Transcript Tutorial Introduction to Kinem

ANTROPOMETRIC DATA
Segment Dimensions – Body segment lengths can
be expressed as a fraction of body height, H.
ANTROPOMETRIC DATA
MASS OF SEGMENT
Calculate COM of thigh and foot using
antropometric data.
Coordinates:
Ankle (84.9, 11.0), metatarsal (101.1,1.3),
greater trocanter (72.1, 92.8), lateral
femoral condyle (86.4, 54.9)
COM of thigh and foot
Based on table 3.1, foot COM is 0.5 of the
distance from the lateral malleolus (ankle
to the metatarsal marker. Thus, the center
of mass of the foot is
• x = (84.9 + 101.1) / 2 = 93.0 cm
• y = (11.0 + 1.3) / 2 = 6.15 cm
• The thigh center of mass is 0.433 from the
proximal end of the segment. Thus, the
center of mass of the thigh is
• x = 72.1 + 0.433 (86.4 - 72.1) = 78.3 cm
• y = 92.8 - 0.433 (92.8 - 54.9) - 76.4 cm
CENTRE OF MASS OF MULTI SEGMENT
Xo = (m1x1+ m2x2 + m3x3)/M
The same for Yo.
MASS MOMENT OF INERTIA
Most body segment do not rotate about their mass center, but rather
the joint at either end. The parallel axis theorem is used to calculate
the moment of inertia in such cases.
I = Io + mx2
A Prosthetic leg has a mass of 3 kg and a center
of mass of 20 cm from the knee joint. The radius of
gyration is 14.1 cm. Calculate I about the knee.
Io = 3(0.141)2 kg.m2
I = Io + mx2 = 0.06 + 3 (0.2)2
LINK SEGMENT MODEL
The process in which the reaction
forces and muscle moments are
calculated is known as link segment
modeling.
ANATOMICAL VS LINK SEGMENT MODEL.
Joints are replaced by hinge joints and segments
are replaced by masses and moments of inertia
located at each segment’s centre of mass.
It represents all the forces acting on the total body
system itself.
JOINT REACTION FORCES
In analyzing a segments one at a time, we need to
calculate the reaction between segments.
FBD
BONE-ON-BONE FORCES
Confusion between joint reaction and bone –
on-bone forces.
Bone-on-bone forces: actual forces acting
on the articulating surfaces and include
the effect of muscle activity.
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FREE BODY DIAGRAM OF A
SINGLE SEGMENT
Equations:
1. X direction
2. Y direction
3. About the segment COM
What are the forces acting in X directions (linear
movement) in the single segment in previous slide?
We can assume that Rx1, Rx2 are
acting in the x direction and right
direction is positive. Therefore
the equation is
Rx1-Rx2=max
If everything is in static condition (standing without
movement for example, then
Rx1-Rx2=max=0 or Rx1=Rx2
What are the forces acting in Y directions (linear movement) in the
single segment in previous slide?
We can assume that Ry1, Ry2
and weight are acting in the y
direction and upward direction
is positive. Therefore the
equation is,
Ry1-Ry2-m1g=may
If everything is in static condition
(standing without movement),
then
Ry1-Ry2-m1g=may=0
Rotation at the top joint (point 1).
Top
segment
length: a
Assume that the length of the
segment is a and this segment is
tilting at angle α from vertical.
ΣM=I1ω
M1-M2 - Rx2.a sin α - Ry2 cos α m1g (a/2) cos α = I1 ω
In static condition, the above
equation is equal to 0.
M1-M2 - Rx2.a sin α - Ry2 cos α m1g (a/2) cos α = 0.
α
CALCULATION 1
A person standing on one foot on a force plate. The GRF is
found to act 4cm anterior to the ankle joint. The COM is 6
cm measured horizontally from the ankle joint. The subject
mass is 60 kg and the mass of the foot is 0.9kg.
Draw a free body Diagram of the foot.
Calculate the joint reaction forces and net muscle moment
at ankle.