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Introduction
During the process of biomechanical analysis in order to present
a body one can use specic point localized on the body, e.g. central
geometric point or some point at the edge of the body. Taking into
account human body this specic point can be e.g. a top of head, an
ear, or a hip joint. Such a point plays a role during simplication of
the body. If one wants to describe trajectory of body’s movement
he or she can use a specic point which would substitute the whole
body. The best representation of the body is its center of mass. This
is an imaginational point not joined with material representation of
the body. It can move outside the body like in an example of a circle.
Since the human body has complicated shape and is built from many
tissues of different density it is not easy to localize position of human
body center of mass. Usually it is localized with the use of radius of
center of mass, i.e. a distance from the center of mass to the reference
system. Center of mass plays also a role of a point of application of
forces – gravitational force and inertial force, including centrifugal
force.1,2
There are several methods of localization of the center of
mass, both direct and indirect. There are also many applications
of the knowledge on location of the center of mass of the body in
maintaining balance, in analyses of locostationary and locomotory
behavior within the areas of everyday living, medicine, engineering,
ergonomics, sport.3 The aim of the paper is to present center of mass
as imaginational point which helps in biomechanical description of
different congurations of the human body during maintaining static
posture and during locostationary and locomotory movements.
Methods of localization of the human body
center of mass
Main direct approaches with live subjects
The oldest approach to localization of center of mass was
performed by Borelli4 in the 17th century. He put a board on a prism
in such a manner that a board was in equilibrium. Then a man was laid
on a board. He moved toward the head or toward the feet to maintain
equilibrium of the whole system – board and the body. In the 19th
century Du Bois-Reymond put two short edges of a board (reaction
board) on two prisms. One prism was rested on a scale. The value
of partial weight of a board resting on a scale was read out. With
known body weight, measured distance between prisms, and reading
of scale value, one could calculate position of body’s center of mass
remembering of subtracting partial weight of a board. Also in the 19th
century Basler developed this method by using three-sided board.
He obtained position of center of mass in two directions. All above
approaches were direct investigations on location of the whole body
center of mass. They were used for one conguration of the body.5
Main direct approaches with cadavers
In order to obtain position of center of mass in different
congurations Harless,6 Braune & Fischer7 in the 19th century, and
then especially Dempster & Clauser et al.8,9 in the 20th century divided
frozen cadavers onto separate body parts. They measured mass and
volume and calculated density, and also they positioned center of mass
of each body part. From them only Dempster divided the trunk onto
four parts: thorax, abdomino-pelvic region, two shoulders. Others
kept the trunk as a one segment. In addition to inertial values (mass
and radius of center of mass) Clauser et al.9 measured dimensions
of body parts and skin-fat thickness above iliac crest. They proposed
equations where dependent variable was body part mass or radius of
center of mass and independent variables were whole body mass and
dimensions of body parts.
Main indirect approaches with live subjects
Zatsiorsky & Seluyanov10 used gamma scanning for obtaining
inertial data. They obtained mass, radius of mass and moment of
inertia of 100 live subjects. They were mostly students of physical
education major. Zatsiorsky and Seluyanov divided the trunk into
three parts with planes perpendicular to the longitudinal axis. Erdmann
and Gos obtained densities of 50 trunk tissues.11 Then, Erdmann used
computerized tomography in order to obtain geometric and inertial
data of the male trunk.1,2 On the picture of trunk layers he differentiated
tissues belonging to separate trunk parts: pelvis, abdomen, thorax, two
shoulders. Having volumes of tissues Erdmann presented equations
for obtaining volume of unchangeable tissues together (bones, lungs,
liver, circulation tissues, visceral tissues) of a new subject. Changeable
MOJ App Bio Biomech. 2018;2(2):144‒148. 144
© 2018 Erdmann.This is an open access article distributed under the terms of the Creative Commons Attribution License, which
permits unrestricted use, distribution, and build upon your work non-commercially.
Center of mass of the human body helps in analysis
of balance and movement
Volume 2 Issue 2 - 2018
Erdmann WS
Department of Biomechanics and Sport Engineering, J Sniadecki
University of Physical Education and Sport, Poland
Correspondence: Erdmann WS, Department of Biomechanics
and Sport Engineering, J Sniadecki University of Physical
Education and Sport, Gdansk, 80-336, Poland,
Email werd@awf.gda.pl
Received: March 22, 2018 | Published: April 18, 2018
Abstract
The paper presents a center of mass as an imaginational point which helps in analysis
of different human body configurations, both in static and movement conditions. To
maintain a balance one need in static condition to keep projection of center of mass
above an area of equilibrium while during a movement a resultant force of gravity and
centrifugal force need to go through the area of equilibrium. Center of mass helps in
drawing an angle of equilibrium. During a movement one can use center of mass as
a point which substitutes the whole body in description of sinusoidal locomotion of
the human body in vertical and horizontal planes. Main direct and indirect methods of
localization of human body center of mass were given. Also applications of knowledge
on location of center of mass were presented.
