PEMP-AML2506
AML2506 … Biomechanics and Flow Simulation
Day 02A
Kinematic Concepts for Analyzing
Human Motion
Session Speaker
Dr. M. D. Deshpande
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
• Session Objectives
– At the end of this session the delegate would
have understood
• Mechanical-Kinematics Concepts
• Reference positions, planes, and axes associated
with the human body
• Human movement and its analysis
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Session Topics
1. Review of Mechanical-Kinematics Concept
2. Description of the reference positions, planes, and
axes associated with the human body
3. Definition and use of directional terms and joint
movement terminology
gy
4. A plan to conduct an effective qualitative human
movement analysis
5. Identification and description of the uses of
available instrumentation for measuring kinematic
quantities
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematics of a Particle
• A particle is a body that is assumed to have mass
but negligible physical dimensions
dimensions.
– Whenever the dimensions of a body are irrelevant to the
problem then the use of particle mechanics may be
expected to provide accurate results. Typical
applications would be the analysis of the motion of a
spacecraft orbiting the earth
• Rigid-body mechanics which is an approach that
needs to be adopted
p when the dimensions of the
body cannot be neglected
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Linear Motion of a Particle under Variable
Acceleration
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Two-Dimensional Motion of a Particle
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Tangential and Normal Coordinates
Velocity Curvilinear Motion
Velocity•
It is often convenient to describe curvilinear motion using path variables,
i.e., measurements made along the tangent t and normal n to the path.
•
The frame can be pictured as a right-angled bracket moving along with
the particle. The t arm always points in the direction of travel, while the
n arm points towards the centre of curvature. Unit vectors et and en are
shown in the Figure
Figure.
The velocityy vector is
tangential to path
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Acceleration- Curvilinear Motion
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 M.S. Ramaiah School of Advanced Studies - Bangalore
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PEMP-AML2506
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Circular Motion
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 M.S. Ramaiah School of Advanced Studies - Bangalore
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PEMP-AML2506
Polar Coordinates
•
The third option is to locate the particle by the radial distance r
and angular position  with respect to a chosen fixed direction.
•
W choose
We
h
unit
it vectors
t er andd e as shown
h
Velocity
Acceleration
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematics of a Rigid Body
• Rigid bodies are different from particles: rigid bodies
are extended in space, and the connection between
different parts of a rigid body are permanent and
unchanged throughout their motion.
• When
Wh we try to imagine
i
i the
h position
i i off a rigid
i id body,
b d
we may first think of an arbitrary point, a marker
(let’ss call it A),
(let
A) on that body.
body The position and motion
of this chosen point can be described in exactly the
same wayy we used for pparticles,, e.g.
g usingg rectangular
g
or polar coordinates.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
Kinematics of a Rigid Body
PEMP-AML2506
• However, the description is insufficient to describe the
motion of the rigid body, since the body as a whole may
rotate around point A. In order to fix the position of the
body we must specify a direction from point A to another
arbitrarily chosen point on the body, say B. Once the
position of A is fixed, and the direction from A to B is
given as well, position of the rigid body is fully specified.
e.g. a rigid rod connecting two points A and B is a rigid
body.
y
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematics of a Rigid Body
• A rigid body is in plane motion if all point of the body
move parallel to one plane, which is called the plane of
motion We can classify the kinds of plane motion into:
motion.
–
–
–
–
(a) translation (rectilinear)
(b) translation (curvilinear)
(c) rotation (around fixed axis)
(d) general plane motion
• In translation every line in the body remains parallel to its
original position, and no rotation is allowed. The trajectory
of motion is the line traced by a point in the body.
• Translation is rectilinear if this line is straight, and
curvilinear otherwise.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematics of a Rigid Body
• Rotation about a fixed axis is the angular motion
about this axis
axis, when all points on the body
follow concentric circular paths.
p
to picture
p
and understand that all
• It is important
lines on the solid body, even those that do not
pass through the centre, rotate through the same
angle in the same time
• General plane motion of a rigid body is a
combination of translation and rotation.
