
Bmass center of whole
arm
Cmass center of forearm
Dmass center of forearm and
hand
Emass center of hand
Fmass center of thigh
Gmass center of whole
leg
Hmass center of shank
Imass center of shank and foot
Jmass center of foot
The location of mass centers with respect
to the proximal and distal joints as determined by W. Dempster (1955) is shown
in Fig. 9.
It is easy to find the equations for the
determination of the coordinates of the mass center when the coordinates of the
segment's proximal and distal joints are given.
By using Fischer's coefficients for mass
center of a particular segment the following formulas were developed:
Coordinates of mass center of
the:
a. forearm:
x = 0.42xd +
0.58xp
y = 0.42yd +
0.58yp
where xd, yd are
coordinates of the distal (wrist) joint and xp, yp are coordinates
of the proximal (elbow) joint.
b. upper arm:
x = 0.47xd + 0.53xp
y = 0.47yd + 0.53xp
where xd, yd are coordinates of
the elbow joint and xp, yp are coordinates of the shoulder
joint.
c. shank:
x = 0.42dx + 0.58xp_{
}y = 0.42yd + 0.58yp_{ }where xd, yd are
coordinates of the ankle
joint and xp, yp are coordinates
of
the knee joint.
d. thigh:
x = 0.44xd + 0.56xp
y = 0.44yd + 0.56yp
where xd, yd are coordinates of
the knee joint and xp, yp are coordinates of the hip
joint.
For the case of threedimensional
recordings of motion, similar equations for z are used. The coordinates
of the mass center of trunk (t) are:
xt = 0.235 (xfr + xfl) +
0.265 (xbr + xbl), with similar equations for the yt and
zt coordinates.
Here xfr is the coordinate of the
right hip and xfl is the coordinate of the left hip, and xbr is
the coordinate of the right shoulder and xbl is the coordinate of the
left shoulder.
In the same manner the equations for
segment systems are developed:
a. entire arm:
mass center x coordinate given by:
xac = 0.130 xgm + 0.148 xm + 0.448 xa + 0.27
xb, where
xacentire arm mass center x
coordinate xgmmass center of the hand xmwrist joint
xaelbow joint xbshoulder joint
Similar equations for y and z
coordinates are used:
b. entire leg:
mass center x coordinate given by:
xlc = 0.096 xgp+ 0.119 xp + 0.437 xs + 0.348 xf ,
where
xlcentire leg mass center x
coordinate xgpmass center of foot xpankle joint
xsknee joint xfhip joint
Similar equations are developed by the
y and z coordinates.
By analogy the formulas for coordinates
determining the location of the mass center of the entire body in two or three
dimensions can be developed.
As regards the coefficient C3, it
is known that the mass moment of inertia (I) is proportional to the
segment's mass and to the square of the segment's radius of gyration (p).
Fischer found that the radius of gyration for rotation about the axis
through the mass center and perpendicular to the longitudinal axis of the
segment can be established by multiplying the segment's length (l) by the
coefficient C3 = 0.3. Hence the mass moment of inertia with respect to
the mass center is Ig = mpp = m(0.3l)(0.31) = 0.09ml
squred.
For the rotation of the segment about its
longitudinal axis, Fischer found the coefficient C4 = 0.35, so that the
radius of gyration p = 0.35 d, where d is the diameter of
the segment.
Since for living subjects the segment
rotates about the proximal or distal joint and not the mass center, the mass
moment of inertia that we are interested in is greater than Ig by the
term mee, where e is the distance of mass center from the joint.
It follows that the mass moment of inertia for segment rotation about the joint
is equal to Ij = mpp + mee = m(pp + ee).
New York University Studies
At present the Biomechanics group of the
Research Division of the School of Engineering and Science, New York University,
is engaged in the determination of volume, mass, center of mass, and mass moment
of inertia of living body segments. The methods employed will now be discussed. Some of these
techniques are extensions of the methods used by previous researchers; others
are procedures introduced by New York University.
Determination of Volume
The two methods being investigated by New
York University to determine segment volumes are (1) immersion and (2) mono and
stereophotogrammetry.
Imersion Method
The Biomechanics group at New York
University uses water displacement as the basis for segment volume
determination. However, the procedure differs from that used by previous
researchers in that the subject does not submerge his segment into a full tank
of water and have the overflow measured. Instead his segment is placed initially
in an empty tank which is subsequently filled with water. In this way, the
subject is more comfortable during the test, and the segment remains stationary
to ensure the proper results.
A variety of tanks for the various
segments hand, arm, foot, and leghas been fabricated. It is desirable that the
tank into which the segment is to be immersed be adequate for the extreme limits
which may be encountered and yet not so large as to impair the accuracy of the
experiments. A typical setup is shown in Fig. 10.
