Figure 1 shows a pumpjack operating at an oil well. Its representation as a linkage is also shown in Figure 1. The pumpjack is driven by a motor attached to crank OA. A constant torque T' is applied to the crank and the crank rotates at a constant angular velocity wOA. A force P is applied vertically downwards at the end of the walking beam BD, which has its centre of mass at point G. To design the mechanism, a careful kinematic analysis of the mechanism needs to be conducted. To avoid mechanical failure and to provide adequate support to the mechanism, the engineer needs to analyse the reaction forces in the joints. Masses of links OA and AB are assumed to be smaller in comparison with the mass of BD and are ignored in the analysis. Magnitude of force P is equal to 10 kN and it is directed vertically upwards. At the instant shown, perform the following tasks using the individual values of lengths OA, AB, BC, OE, CE, L, H, angle ß, angular velocity wOA, mass mBD, and moment of inertia JBD. Length of the walking beam BD is equal to 2-BC. Distance CG from point C to the centre of mass of the walking BC beam is equal to
Figure 1 shows a pumpjack operating at an oil well. Its representation as a linkage is also shown in Figure 1. The pumpjack is driven by a motor attached to crank OA. A constant torque T' is applied to the crank and the crank rotates at a constant angular velocity wOA. A force P is applied vertically downwards at the end of the walking beam BD, which has its centre of mass at point G. To design the mechanism, a careful kinematic analysis of the mechanism needs to be conducted. To avoid mechanical failure and to provide adequate support to the mechanism, the engineer needs to analyse the reaction forces in the joints. Masses of links OA and AB are assumed to be smaller in comparison with the mass of BD and are ignored in the analysis. Magnitude of force P is equal to 10 kN and it is directed vertically upwards. At the instant shown, perform the following tasks using the individual values of lengths OA, AB, BC, OE, CE, L, H, angle ß, angular velocity wOA, mass mBD, and moment of inertia JBD. Length of the walking beam BD is equal to 2-BC. Distance CG from point C to the centre of mass of the walking BC beam is equal to
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
(Repost) Dynamic force analysis for linkage
![OA
0.90
CG
Length
[m]
3.25 2.75 5.50 0.55 1.85
AB
BC
BD
2. Velocity Analysis
OE
CE
2.20 2.581 3.15
Present a clearly labelled velocity diagram;
4. Dynamic Forces Analysis
• Calculate the magnitude and direction of:
o velocity of point A;
o velocity of point B.
• Calculate angular velocities of links AB and BC.
H
3. Acceleration Analysis
• Present a clearly labelled acceleration diagram;
Calculate the magnitudes and directions of:
o acceleration of points A and B;
o angular acceleration of links AB and BC;
o accelerations of points G.
B
WOA
[deg] [rad/s]
1. Geometry Calculations
Using the given geometrical parameters above, calculate angles and Y, distance OC and any
other required angles and distances.
160.0 3.0
M BD
Mass
[kg]
3000
J BD
Mass moment of
inertia
[kg.m²]
2200
Present a clearly labelled free body diagram for each rod and the slider;
• Calculate the magnitudes and directions of all reaction forces at the instant shown using
accelerations obtained in acceleration analysis part;
Calculate the instantaneous torque, T, required to drive the mechanism at the instant
shown.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe06819f9-dae6-4bd0-9585-26daba0604c4%2F825358d1-1ece-4aac-9bf6-4f63dd79646a%2Fv5vafv5_processed.png&w=3840&q=75)
Transcribed Image Text:OA
0.90
CG
Length
[m]
3.25 2.75 5.50 0.55 1.85
AB
BC
BD
2. Velocity Analysis
OE
CE
2.20 2.581 3.15
Present a clearly labelled velocity diagram;
4. Dynamic Forces Analysis
• Calculate the magnitude and direction of:
o velocity of point A;
o velocity of point B.
• Calculate angular velocities of links AB and BC.
H
3. Acceleration Analysis
• Present a clearly labelled acceleration diagram;
Calculate the magnitudes and directions of:
o acceleration of points A and B;
o angular acceleration of links AB and BC;
o accelerations of points G.
B
WOA
[deg] [rad/s]
1. Geometry Calculations
Using the given geometrical parameters above, calculate angles and Y, distance OC and any
other required angles and distances.
160.0 3.0
M BD
Mass
[kg]
3000
J BD
Mass moment of
inertia
[kg.m²]
2200
Present a clearly labelled free body diagram for each rod and the slider;
• Calculate the magnitudes and directions of all reaction forces at the instant shown using
accelerations obtained in acceleration analysis part;
Calculate the instantaneous torque, T, required to drive the mechanism at the instant
shown.
Transcribed Image Text:conduct a full kinematic analysis and calculate dynamic reaction forces in a linkage
mechanism, calculate instantaneous torque, required to drive the mechanism
470
Figure 1. Left: An operating pumpjack
linkage mechanism.
D
G
E
A
Φ
B
B
T
H
WOA
Right: A mechanical
Figure 1 shows a pumpjack operating at an oil well. Its representation as a linkage is
also shown in Figure 1. The pumpjack is driven by a motor attached to crank OA. A constant torque
T' is applied to the crank and the crank rotates at a constant angular velocity wOA. A force P is applied
vertically downwards at the end of the walking beam BD, which has its centre of mass at point G.
