em26 rigidbodykinematics...
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Engineering Mechanics
Engineering Mechanics
L26: Rigid body Kinematics: Relative Acceleration
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Indian Institute of Technology Jodhpur
Engineering Mechanics
We can define a unique reference point which momentarily has zero velocity. The axis , normal to the plane of motion, passing through this point is called the instantaneous axis of zero velocity, Intersection of this axis with the plane of motion is known as the instantaneous center of zero velocity.The instantaneous center need not be a fixed point in the body or a fixed point in the plane.
INSTANTANEOUS CENTER OF ZERO VELOCITY
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Engineering Mechanics
Linear Velocity
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!" = $ × &"
!" is normal to &"!" is normal to$
·
w
OA
rA
!"
B
rB!' !' = $ × &'
!' is normal to &'!' is normal to$
Engineering Mechanics
INSTANTANEOUS CENTER OF ZERO VELOCITY
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C
A
BrA
vA vAA
vB
A vA
C
rD
C
ω = #$%$
#& = %'ω
BvB
rA
rBBvB
Parallel VelocitiesNon parallel Velocities
ω = ()*)= (+
*+
Once the instantaneous center is located, the direction of the instantaneous velocity of every point in the body is readily found since it must be perpendicular to the radial line joining the point in question with C.
D
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Engineering Mechanics
Example 2
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Engineering Mechanics
Body extended
Example 2
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A
O¢
D B
vB
45°
O
C
14²
15.23²
14 2²
AvDv
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Engineering Mechanics
Fixed axis rotation: Velocity and Acceleration
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! = # × %
& = #× #× % + ( × %
)&* = # × (# × %&, = ( × %
& = &* + &,
Engineering Mechanics
Relative acceleration analysis
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!" = !$ + !"/$ !"/$ = '×)
*" = *$ + *"/$
*+ = *, + *"/$- + *"/$.
*//0 = ' × ' × ) + 1 × )
2*"/$- = ' × (' × )
*"/$. = 1 × )
4"/$- = 5 67 = 89"/$75
4"/$. = 5 α = 9̇ ⁄" $
where
where
where
9"/$ = 56
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Engineering Mechanics
Relative acceleration analysis
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A
B
aB
aB
(aA/B)t aA/B
aA
A
B
t
a
(aA/B)t
(aA/B)nw
aA/B
n
A
BPathofA
PathofB
=r
aA
aB
+
(aA/B)naB
Engineering Mechanics
Example 1
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Engineering Mechanics
Example 1
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Engineering Mechanics
Example 1
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substitute these the relative-acceleration equation and equate separately the coeffi cients of the i-terms and the coefficients of the j-terms to give
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Engineering Mechanics
GRAPHICAL Acceleration ANALYSIS
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Engineering Mechanics 14
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Thanking you15
References :
Engineering Mechanics
Slider Crank
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