Chungnam National University 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 motion Rigid body: translational and rotational motion How to describe rigid body motion? Need body fixed reference frame to describe translational and rotational motion.
Transcript
Chungnam National University
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 A=v v
B A=a 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 .dq
q
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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 dtw qa a a q w w= = =
0
20 0
2 20 0
12
2 ( )
c
c
c
t
t t
a
w w a
q q w a
w w q q
= +
= + +
= + -
ddtqw =
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Motion of point P
Position vector
velocity
v rw= ´=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 rw
w
=
= ´ + ´ ´
= +
= ´ -
a α r ω ω ra a a
α r r
Acceleration
Rotation About a Fixed Axis
ta ra=
( )
( )
d d d ddt dt dt dt
a
= = ´ = ´ + ´
= ´ + ´ ´
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 rdt dt
q w
= +
= =
= +
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 tow
===
=
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 A to B