To design the mechanism, a careful kinematic analysis of the mechanism needs to be
conducted. To avoid mechanical failure and to provide adequate support to the mechanism, the
engineer needs to analyse the reaction forces in the joints. Masses of links OA and AB are assumed
to be smaller in comparison with the mass of BD and are ignored in the analysis. Magnitude of force
P is equal to 10 kN and it is directed vertically upwards.
At the instant shown, perform the following tasks using the individual values of lengths OA, AB, BC,
OE, CE, L, H, angle ß, angular velocity wOA, mass mBD, and moment of inertia JBD. Length of the
walking beam BD is equal to 2-BC. Distance CG from point C to the centre of mass of the walking
BC
beam is equal to
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Follow-up Question
Apologies but unsure how values for Vb (2.64) and the other value 4.08 were actually calculated from the velocity diagram
Transcribed Image Text:conduct a full kinematic analysis and calculate dynamic reaction forces in a linkage
mechanism, calculate instantaneous torque, required to drive the mechanism
470
Figure 1. Left: An operating pumpjack
linkage mechanism.
D
G
E
A
Φ
B
B
T
H
WOA
Right: A mechanical
Figure 1 shows a pumpjack operating at an oil well. Its representation as a linkage is
also shown in Figure 1. The pumpjack is driven by a motor attached to crank OA. A constant torque
T' is applied to the crank and the crank rotates at a constant angular velocity wOA. A force P is applied
vertically downwards at the end of the walking beam BD, which has its centre of mass at point G.
To design the mechanism, a careful kinematic analysis of the mechanism needs to be
conducted. To avoid mechanical failure and to provide adequate support to the mechanism, the
engineer needs to analyse the reaction forces in the joints. Masses of links OA and AB are assumed
to be smaller in comparison with the mass of BD and are ignored in the analysis. Magnitude of force
P is equal to 10 kN and it is directed vertically upwards.
At the instant shown, perform the following tasks using the individual values of lengths OA, AB, BC,
OE, CE, L, H, angle ß, angular velocity wOA, mass mBD, and moment of inertia JBD. Length of the
walking beam BD is equal to 2-BC. Distance CG from point C to the centre of mass of the walking
BC
beam is equal to
![OA
0.90
CG
Length
[m]
3.25 2.75 5.50 0.55 1.85
AB
BC
BD
2. Velocity Analysis
OE
CE
2.20 2.581 3.15
Present a clearly labelled velocity diagram;
4. Dynamic Forces Analysis
• Calculate the magnitude and direction of:
o velocity of point A;
o velocity of point B.
• Calculate angular velocities of links AB and BC.
H
3. Acceleration Analysis
• Present a clearly labelled acceleration diagram;
Calculate the magnitudes and directions of:
o acceleration of points A and B;
o angular acceleration of links AB and BC;
o accelerations of points G.
B
WOA
[deg] [rad/s]
1. Geometry Calculations
Using the given geometrical parameters above, calculate angles and Y, distance OC and any
other required angles and distances.
160.0 3.0
M BD
Mass
[kg]
3000
J BD
Mass moment of
inertia
[kg.m²]
2200
Present a clearly labelled free body diagram for each rod and the slider;
• Calculate the magnitudes and directions of all reaction forces at the instant shown using
accelerations obtained in acceleration analysis part;
Calculate the instantaneous torque, T, required to drive the mechanism at the instant
shown.](https://content.bartleby.com/qna-images/question/e06819f9-dae6-4bd0-9585-26daba0604c4/12ba5bfe-6ad0-4520-8d1a-6ec0b965fe65/o8cyttl_processed.png)
Transcribed Image Text:OA
0.90
CG
Length
[m]
3.25 2.75 5.50 0.55 1.85
AB
BC
BD
2. Velocity Analysis
OE
CE
2.20 2.581 3.15
Present a clearly labelled velocity diagram;
4. Dynamic Forces Analysis
• Calculate the magnitude and direction of:
o velocity of point A;
o velocity of point B.
• Calculate angular velocities of links AB and BC.
H
3. Acceleration Analysis
• Present a clearly labelled acceleration diagram;
Calculate the magnitudes and directions of:
o acceleration of points A and B;
o angular acceleration of links AB and BC;
o accelerations of points G.
B
WOA
[deg] [rad/s]
1. Geometry Calculations
Using the given geometrical parameters above, calculate angles and Y, distance OC and any
other required angles and distances.
160.0 3.0
M BD
Mass
[kg]
3000
J BD
Mass moment of
inertia
[kg.m²]
2200
Present a clearly labelled free body diagram for each rod and the slider;
• Calculate the magnitudes and directions of all reaction forces at the instant shown using
accelerations obtained in acceleration analysis part;
Calculate the instantaneous torque, T, required to drive the mechanism at the instant
shown.
Solution
by Bartleby ExpertFollow-up Question
Confused where the value 2.64 came for vb. You say vb equals 2.64 but also 4.08
Solution
by Bartleby ExpertKnowledge Booster
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