• The concept of relative motion comes into picture
in order to describe this case.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Rigid Body Rotation
• All lines on a rigid body have the same angular
displacement, the same angular velocity and the
same angular acceleration.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Relative Motion
• Let A and B be two points on the rigid body. We start with
the following vector relation:
Ra = Rb + Ra/b
• Here Ra and Rb represent absolute position vectors of A
and B with respect to some fixed axes, and Ra/b stands for
the relative position vector of A with respect to B
• By differentiating the above equation with respect to time,
we obtain the basis of the relative motion analysis,
y , known
as the relative velocity equation:
Va = Vb + Va/b
• To determine the velocity of A with respect to the fixed
axes (the absolute velocity Va) we represent it as the sum of
the absolute velocity of point B, Vb, and the relative
velocity of point A with respect to point B,
B Va/b
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
•
When the solid body is rotating around a fixed axis with
angular velocity ω, all vectors on that solid body also rotate
with the same angular velocity.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Instantaneous Centre of Rotation
• The point of reference (about which the references
have been made in the previous discussion) is not
always fixed. The reference point will be moving
alongg with the body
y and the coordinate system.
y
The reference point can be taken as centre at a
given instant, that is why the centre is known as
Instantaneous Centre.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
Kinematic Constraints
PEMP-AML2506
• Two or more rigid bodies in space are collectively called a
rigid body system.
• The motion of independent rigid bodies can be hindered with
kinematic constraints.
constraints
• Kinematic constraints are constraints between rigid bodies
that result in the decrease of the degrees of freedom of rigid
b d system.
body
t
• The term kinematic pairs actually refers to kinematic
constraints between rigid bodies.
• The kinematic pairs are divided into lower pairs and higher
pairs, depending on how the two bodies are in contact.
• Surface-contact
Surface contact pairs are called lower pairs.
pairs
• There are two subcategories of lower pairs -- revolute pairs
and prismatic pairs.
• Point-, line-, or curve-contact pairs are called higher pairs.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
Kinematic Constraints
PEMP-AML2506
• There are two kinds of lower pairs in planar
mechanisms: revolute pairs and prismatic pairs.
• A rigid body in a plane has only three independent
motions -- two translational and one rotary -- so
introducing either a revolute pair or a prismatic
pair between two rigid bodies removes two
degrees of freedom.
A planar revolute
pair (R-pair)
A planar prismatic
pair (P-pair)
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematic Constraints
• There are six kinds of lower pairs under the
category of spatial mechanisms. The types are:
spherical
h i l pair,
i plane
l
pair,
i cylindrical
li d i l pair,
i revolute
l
pair, prismatic pair, and screw pair.
• A spherical pair keeps two spherical centres
together. Two rigid bodies connected by this
constraint will be able to rotate relatively around x,
y and z axes, but there will be no relative translation
along any of these axes. Therefore, a spherical pair
removes three degrees of freedom in spatial
mechanism. DOF = 3.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematic Constraints
• A plane pair keeps the surfaces of two rigid
bodies together. To visualize this, imagine a book
lying on a table where is can move in any
direction except off the table. Two rigid bodies
connected byy this kind of pair
p will have two
independent translational motions in the plane,
and a rotary motion around the axis that is
perpendicular to the plane.
plane Therefore,
Therefore a plane pair
removes three degrees of freedom in spatial
mechanism. In our example, the book would not
be able to rise off the table or to rotate into the
table. DOF = 3.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematic Constraints
• A cylindrical pair keeps two axes of two rigid
bodies aligned. Two rigid bodies that are part of
this
hi ki
kind
d off system will
ill have
h
an independent
i d
d
translational motion along the axis and a relative
rotary motion around the axis. Therefore, a
cylindrical pair removes four degrees of freedom
from spatial mechanism. DOF = 2.
A 33-D
D cylindrical
li d i l pair
i (C-pair)
(C i )
Compare with a spatial
revolute pair (R-pair).
(R pair)
Next figure
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematic Constraints
• A Revolute pair keeps the axes of two rigid bodies
together.
g
Two rigid
g bodies constrained byy a
revolute pair have an independent rotary motion
around their common axis. Therefore, a revolute
pair
i removes five
fi degrees
d
off freedom
f d
in
i spatial
i l
mechanism. DOF = 1
A spatial revolute
pair (R-pair)
A planar revolute
pair (R
(R-pair)
pair)
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
Kinematic Constraints
PEMP-AML2506
• A prismatic pair keeps two axes of two rigid
bodies aligned and allows no relative rotation.
Two rigid bodies constrained by this kind of
constraint will be able to have an independent
translational motion along the axis. Therefore, a
prismatic pair removes five degrees of freedom in
spatial
ti l mechanism.
h i
DOF = 1.
