Lecture 15 - Relative Motion Analysis

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BNG 202 – Biomechanics II
Lecture 15 – Relative Motion Analysis:
Velocity
Instructor: Sudhir Khetan, Ph.D.
May 3, 2013
Types of rigid body motion
• Kinematically
speaking…
B
– Translation
A
• Orientation of AB
constant
– Rotation
B
B
• All particles rotate
about fixed axis
– General Plane Motion
(both)
• Combination of both
types of motion
A
A
B
focus of today!
A
Kinematics of translation
• Kinematics
– Position
y
B



rB  rA  rB / A
– Velocity


vB  vA
A
rB
rA
– Acceleration
x


aB  aA
• True for all points in R.B.
(follows particle kinematics)
Simplified case of our relative motion of particles
discussion – this situation same as cars driving
side-by-side at same speed example
fixed in the body
Relative motion analysis: velocity
• Transl. & Rotation
(General Plane Motion)
y
rB/A
– Position
B



rB  rA  rB / A
• Let’s say motion of A is known
• We would like to find motion of B



vB  v A  vB / A
where
rotation
why is this?
 

v B / A    rB / A
and (ω is rotation of
member about A)
drA
drB
rA
– Velocity (time deriv)
translation
drA
A
rB
x
dθ
rB/A (new)
drB/A
Review of cross products
• See Chapter 4 of your statics text for full details
 
A  B  Ax
ˆj
kˆ
Ay
Az
Bx
By
Bz
iˆ
or
Example Problem
If the block at C is moving downward at 4 ft/s, determine
the angular velocity of bar AB at the instant shown.
(F16-58, 2 rad/s)
Strategy: In beginning of the solution (“data” section should just be the sketch of
the setup), what other information do we know about the components?
Example Problem
If rod AB slides along the horizontal slot with a velocity of
60 ft/s, determine the angular velocity of link BC at the
instant shown.
(F16-11, 48 rad/s)

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