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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.