Keywords: human body, center of mass, balance, statics, movement
MOJ Applied Bionics and Biomechanics
Review Article Open Access
Center of mass of the human body helps in analysis of balance and movement 145
Copyright:
©2018 Erdmann
Citation: Erdmann WS. Center of mass of the human body helps in analysis of balance and movement. MOJ App Bio Biomech. 2018;2(2):144‒148.
DOI: 10.15406/mojabb.2018.02.00057
tissues (skin and fat) has to be obtained by direct measurement of
skin-fat folds in few places and then regression equations are used for
obtaining volume of fat tissues and of the skin for separate trunk parts.
Then muscle tissue is obtained by subtracting from the whole volume
of body parts volume of unchangeable tissues and skin and fat tissue.
During the investigation a subject is photographed from two sides or
a laser scanner is used in order to obtain volume of trunk layers and
then trunk parts. Inertial data of extremities are still obtained using a
Clauser et al.9 approach. When comparing above indirect method with
direct (Du Bois Reymond) method the outcome was almost identical.
For the whole body mass Pearson coefcient r=0.998, for the radius
of center of mass from the soles r=0.995.12 Other researchers used
for obtaining inertial segment parameters nuclear magnetic resonance
imaging, e.g. Martin et al.13 and dual energy X-ray absorptiometry
(DEXA) imaging, e.g. Durkin & Dowling.14
Localization of the whole body center of mass
Mass of body parts and location of its centers of mass
Based on data gathered by several authors relative mass (in %)
of body parts for untrained adult males (but not overweight) is as
follows: head 5, neck 3, thorax 11, abdomen 16, pelvis 11, shoulder
5, arm 3, forearm 2, hand 1, thigh 10, shank 4, foot 2. Trained males
and those with longer lower extremities have usually higher data of
mass of thigh (11) and shank (5) and less mass of shoulder 4, abdomen
14. According to Erdmann’s data1,2 when the length of a trunk, i.e.
distance between base of a neck (cervicale) and a line connecting hip
joints, could be presented as 100%, so location of centers of mass of
trunk parts is as follows: pelvis 7% from the hips, abdomen 40% from
the hip, thorax 28% from the base of a neck. A mass of a shoulder is
obtained as follows: a) a level at a distance of 35 % from a base of a
neck is obtained; b) in sagittal plane an auxiliary point is drawn 35 %
from the back where 100% is an antero-posterior distance; in frontal
plane at the same 35% distance from a base of a neck a line is drawn
to the side of a trunk, then along this half-trunk distance an auxiliary
point is drawn 41% from the trunk’s center; c) from the auxiliary point
a line is drawn to the arm axis and then on this line center of mass
of a shoulder is drawn 49% from arm axis. For parts of extremities
a length of a part is acquired as 100%. According to Clauser et al.9
location of center of mass for thigh, shank, forearm is 43% from the
proximal end, for an arm and foot there is 44%. For a hand there is
37% from the wrist when extended and 51% when exed in proximal
interphalangeal joints.
Finding common centers of mass
When masses and location of centers of mass of body parts are
obtained one can use one of two methods in obtaining location of center
of mass of the whole body. The rst one is sum of masses (graphical)
method, the other is sum of moments of masses (analytical) method.
For the rst method data on two adding masses and distance between
them should be taken into account. For example common center of
mass of foot and shank can be obtained by connecting centers of
mass of foot and shank. The common center of mass will lie on a line
connecting these two centers of mass. Comparison of values of adding
masses gives information on location of common center of mass from
the center of mass of a shank. Here, mass of a lighter part is divided by
sum of added masses and then multiplied by the distance between two
masses. Using this approach one can obtain further common centers
of mass up to the center of mass of the whole body. For the second
method a reference system is used drawn near the centers of mass of
two body parts. Then distances are measured between centers of mass
and the reference system (for both axes). Next, masses are multiplied
by distances separately for both axes. Thus moments of mass are
obtained. These moments are summed and the result is divided by
sum of masses. This gives a distance of common center of body parts
from the reference system. For the whole body center of mass one
need to make projection onto the reference system of all centers of
mass of body parts. The sum of moments of masses method is used for
computerized approach where instead of centers of mass a position of
joints is given for computer program. Next, all necessary calculations
are performed by a computer program.
