lecture 15 – relative motion analysis: velocity
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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… Translation Orientation of AB constant Rotation All particles rotate about fixed axis - PowerPoint PPT PresentationTRANSCRIPT
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…
– Translation• Orientation of AB constant
– Rotation • All particles rotate about fixed axis
– General Plane Motion (both)
• Combination of both types of motion
B
A
B
A
B
A
B
Afocus of today!
Kinematics of translation
• Kinematics– Position
– Velocity
– Acceleration
• True for all points in R.B. (follows particle kinematics)
B
AABAB rrr /
AB vv
AB aa
x
y
rB
rA
fixed in the bodySimplified case of our relative motion of particles discussion – this situation same as cars driving side-by-side at same speed example
Relative motion analysis: velocity
• Transl. & Rotation(General Plane Motion)
– Position
– Velocity (time deriv)• Let’s say motion of A is known• We would like to find motion of
B
and (ω is rotation of member about A)
A
B
ABAB rrr /
ABAB vvv /
x
y
rA
rB
dθdrA
drB
drA
rB/A rB/A (new)drB/A
ABAB rv //
why is this?translation rotation
where
Review of cross products
zyx
zyx
BBB
AAA
kji
BA
ˆˆˆ
or
• See Chapter 4 of your statics text for full details
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)