The arm is suspended into the lower tank
and set in a fixed position for the duration of the test. The tank is then
filled to successive predetermined levels at twocentimeter increments from the
supply tank of water above. At each level, readings are taken of the height of
the water in each tank, using the meter sticks shown. The volume occupied by
water between any two levels is found by taking the difference between heights
of water levels and applying suitable area factors. Thus to find the volume of
the forearm the displacement volume is found for the wrist to elbow levels in
the lower tank and between the corresponding levels in the upper tank. The
difference between these two volumes is the desired forearm volume.
To find the center of volume obtain
volumes in the same manner of consecutive twocentimeter sections of the limb.
Assuming the volume center of each section as one
centimeter from each face, sum the products of section volume and section moment
arm about the desired axis of rotation. The net volume center for the body
segment is then this sum divided by the total volume of the segment. In a
similar fashion, using the appropriate combination of tanks, we find the volumes
of other segments, hand, foot, and leg. The use of an immersion tank to find
hand volume is shown in Fig. 11. The data on volume and volume centers can
also be used along with density as a check against methods of obtaining mass and
center of mass.
Photogrammetry Method
In order to find the volume of an
irregularly shaped body part such as the head or face a photographic method may be employed. Such
a procedure, called photogrammetry, allows not only the volume to be found, but
a visual picture of the surface irregularity to be recorded as well. The two
types of this technique are mono and stereophotogrammetry. The principles are
the same for each, except that in the latter procedure two cameras are used side
by side to give the illusion of depth when the two photographs are juxtaposed.
The segment of interest is photographed and the resulting picture is treated as
an aerial photograph of terrain upon which contour levels are applied. The
portions of the body part between successive contour levels form segments whose
volumes can be found by use of a polar planimeter on the photograph as
described by Wild (1954). By summing the segmental volumes, the total body
segment volume can be found. A controlled experiment by Pierson (1959) using a
basketball verified the accuracy of such a procedure. Hertzberg, Dupertuis, and
Emanuel (1957) applied the technique to the measurement of the living with great
success. The reliability of the photographic technique was proven by Tanner and
Weiner (1949). For a more detailed discussion of the photogrammetric method,
refer to the paper by Contini, Drillis, and Bluestein (1963).
Method of Reaction Change
In searching for a method which will
determine the segment mass of a living subject with sufficient accuracy, the
principle of moments or of the lever has been utilized. The use of this method
was suggested by Hebestreit in a letter to Steinhausen (1926). This procedure
was later used by Drillis (1959) of New York University. Essentially it consists
of the determination of reaction forces of a board while the subject lies at
rest on it. The board is supported by a fixed base at one end (A) and a
very sensitive weighing scale at the other end (B). The location of the
segment center of mass can be found by the methods described elsewhere in this
paper. The segment mass is m, the mass of the rest of the body is M.
The reaction force (measured on the scale) due to the board only should be
subtracted from the reaction force due to the subject and board. First the
reaction force (S0) is determined when the segment (say the arm) is in
the horizontal position and rests alongside the body; second, the reaction force
(S) is determined when the segment is flexed vertically to 90 deg. with
the horizontal. The distance between the board support points A and B
is constant and equal to D. The distance (d) of the segment
mass center from the proximal joint is known and the distance b from the
proximal joint to support axis A can be measured. From the data it is
possible to write the corresponding moment equations about A. The
solution of these equations gives the magnitude of the segment's mass
as: Eq. 7
To check the test results, the segment is
placed in a middle position, approximately at an angle that is 45 deg. to
the horizontal, in which it is held by a special adjustable supporting frame
shown at the right in Fig. 13.