1
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematic Constraints
• A screw pair keeps two axes of two rigid bodies
aligned and allows a relative screw motion. Two
rigid bodies constrained by a screw pair of motion
which is a composition of a translational motion
along the axis and a corresponding rotary motion
around the axis. Therefore, a screw pair removes
fi degrees
five
d
off freedom
f d
in
i spatial
ti l mechanism.
h i
DOF = 1.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Gruebler's Equation
F = total degrees of freedom in the mechanism
n = number
b off links
li k (including
(i l di the
th frame)
f
)
l = number of lower pairs (one degree of freedom)
h = number
b off hi
higher
h pairs
i (two
(
degrees
d
off
freedom)
This equation is known as Gruebler
Gruebler'ss Equation
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
Gruebler's Equation
Type of kinematic
pairs (constraints)
n
Number
of links
l
Number
of lower
pairs
(S f
(Surface
s)
h
Number of
higher
pairs
(P i t &
(Points
Lines)
F
Degrees of
freedom (=
Translation
+ Rotation
PEMP-AML2506
Comments on constraints
n =2 (fixed, Bar)
1
2-D Free motion
2
0
0
3 (= 2 + 1)
2
2-D Revolute p
pair
2
1
0
1 ((= 0+ 1))
3
2-D prismatic pair
2
1
0
1 (= 1 + 0)
4
3-D Free motion
3
0
0
6 (= 3 + 3)
n =3 (fixed, Bar, Bar in transverse
direction)
5
3 D spherical
3-D
h i l pair
i
3
1
1
3 (=
( 0 + 3)
S h i l surface,
Spherical
f
Sphere
S h centre
6
3-D plane pair
3
1
1
3 (= 2 + 1)
Planar surface, Line stops rotation
7
3-D cylindrical pair
1
2
2 (= 1 + 1)
Cylindrical surface allows Translation
& Rotation
8
3-D revolute pair
2
1
1 (= 0 + 1)
Translation is blocked n = 1
9
3-D prismatic pair
2
1
1 (= 1 + 0)
Two planar surfaces l = 2 block
rotation
10
3-D screw pair
2
1
1 ((= 0 + 1)
or (= 1 + 0)
Translation & Rotation are coupled
3
3
3
3
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Kinematic Analysis
• Ideas discussed in the context of kinematics of
particles and rigid bodies will now be used in the
analysis of human linkages
j
of kinematic analysis
y of a
• The objective
mechanism is to determine the linear and angular
velocities of the various components of the
mechanism when some part of it is subjected to a
known linear or angular velocity.
p
, Analytical
y
and Computer
p
Based
• Graphical,
Methods are followed for Kinematic Analysis.
Here we use LifeMod and ADAMS software
packages to do the analysis
anal sis
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Example-Kinematic Analysis
Analytical Approach
Find the velocity of C and the angular velocity of link BC in
the
h crankslider
k lid mechanism
h i at the
h instant
i
shown
h
below.
b l
The
Th
crank AB is rotating anti-clockwise with angular velocity ω =
d/dt = 500 rad/s (approx. 4800 rpm).
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 M.S. Ramaiah School of Advanced Studies - Bangalore
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Using the analytical approach, we first write down equations
defining the geometry of the mechanism:
Next, we need to differentiate the expressions for z and cos. The
derivative of the expression for z gives:
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
We are now able to calculate the velocity of point C by inserting
the appropriate values of r, , d  /dt and l into the above
expression (noting that d  /dt is simply the angular velocity of
link AB and therefore equal to 500 rad/s). In this particular case
this leads to the solution
The angular
Th
l velocity
l i off link
li k BC is
i given
i
by
b d/dt.
/d To
T evaluate
l
this expression we differentiate the expression for sin  (above)
to give:
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
If specific
p
values of r,, , d  /dt and l are substituted into the
above expression then this gives a value for the angular velocity
of link BC of 189 rad/s.
In addition to computing the values of linear and angular
velocity for the particular position of the mechanism shown in
the example, the results of the analysis can alsobe used to
determine the kinematics of the mechanism for all values of  .
