kinematics of a rigid body -...
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Kinematics of a Rigid Body
Definition of Rigid Body: A system of particles for which the distances between particles remain unchanged.
Kinematics: Study of motion without considering force.
What is the difference between particle motion and rigid body motion?Particle: only translational motionRigid body: translational and rotational motion
How to describe rigid body motion?Need body fixed reference frame to describe translational
and rotational motion.
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Rigid Body Motion
Translational motion
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Rigid Body Motion
Rotational motion General motion = translational + rotational motion
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Rigid Body Motion
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Translation
/B A B A r r r
B Av v
B Aa a
position
velocityacceleration
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Rotation About a Fixed Axis
Angular motion
Angular position: at the instant shown, the angular position of r is defined by the angle , measured between a fixed reference line and r.
Angular displacement: the change in the angular position, which can be measured as a differential .d
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Angular velocity
Rotation About a Fixed Axis
Unit: rad/sec
Angular Acceleration
Constant Angular Acceleration
2
2
d d d ddt dt
0
20 0
2 20 0
12
2 ( )
c
c
c
t
t t
a
dd t
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Motion of point P
Position vector
velocity
v r
v ω r
Rotation About a Fixed Axis
r
ddt
rv ω r
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2
2
( )n
p p
t n
a r
a α r ω ω r
a a a
α r r
Acceleration
Rotation About a Fixed Axis
ta r
( )
( )
d d d ddt dt dt dt
v ω ra ω r r ω
r ω ω r
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Rotation
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Absolute Motion Analysis
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Relative Motion Analysis: Velocity
position
/B A B A r r r
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Displacement
Relative Motion Analysis: Velocity
/B A B Ad d d r r r
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Relative Motion Analysis: VelocityVelocity
/ //
BA
BA
B A
B A B AB A
B A
dd ddt dt dtdr r d r
dt dt
rr r
v v v
/
velocity of Point Bvelocity of the base Point A
" "
BA
BA
B
A
B A
BA
relative velocity of B with respect to AThis relative motion is circular the magnitude is
r and the direction is perpendicular to
vvv
v
r
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Relative Motion Analysis: Velocity
BA
BA
B A
B
A
velocity of Bvelocity of the base Point Aangular velocity of the bodyrelative position vector drawn from Ato B
v v ω r
vvωr
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Relative Motion Analysis: Velocity
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Relative Velocity Example
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Relative Velocity Example
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