The magnitude of the segment mass in this
case will be determined by the formula:Eq. 8
By replacing the sensitive scale with an
electrical pressure cell or using one force plate, it is also possible to record
the changing reaction forces. If the subsequent positions of the whole arm or forearm in flexion are
optically fixed as in Stick Diagrams, the corresponding changing reaction forces
can be recorded by electrical oscillograph.Fig. 12
It is assumed that in flexion the elbow
ioint has only one degree of freedom, i.e., it is uniaxial; hence the
mass determination of forearm and hand is comparatively simple. The shoulder
joint has several degrees of freedom and for each arm position the center of
rotation changes its location so that the successive loci describe a path of the
instantaneous centers. If the displacement (e) of the instantaneous
center in the horizontal direction is known from the Slick Diagram, the
magnitude of the segment mass will be: Eq. 9(Fig. 14 and Fig. 15)
Quick Release Method
This technique for the determination of
segment moments of inertia is based on Newton's Law for rotation. This law
states that the torque acting on a body is proportional
to its angular acceleration, the proportionality constant being the mass moment
of inertia. Thus if the body segment, say the arm, can be made to move at a
known acceleration by a torque which can be evaluated by applying a known force
at a given distance, its moment of inertia could be determined. Such a procedure
is the basis for the socalled "quick release" method. To determine the mass
moment of inertia of a body segment, the limb is placed so that its proximal
joint does not move. At a known distance from the proximal joint at the distal
end of the limb, a band with an attached cord or cable is fixed. The subject
pulls the cord against a restraint of known force, such as a spring whose force
can be found by measuring its deflection. The activating torque about the
proximal joint is thus proportional to the force and the distance between the
joint and the band (moment arm). The acceleration of the limb is produced by sharply cutting the
cord or cable. This instantaneous acceleration may be measured by optical or
electrical means and the mass moment of inertia about the proximal joint
determined.
This technique is illustrated in Fig. 16. The subject rotates his forearm about the elbow, thereby pulling against the
spring shown at the right through a cord wrapped around a pulley. The mechanism
on the platform to the right contains the cutter mechanism with an engagement
switch which activates the circuit of the two accelerometers mounted on the
subject's forearm. The potentiometer at the base of the spring records the force
by measuring the spring's deflection. The accelerometers in tandem give the
angular acceleration of the forearm and hand at the instant of cutting. A scale
is used to determine the moment arm of the force. This method is further
discussed by Drillis (1959).
Compound Pendulum Method
This technique for finding both mass
moment of inertia of the segment and center of mass may be used in one of two
ways: (1) considering the segment as a compound pendulum and oscillating it
about the proximal joint, and (2) making a casting of plaster of Paris or dental
stone and swinging this casting about a fixed point.
Using the first method, it is necessary
to find the moment of inertia, the effective point of suspension of the segment,
and the mass center; thus, there are three unknown quantities.
A study by Nubar (1960) showed that these
unknowns may be obtained if it is assumed that the restraining moment generated
by the individual is negligible. In order to simplify the calculations, any
damping moment (resulting from the skin and the ligaments at the joint) is also
neglected. The segment is then allowed to oscillate, and its period, or time for
a complete cycle, is measured for three cases: (1) body segment alone, (2)
segment with a known weight fixed to it at a known point, (3) segment with
another known weight fixed at that point. Knowing these three periods and the
masses, one can find the effective point of suspension, the center of mass, and
the mass moment of inertia from the three equations of motion. If the damping
moment at the joint is not negligible, it may be included in the problem as a
viscous moment. The above procedure is then extended by the measurement of the
decrement in the succeeding oscillations.
In the second procedure, the casting is
oscillated about the fixed suspension point. The moment of inertia of the
casting is found from the measurement of the period. The mass center can also be
determined by oscillating the segment casting consecutively about two suspension
points. This method is described in detail by Drillis el al. (1963).
Since the weight of both the actual segment and cast replica can be found, the
measured period can be corrected on the basis of the relative weights to
represent the desired parameter (mass center or mass moment of inertia) of the
actual segment. The setup for the determination of the period of oscillation is
shown in Fig. 17.
The photograph in Fig. 17 has been
doubleexposed to illustrate the plane of oscillation.
Torsional Pendulum Method
The torsional pendulum may be used to
obtain moments of inertia of body segments and of the entire body. The pendulum
is merely a platform upon which the subject is placed. Together they oscillate
about a vertical axis. The platform is restrained by a torsion bar fastened to
the platform at one end and to the ground at the other. Knowing the physical
constants of the pendulum, i.e., of the supporting platform and of the
spring or torsion bar, the measurement of the period gives the mass moment of
inertia of the whole body. The principle of the torsional pendulum is
illustrated schematically in Fig. 18.
Fig. 19 and Fig. 20 describe the setup in
use. There are two platforms available: a larger one for studying the supine
subject and a smaller one for obtaining data on the erect or crouching subject.
In this way, the moments of inertia for both mutually perpendicular axes of the
body can be found.
Fig. 19 shows a schematic top view of
the subject lying supine on the large table. Recording the period of oscillation
gives the mass moment of inertia of the body about the sagittal axis for the
body position indicated. Figure 20 is a side view of the small table used for
the standing and crouching positions. This view shows the torsion bar in the
lower center of the picture encased in the supporting structure.
