lec10 me313 tom
DESCRIPTION
Acceleration AnalysisTRANSCRIPT
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TOM Acceleration Analysis
(WEEK 09)
Course Instructor
Engr. Uzair Khaleeq uz Zaman
400 parts, 30 cm long, 15 cm highused for arithmetic operations (Grant Calculating Machine - 1876)
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Acceleration Rate of change of velocity with respect to time
- Linear:
A = dV / dt
Introduction
- Angular = d / dt
Tangential acceleration:
AtPA = p
Normal / Centripetal acceleration:
AnPA = p2
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Acceleration Difference
/ Relative Acceleration
AP = AA + APA Absolute acceleration of point P is
equal to acceleration of P relative
to A plus acceleration of A relative
to ground
APA = AP - AA
Introduction (contd)
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Motor attached at point O2 Main task is to find rate of change
of output velocities (3 and 4) given:
Value of input variable (2)
Value of input velocity (2)
Rate of change of input velocity (2)
Length of all the links
Need to know values of output variables (3, 4) and output velocities (3 , 4)
Need to perform complete position and velocity analysis(Chapters 4 and 6) before starting.
Analytical Acceleration Analysis
4-bar Pin Jointed linkage
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Analytical Acceleration Analysis (contd)
4-bar Pin Jointed linkage (contd)
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From position analysis:
R2 + R3 R4 + R1 = 0
From velocity analysis:
Analytical Acceleration Analysis (contd)
4-bar Pin Jointed linkage (contd)
Each term contains 2 functions of time and
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Analytical Acceleration Analysis (contd)
4-bar Pin Jointed linkage (contd)
Derivation of 3 and 4 is part of the HOMEWORK
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Ex: Calculate the angular acceleration of Link 4, 4 , when the
input angular acceleration, 2 = 0 rad/s2 , 2 = 1 rad/s and 2
= 30
Analytical Acceleration Analysis (contd)
4-bar Pin Jointed linkage (contd)
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Ex: Calculate the angular acceleration of Link 4, 4 , when the
input angular acceleration, 2 = 0 rad/s2 , 2 = 1 rad/s and 2
= 30
Analytical Acceleration Analysis (contd)
4-bar Pin Jointed linkage (contd)
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Ex: Calculate the angular acceleration of Link 4, 4 , when the input angular acceleration, 2 = 0 rad/s
2 , 2 = 1 rad/s and 2 = 30
Find values of output variables (3, 4) and output velocities (3 ,4) first
Get above values by performing complete position analysis (Chapter 4) and velocity analysis (Chapter 6)
For Open Configuration: From Chapter 4: When 2 = 30 3 = 35.4 and 4 =
84.4 From Chapter 6: When 2 = 30 and 2 = 1 rad/s
3 = -0.54 rad/s and 4 = -0.075 rad/s
Analytical Acceleration Analysis (contd)
4-bar Pin Jointed linkage (contd)
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Analytical Acceleration Analysis (contd)
4-bar Pin Jointed linkage (contd)
Repeat the same steps to obtain values for the Cross Configuration.
Ex: Calculate the angular acceleration of Link 4, 4 , when the input angular
acceleration, 2 = 0 rad/s2 , 2 = 1 rad/s and 2 = 30
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Using a math program (MATLab), we can plot the output
acceleration (4) for all values of the input variable (0 2
360)
For instance when 2= 0 rad/s2 and 2= 1 rad/s:
Analytical Acceleration Analysis (contd)
4-bar Pin Jointed linkage (contd)
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From position analysis:
R2R3R4 R1= 0
From velocity analysis:
Analytical Acceleration Analysis (contd)
4-bar Slider Crank
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Analytical Acceleration Analysis (contd)
4-bar Slider Crank (contd)
Derivation of 3 and d (double
dot) is part of the HOMEWORK
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The Coriolis component will always be present when there is
a slider sliding on a rotating link
It will automatically be accounted for as long as the
differentiation is correctly done.
Analytical Acceleration Analysis (contd)
4-bar Slider Crank Coriolis Acceleration
Rotating and changing length as system moves 2 DOF
2 inputs = and VP, slip
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Analytical Acceleration Analysis (contd)4-bar Slider Crank Coriolis Acceleration (contd)
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From position analysis:
R2R3R4 R1= 0
From velocity analysis:
Analytical Acceleration Analysis (contd)
4-bar Inverted Slider Crank
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Analytical Acceleration Analysis (contd)
4-bar Inverted Slider Crank (contd)
Derivation of 4 and b (double
dot) is part of the HOMEWORK
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Determine accelerations of points on the mechanism, instead of
accelerations of output variables
Can only be done once all output variables, output velocities and output
accelerations are found
Analytical Acceleration Analysis (contd)
Acceleration of a Point on a Linkage
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Analytical Acceleration Analysis (contd)Acceleration of a Point on a Linkage (contd)
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Analytical Acceleration Analysis (contd)Acceleration of a Point on a Linkage (contd)
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Analytical Acceleration Analysis (contd)Acceleration of a Point on a Linkage (contd)
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Analytical Acceleration Analysis (contd)Acceleration of a Point on a Linkage (contd)