### Lecture 15 - Relative Motion Analysis

```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
– 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
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.