The figure below shows a pin-jointed four-bar mechanism. The input link (EC) has a constant angular velocity of 15 rad/s CCW. (DB) is the output link and (CB) is the coupler link. At the instant shown: a) Draw the vector loop of the mechanism b) If 0: 85, prove that the input angle in (X,Y) the global coordinate system is 02, global = 10.52' c) Determine the angular velocity of output link (DB) and coupler link (CB). d) Determine the absolute velocity of point A in cartesian form (also find its magnitude and direction); if 8=15.8° and CA = a = 1.84 m. Y' 0.9 m 0.5 m C 03 0.6 m 0.25 m B 2.1 m D- B 04 2.0 m X Position, Velocity and Acceleration Analysis: Pin-jointed Fourbar linkage VBA R3 R4 R2 004 d R1 -B±√B²-4AC 041,2 = 2arctan 2A Position Analysis VBA (-E±√√E²-4DF 031.2 = 2arctan 2D A = cos 2-K₁ - K₂cos02 + K3 B = -2sin02 C K₁ (K₂+ 1)cos02 + K3 - D= cose₂-K₁- K₁cos02 + K5 ⚫ E = -2sin02 ⚫F K₁+(K4-1)cos82 + K5 K₁ == K₂ +d2 • K3 2ac d K₁ = • K4 c2-d2-a2-b2 ⚫ K5 2ab PS: if is calculated before you can use one of the equations below to solve for 03 bcos03=-acos02+ ccos04+d bsin03 = −asin02 + csin04 aw2 sin(02-03) 004= c sin(04-03) Velocity Analysis aw2 sin(04-02) 003 = b sin(03-04) Position Velocity and Acceleration Analysis: Slider-Crank Linkage AA R2 AB R3 R₁ ABA R4 ABA x AB AA A Position analysis 031 = arcsin (asin02 b (b) d = acos02-bcos03 asino2 03: =arcsin +π Velocity analysis a cos02 d= =-a02 sine₂+b03 sin03 03 -002 b cose 02 аз Acceleration Analysis aα₂ cosе₂-asin02 +bsin03 bcos03 d=-aa2 sine₂-awcos02 +bα3 sin 03 +bwcose Acceleration Analysis: Inverted Slider-Crank Linkage B AABoriali R₂ b dot AAB R1 X A X α4= aacos(0-0)+sin(03-03)]+co sin(0,-03)-2003 b+ccos(03-04) Jamboos(0-0)+cos(0-0)]+ax[sin(0-0)-csin(04 −0₂)|| - • 26cm, sin(0, −0,)−m;[b² +c² +2bccos(0, −03)] b+ccos(03-04) " k=2 Energy Equation Fk Vk + kk = mak • Vk + Σkαk ·@k k=2 -,。, k=2 k=2
The figure below shows a pin-jointed four-bar mechanism. The input link (EC) has a constant angular velocity of 15 rad/s CCW. (DB) is the output link and (CB) is the coupler link. At the instant shown: a) Draw the vector loop of the mechanism b) If 0: 85, prove that the input angle in (X,Y) the global coordinate system is 02, global = 10.52' c) Determine the angular velocity of output link (DB) and coupler link (CB). d) Determine the absolute velocity of point A in cartesian form (also find its magnitude and direction); if 8=15.8° and CA = a = 1.84 m. Y' 0.9 m 0.5 m C 03 0.6 m 0.25 m B 2.1 m D- B 04 2.0 m X Position, Velocity and Acceleration Analysis: Pin-jointed Fourbar linkage VBA R3 R4 R2 004 d R1 -B±√B²-4AC 041,2 = 2arctan 2A Position Analysis VBA (-E±√√E²-4DF 031.2 = 2arctan 2D A = cos 2-K₁ - K₂cos02 + K3 B = -2sin02 C K₁ (K₂+ 1)cos02 + K3 - D= cose₂-K₁- K₁cos02 + K5 ⚫ E = -2sin02 ⚫F K₁+(K4-1)cos82 + K5 K₁ == K₂ +d2 • K3 2ac d K₁ = • K4 c2-d2-a2-b2 ⚫ K5 2ab PS: if is calculated before you can use one of the equations below to solve for 03 bcos03=-acos02+ ccos04+d bsin03 = −asin02 + csin04 aw2 sin(02-03) 004= c sin(04-03) Velocity Analysis aw2 sin(04-02) 003 = b sin(03-04) Position Velocity and Acceleration Analysis: Slider-Crank Linkage AA R2 AB R3 R₁ ABA R4 ABA x AB AA A Position analysis 031 = arcsin (asin02 b (b) d = acos02-bcos03 asino2 03: =arcsin +π Velocity analysis a cos02 d= =-a02 sine₂+b03 sin03 03 -002 b cose 02 аз Acceleration Analysis aα₂ cosе₂-asin02 +bsin03 bcos03 d=-aa2 sine₂-awcos02 +bα3 sin 03 +bwcose Acceleration Analysis: Inverted Slider-Crank Linkage B AABoriali R₂ b dot AAB R1 X A X α4= aacos(0-0)+sin(03-03)]+co sin(0,-03)-2003 b+ccos(03-04) Jamboos(0-0)+cos(0-0)]+ax[sin(0-0)-csin(04 −0₂)|| - • 26cm, sin(0, −0,)−m;[b² +c² +2bccos(0, −03)] b+ccos(03-04) " k=2 Energy Equation Fk Vk + kk = mak • Vk + Σkαk ·@k k=2 -,。, k=2 k=2
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
pls very urgent using the formulas required
Transcribed Image Text:The figure below shows a pin-jointed four-bar mechanism. The input link (EC) has a constant angular
velocity of 15 rad/s CCW. (DB) is the output link and (CB) is the coupler link. At the instant shown:
a) Draw the vector loop of the mechanism
b) If 0: 85, prove that the input angle in (X,Y) the global coordinate system is 02, global = 10.52'
c) Determine the angular velocity of output link (DB) and coupler link (CB).