This method can also be used to find mass
moments of inertia of body segments. Nubar (1962) describes the necessary
procedure and equations. Basically it entails holding the rest of the body in
the same position while oscillating the system for two different positions of
the segment in question. Knowing the location of the segment in each of these
positions, together with the periods of oscillation of the
pendulum, the segment moment of inertia with respect to the mediolateral
centroidal axis may be found. This technique is illustrated by the schematic
Figure 19 for the case of the arm. The extended position is shown; the period
would then be obtained for the case where the arm is placed down at the
subject's side.
Both the mass and center of mass of the
arm can be determined using the large torsion table. The table and supine
subject are rotated for three arm positionsarms at sides, arms outstretched,
and arms overheadand respective total moments of inertia are found from the
three periods of oscillation. Assuming that the position of the longitudinal
axis of the arm can be defined, i.e., the axis upon which the mass center
lies can be clearly positioned, the following equations may be
applied:Eq. 10
where I1, I2, I3 are the total
moments of inertia of table, supports, and subject, found from the periods of oscillation, for the
subject with arms at sides, outstretched, and overhead, respectively.
h is the distance from middle
fingertip when arms are at the sides to the tip when arms are
overhead.
l is the total arm length
(fingertip to shoulder joint).
g is the distance from middle
fingertip to the lateral center line of the table when the arms are at the
sides.
p is the distance from middle
fingertip to the lateral center line when the arms are outstretched.
s is the distance between the
longitudinal center line of the table and the longitudinal axis of the arm when
the arms are at the sides.
d is the distance between the mass
center of the arm and the shoulder joint.
In this case, the subject is placed so
that his total body mass center coincides with the table's fixed point of
rotation and there are no initial imbalances. The explanation of the above
symbols may be clarified by reference to Fig. 19.
Difficulties in Obtaining Proper Data
In the commonplace technical area, where
it has been necessary to evaluate the volume, mass, center of mass, etc., of an
inanimate object, this object is usually one of fixed dimensions; that is, there
is no involuntary movement of parts. The living human organism, on the other
hand, is totally different in that none of its properties is constant for any
significant period of time. There are differences in standing erect and in lying
down, in inhaling and in exhaling, in closing and in opening the hand. It is
necessary, therefore, to develop a procedure of measurement which can contend
with these changes, and to evaluate data with particular reference to a
specified orientation of the body.
One everpresent problem in dealing with
the body is the location of joints. When a segment changes its attitude with
respect to adjacent segments (such as the flexion of the elbow), the joint
center or center of rotation shifts its position as well. Thus, in obtaining
measurements on body segments, it is necessary to specify exactly what the
boundaries are. As yet there is no generally accepted method of dividing the
body into segments.
When an attempt is made to delineate the
boundary between segments for purposes of experimental measurement, one cannot
avoid the method of placing a mark on the subject at the joint. This mark will
have to serve as the segment boundary throughout the experiment. Unfortunately
an error is introduced here when the elasticity of the skin causes the mark to
shift as the subject moves. This shift does not correspond to a shift in the
actual joint.
In an analysis of a particular body
segment involving movement of the segment, such as the quick release, reaction,
and torsional pendulum methods which have been described, one must take care to
ensure that only the segment moves. Usually this involves both physical and
mental preparations on the part of the subject.
Finally, the greatest error in obtaining
results on body parameters is due to variations in body build. As can be seen
from the previous data brought forth, different researchers using identical
techniques have gotten quite dissimilar data on the same body segment due to the
use of subjects with greatly varying body types.
In an effort to resolve this conflict,
the Biomechanics group at New York University is endeavoring to relate their
data on body segment parameters to a standard system of body
typology.
Anthropometric Studies
In order to develop a means of
classifying the subjects according to body build, the method of somatotyping is
utilized. Here the body build is designated according to relative amounts of
"endomorphy, ectomorphy, and mesomorphy" as described by W. H. Sheldon et al.
(1940, 1954) in the classic works in the field. In order to determine the
subject's somatotype, photographs are taken of three views: front, side, and
back. These are illustrated in Fig. 21.
The Biomechanics group of New York
University has obtained the services of an authority in the field, Dr. C. W.
Dupertuis, to establish the somatotype of the subjects. The photographs also
will be used to obtain certain body measurements.
The aim of the study is to develop
relationships between body parameters and body build or important anthropometric
dimensions so that a pattern will be established enabling body parameters to be
accurately found for all body types.
If sufficient subjects are measured it
should be possible to obtain a set of parameter coefficients which take into
consideration the effect of the particular body type. When these coefficients
are applied to some set of easily measurable body dimensions on any new subject,
the appropriate body parameters could easily be determined.
It is planned to prepare tables of these
body parameter coefficients (when their validity has been established) for some
future edition of Artificial Limbs.
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