Application of knowledge on location of
center of mass
Static positions
Taking into account mechanical explanation of conservation of
balance, a body with greater mass which has larger base and has lower
position of center of mass can better maintain balance when is pulled
or pushed. As an example there is a position of a coach helping a
novice gymnast in executing an exercise. A coach acquires a position
with feet far apart and much lowering his or her body. In order to draw
an equilibrium angle lines are drawn from the center of mass to the
edges of feet. A very good balance maintains also very young baby
during a squat position (Figure 1). This gives high value of equilibrium
angle (yellow). Trunk is maintained in vertical position. Taking into
account feet touching the ground one can draw a line around two
feet. The area between the feet including area below the feet is called
area of equilibrium. A toddler moves touching all four extremities to
the ground, usually hands and knees. In this situation its equilibrium
status is very good. In static condition when projection of center of
mass moves outside area of equilibrium a person falls down. Some
people sitting on a chair make balancing movements forward and
backward. This is dangerous situation. Projection of center of mass is
near the edge of area of equilibrium. Here the situation happens when
projection of center of mass can go outside this area and a person falls
down to the rear. Often a head and neck is injured (Figure 2).
Figure 1 Correct position for maintaining balance of a coach (A) and of a small
baby which was not taught to assume this position (B): feet far apart (orange
arrow), low position of center of mass by exion of hip and knee joints.
Locostationary movement
In judo ghting competitors during an attack have their centers of
mass in different locations. An attacker (tori) should have his center
of mass lower comparing to location of center of mass of the defender
(uke). This is because tori should get below uke’s body and from that
position to lift his own body and uke’s body in order to execute a
throw. Centers of mass help to draw: a) angle of equilibrium, and b)
angle of attack (Figure 3). In a sport of weightlifting common center
of mass of a competitor and of a barrel is high above the ground.
Center of mass of the human body helps in analysis of balance and movement 146
Copyright:
©2018 Erdmann
Citation: Erdmann WS. Center of mass of the human body helps in analysis of balance and movement. MOJ App Bio Biomech. 2018;2(2):144‒148.
DOI: 10.15406/mojabb.2018.02.00057
A barrel can be twice as much of mass comparing to sportsperson’s
mass. In order to maintain balance a sportsperson during lifting a
barrel moves his or her lower extremities forward and backward.
Calculation of vertical mechanical work (weight multiplied by
vertical displacement) takes into account separately displacement of
center of mass of a sportsperson and of a barrel. Then these two works
are added giving the total work done by the weightlifter.15
Figure 2 Some people sitting on a chair (A) make balance movements forward
and backward (B). When not well controlled an accident happens. It is not
recommended to perform such movements.
Figure 3 In judo attacking competitor during the preparatory move (A)
should maintain balance position with feet far apart (orange arrow) obtaining
substantial equilibrium angle (yellow) and just before the throw should lower
his body and get below opponent’s body (B) obtaining substantial attacking
angle (red); black vertical vectors – gravity force, black oblique vectors –
activity of muscle force.15
Locomotion
During walking a vertical projection on the ground of body center
of mass is presented often together with center of pressure (COP).
These two points draw during straight walking a sinusoidal line
(in mediolateral direction) with higher amplitude of COP. During
walking or running COP jumps from one foot to another, while
center of mass keeps a space between two feet. If a person would
accidentally stop he or she would fall down. Sinusoidal track of center
of mass is present also in vertical dimension. It is usually fewcm.16 But
when disabled person is taken into account where he or she suffered
disability in lower extremities and walks very slowly, even about
0.5m/s (during normal walking velocity of about 1.5 m/s is achieved)
vertical oscillation of center of mass is very small, about 1-2cm and
mediolateral oscillation is about 6cm.17 When dash running is taken
into account vertical oscillation of center of mass for sprint running
is about 10cm and for long distance running just few cm. For hurdle
running center of mass is raised about 40cm above the obstacle. When
lower raising of center of mass exists then less energy is needed for
clearing the obstacle. Similarly is in high jump and especially in pole
vault. When a body is substantially curved over the bar and upper
extremities are over the head then while a body clears over the bar a
center of mass can go near or a little bit below the bar. But here a body
needs to go very close to the bar. Some people say that during a high
jump when a body is well curved center of mass goes deep below the
bar. But Kowalczyk18 in his dissertation proved this is untrue. Among
30 high jumpers of international level investigated only once center
of mass went a little bit below the bar because a jumper hit the bar. It
did not fell down and a jump was accepted. In specic situations like
narrow mountain track, or in the case of disease of osteo-muscular or
nervous system, using additional equipment like sticks or crutches is
very helpful. For analysis of those kinds of locomotion center of mass
is used for drawing of angles of equilibrium and for comparison of
them without and with using special equipment (Figure 4). During
the movement along the curve projection of center of mass can go
beyond area of equilibrium. This happens during sprint running,
bicycle riding, alpine skiing when competitor makes a turn. In this
situation centrifugal force can be of high amount and a runner or rider
can lean his or her body to the side. Resultant force of gravity force
and centrifugal force should be directed to the place where the body
or equipment touches the ground.