d) Determine the absolute velocity of point A in cartesian form (also find its magnitude
and direction); if 8=15.8° and CA = a = 1.84 m.
Y'
0.9 m
0.5 m
C
03
0.6 m
0.25 m
B
2.1 m
D-
B
04
2.0 m
X
Position, Velocity and Acceleration Analysis: Pin-jointed Fourbar linkage
VBA
R3
R4
R2
004
d
R1
-B±√B²-4AC
041,2
= 2arctan
2A
Position Analysis
VBA
(-E±√√E²-4DF
031.2
= 2arctan
2D
A = cos 2-K₁ - K₂cos02 + K3
B = -2sin02
C K₁ (K₂+ 1)cos02 + K3
-
D= cose₂-K₁- K₁cos02 + K5
⚫ E = -2sin02
⚫F K₁+(K4-1)cos82 + K5
K₁ ==
K₂
+d2
• K3
2ac
d
K₁ =
• K4
c2-d2-a2-b2
⚫
K5
2ab
PS: if is calculated before you can use one of the equations below to solve for 03
bcos03=-acos02+ ccos04+d
bsin03 = −asin02 + csin04
aw2 sin(02-03)
004=
c sin(04-03)
Velocity Analysis
aw2
sin(04-02)
003 =
b sin(03-04)
![Position Velocity and Acceleration Analysis: Slider-Crank Linkage
AA
R2
AB
R3
R₁
ABA
R4
ABA
x
AB
AA
A
Position analysis
031
= arcsin
(asin02
b
(b)
d = acos02-bcos03
asino2
03:
=arcsin
+π
Velocity analysis
a cos02
d=
=-a02 sine₂+b03 sin03
03
-002
b cose
02
аз
Acceleration Analysis
aα₂ cosе₂-asin02 +bsin03
bcos03
d=-aa2 sine₂-awcos02 +bα3 sin 03 +bwcose
Acceleration Analysis: Inverted Slider-Crank Linkage
B
AABoriali
R₂
b dot
AAB
R1
X
A
X
α4=
aacos(0-0)+sin(03-03)]+co sin(0,-03)-2003
b+ccos(03-04)
Jamboos(0-0)+cos(0-0)]+ax[sin(0-0)-csin(04 −0₂)||
-
• 26cm, sin(0, −0,)−m;[b² +c² +2bccos(0, −03)]
b+ccos(03-04)
"
k=2
Energy Equation
Fk Vk + kk = mak • Vk + Σkαk ·@k
k=2
-,。,
k=2
k=2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F513839f2-dba8-480f-99ba-a9cdadee07a8%2F67ebcd88-9e0d-4e78-b109-c80782cff900%2Frgc3foy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Position Velocity and Acceleration Analysis: Slider-Crank Linkage
AA
R2
AB
R3
R₁
ABA
R4
ABA
x
AB
AA
A
Position analysis
031
= arcsin
(asin02
b
(b)
d = acos02-bcos03
asino2
03:
=arcsin
+π
Velocity analysis
a cos02
d=
=-a02 sine₂+b03 sin03
03
-002
b cose
02
аз
Acceleration Analysis
aα₂ cosе₂-asin02 +bsin03
bcos03
d=-aa2 sine₂-awcos02 +bα3 sin 03 +bwcose
Acceleration Analysis: Inverted Slider-Crank Linkage
B
AABoriali
R₂
b dot
AAB
R1
X
A
X
α4=
aacos(0-0)+sin(03-03)]+co sin(0,-03)-2003
b+ccos(03-04)
Jamboos(0-0)+cos(0-0)]+ax[sin(0-0)-csin(04 −0₂)||
-
• 26cm, sin(0, −0,)−m;[b² +c² +2bccos(0, −03)]
b+ccos(03-04)
"
k=2
Energy Equation
Fk Vk + kk = mak • Vk + Σkαk ·@k
k=2
-,。,
k=2
k=2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY