General Plane Motion
Transcript of General Plane Motion
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GENERAL
PLANE
MOTION
LEARNING OUTCOMES (LO)
a) Explain and apply the relativemotion analysis for thedisplacement in the generalplane motion problems.
b) Explain and apply the relativemotion analysis for velocityinthe general plane motionproblems.
c) Explain and applyInstantaneuos Center of ZeroVelocity in the general plane
motion problems.d) Explain, apply and analyse
the relative motion analysisfor accelerationin the generalplane motion problems.
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What is the General Plane
Motion ?A plane motion which is neither translation
nor a rotation.
However, the general plane motion can
always be considered as the sum oftranslation and rotation.
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Velocity Analysis in GeneralPlane Motion
Absolute and relative velocity in planemotion.
Using Trigonometry Rules
Using Cartesian Elements
Instantaneous centre of zero velocity
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Absolute Relative Velocity inPlane Motion
Any plane motion can be replaced by a translation of an arbitraryreference point Aand a simultaneous rotation about A.
rvrkv ABABAB
ABAB rkvv
ABAB vvv
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ExampleDetermine the angular velocity BCand
velocity VCif for the instant shownmember AB is rotating clockwise with an
angular velocity AB= 4 rad/s
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Instantaneous center of zero
velocity (ICZV) in plane motion.
If the velocity at two points Aand Bare known,
the instantaneous center of rotation lies at theintersection of the perpendiculars to the velocity
vectors through Aand B.
At point C, the velocity was considered to be
zero.
Point C is the Instantaneous Center of Zero
Velocity point.
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Special Cases in using ICZV
method
Case 1
No point ofintersection
Both perpendicularlines to their respectivevelocities are parallel.
=
= 0
Case 2
The line used todetermine I from a pointpasses through the otherpoint
Both velocities are notparallel to each other.
= 0
=
=
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Special Cases in using ICZV
method
Case 3
The line used to determine Ifrom a pointpassed through the other point and bothvelocities are parallel to each other
Usually magnitude of the two velocitiesare known
=
=
Case 4
Wheel /Disc rolling on a surfacewithout slipping
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ExampleDetermine the angular velocity BCand
velocity VCif for the instant shownmember AB is rotating clockwise with an
angular velocity AB= 4 rad/s
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ExampleDetermine the angular velocities BC, AB
and velocity VDif for the instant roller C ismoving horizontally to the right with a
velocity VC= 4 m/s
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Acceleration analysis ingeneral plane motion.
Absolute and relative acceleration ingeneral plane motion.
Analysis of plane motion in term ofparameters (in some cases)
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Absolute and relative acceleration in
general plane motion
Absolute acceleration of a particle of the
slab,ABAB aaa
Relative acceleration associated with rotation
about Aincludes tangential and normal components,
ABa
ABn
AB
ABt
AB
ra
rka
2
2
ra
ra
nAB
tAB
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Example For the instant shown, member AB is
rotating clockwise with an angularvelocity AB= 6 rad/s and angularacceleration AB= 12 rad.s-2. Determine
angular acceleration of member BC, BC,and acceleration of point C, aC.
AB AB
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ExampleA 0.5 m radius disc rolls without slipping with
an angular velocity = 4 rad/s and angularacceleration = 10 rad.s-2 as shown.Determine the angular acceleration of rod
AB and the acceleration of end B.