Figure 4 Increase of angle of equilibrium (about threefold) by using sticks (A)
or crutches (B) with its ends far apart (orange arrow).
Center of mass of the human body or its parts is also used in
engineering design of transport vehicles: a) of land vehicles–for driver
and passengers, b) boats, especially sailing boats, where counter-
ballast of the crew is important factor for maintaining balance, c)
airplanes, where especially for gliders or small airplanes with one
or two pilots problem of equilibrium is important. After a design is
proposed then there are several investigations on safety problems.
Displacement of center of mass is taken into account to track the
movement of crucial body parts (Figure 5).
Figure 5 Model of the human head and neck during car crash tests. Figure
based on photograph presented by Hodgson .19
Center of mass of the human body helps in analysis of balance and movement 147
Copyright:
©2018 Erdmann
Citation: Erdmann WS. Center of mass of the human body helps in analysis of balance and movement. MOJ App Bio Biomech. 2018;2(2):144‒148.
DOI: 10.15406/mojabb.2018.02.00057
Discussion
Analysis of the human body is difcult since it is of irregular shape
and is constantly changing its conguration. One of the solutions to
this problem can be center of mass. Center of mass is one of the main
problems of biomechanics and locomotion. It helps during modelling
of the human body and its activity. This point helps in assessment of
the technique of static positions and different kinds of movement. It
also helps in calculation of work done during lifting. There are several
approaches to localization of center of mass. In some situations one
can use laboratory approach with the reaction board on which a
subject can lie and direct localization of the body center of mass can
be obtained. But this needs time and wearing off subject’s clothes.
Also this is only for one, regular conguration of the body. For other
congurations, especially during movement, one can use different
methods. The most convenient method for different tasks and not
disturbing a subject (who can be a sportsperson performing movement
at the stadium) is taking an image of a subject and then localization
of center of mass using one of the indirect methods. Location of
center of mass depends on body build and body proportions. Within
sportspeople those who train football (soccer), cycling, horizontal
jumping have more muscles at lower extremities. They have relative
location of center of mass lower. Sportspeople who train gymnastics,
ghting sports, athletic throwing has more developed upper body
part. They have relatively higher location of center of mass. Women
because of more developed lower girdle have center of mass located
relatively lower. Zhao et al20 reported research results of previous
works21,22 on differences of lower extremities’ length among ethnic
groups with African-American having longer legs than Caucasians
and Asians having shorter legs than Caucasians. In young people
lower extremities have more muscles than adipose tissue, so location
of center of mass of young black people is lower comparing with
representatives of other ethnic groups.
Virmavirta & Isolehto23 compared localization of center of mass
using three different approaches: 1) direct method with reaction
board, 2) using Dempster’s data, 3) Zatsiorsky and Seluyanov’s data
adjusted by de Leva.24 De Leva calculated locations of body parts’
centers of mass from according to anthropological landmarks to
according to joints’ axes. Virmavirta and Isolehto observed signicant
differences in location of center of mass within 1 %. Dempster’s
data overestimated data from reaction board, while Zatsiorsky and
Seluyanov’s data underestimated data of reaction board. The reason
of above discrepancies was Virmavirta and Isolehto used generalized
data of Dempster and Zatsiorsky and Seluyanov instead of individual
data approach as proposed by Clauser,9 Erdmann,2 Erdmann &
Kowalczyk.12 Localization of center of mass while standing with
asymmetrical load attached to the body is not a difcult task. Wu
& McLeod25 investigated subjects who moved whole body center
of mass from the center between two feet only half of the distance
predicted theoretically. This was investigated for different positions
of feet (narrow, medium, wide) and for different loads (10 and 30%
of body mass). But intuitive localization of center of mass of objects
with irregular, asymmetrical shape shown on the screen is not an easy
task. Baud-Bovy & Soechting26 presented results of investigations of
subjects who were asked to point center of mass of different two-
dimensional objects of different shapes shown on a screen. They
concluded that participants tended to locate the center of mass at the
center of inscribed circle inside an object instead of the true center of
mass.
Conclusion
Unfortunately, localization of center of mass is not easy. It can be
computerized but still often needs input on human joints, some end
parts like head or hands, and trunk specic points. There are inertial
measurement units (IMU) mounted on human body that can give data
on positions of joints automatically. These units are costly and they
must be mounted on subject’s body. So, the best option is using images
of the human body. Taking into account experience of the author in
teaching localization of center of mass on a photograph of the body
it is difcult task for about a half of university students of physical
education major. This should be taught with simple explanations, with
several gures, examples, etc. In this way for example a textbook on
biomechanics for students of biomedical engineering was published.3
Acknowledgement
None.
Conict of interest
The authors declare, that there is no conict of interest.
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