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Example-Kinematic Analysis
G hi l Approach
Graphical
A
h
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Example-Kinematic Analysis
Solution Using ADAMS
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Anatomical Reference Position
• Erect standing position with all body parts facing
forward considered the starting point for all body
segment movements
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Directional Terms
•
superior: closer to the head
•
inferior: farther away from the head
•
anterior: toward the front of the body
•
posterior: toward the back of the bodyy
p
•
medial: toward the midline of the body
•
lateral: away form the midline of the body
•
proximal: closer to the trunk
•
distal: away from the trunk
•
superficial: toward the surface of the body
•
deep: inside the body away from the surface
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Anatomical Reference Planes
Longitudinal axis
Anteroposterior axis
Medio-lateral axis
Frontal plane
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Anatomical Reference Planes
•
Cardinal Planes: Three imaginary perpendicular reference planes that
divide the body in hlaf by mass
– Sagittal
g
plane
p
– Plane in which forward and backward movements of the bodyy and
body segments occur. It is also known as anteroposterior (AP) plane, divides the
body vertically into left and right halves of equal mass
– Frontal plane – plane in which lateral movements of the body and body segments
occur. It is also known as coronal plane, divides the body vertically into front and
back halves of equal mass
– Transverse plane – Plane in which horizontal body and body segments movement
occur when the body is an erect standing position. It is also known as horizontal
plane, divides the body into top and bottom halves of equal mass
– For an individual standing in anatomical reference position, the three cardinal
planes all intersect at a single point known as the body’s centre of mass or centre of
gravity
•
Although most human movements are not strictly planar, the cardinal planes
provide a useful way to describe movements that are primarily planar
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Sagittal plane movements-Example
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Anatomical Reference Axes
•
Mediolateral axis - around which rotations in the sagittal plane occur.
It is also known as the frontal-horizontal axis, is perpendicular to the
sagittal plane
• Anteroposterior axis - around which rotations in the sagittal plane
occur. It is also known as sagittal horizontal axis and perpendicular to
frontal plane.
• Longitudinal axis - around which rotational movements occur. It is
also known as vertical axis.
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Joint Movement
• All body segments are considered to be at zero degrees at
anatomical reference pposition. Rotation of a body
y segment
g
away from anatomical position is named according to the
direction of motion and measured as the angle between the
body segment
segment’ss position and anatomical position
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Sagittal Plane Movements
• Flexion:
•
Extension:
•
Hyperextension:
•
Dorsiflexion:
•
Plantar flexion:
Flexion
Extension
Dorsiflexion
Hyperextension
Plantar flexion
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Frontal Plane Movements
•Elevation & Depression
•
Abduction & Adduction
•
Lateral flexion
I
i & Eversion
E
i
• Inversion
• Radial & Ulnar deviation
Radial
deviation
Abduction
Ulnar
deviation
Adduction
Lateral flexion
Elevation
Depression
Eversion
Inversion
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 M.S.
M.S. Ramaiah
Ramaiah School
School of
of Advanced
Advanced Studies
Studies -- Bangalore
Bangalore
02A

PEMP-AML2506
Movements in Horizontal Plane
•
Left & Right rotation
•
Medial & Lateral rotation
•
Supination & Pronation
•
Horizontal abduction & adduction
Horizontal
adduction
Horizontal
abduction
Medial
rotation
t ti
Lateral
rotation
Pronation Supination
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Spatial Reference Systems
• Useful for standardizing descriptions of human motion
• Most commonly used is the Cartesian coordinate system
• Human body joint centers are labeled with numerical x
Y
and y coordinates
(x,y) = (3,7)
(0,0)
X
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Qualitative Human Movement Analysis
•
Planning for human movement analysis
•
Performer attire
•
Lighting conditions
•
Background
•
Use of video
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Qualitative Analysis: Conducting
M
Movement
t Analysis
A l i
Identify
Question/Problem
Viewing
g Angle
g
Viewing Distance
Performer Attire
Refine Question
Make Decisions
Use of Video
End Analysis
Communicate
with Performer
Environmental
Modifications
Collect
Observations
Visual
A dit
Auditory
From Performer
Interpret Observations From Other Analysts
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Tools for Measuring Kinematic Quantities
• Videocamera
• Electrogoniometer: is a device
de ice that can be
interfaced to a recorder to provide a graphical
record of the angle present at a joint
• Lights, photocell and Timer are used to measure
movement
ove e velocity
ve oc y
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
Demos
PEMP-AML2506
• Dynamic Human CD - Available in
Windows ((ISBN 0-697-34173-9))
• Further Demos
– Ariel Dynamics Worldwide www.arielnet.com
– Motion Analysis
Corporation www.motionanalysis.com
– SIMI Reality
R li Motion
M i Systems
S
www.simi.com
i i
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Laboratory
• Refer laboratory exercises
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Review
In this session the delegates are taught:
•
•
•
•
•
•
•
Kinematics of a particle
Curvilinear motion
Kinematics of a rigid body
Kinematic constraints
Reference planes and axes associated with the human body
Qualitative human movement analysis
Identification and description of the uses of instrumentation
for measuring kinematic quantities
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A
PEMP-AML2506
Thank you
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 M.S. Ramaiah School of Advanced Studies - Bangalore
02A