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Find the veocities VA, VB, Vbox, and accelerations aд, ag, abox for the mechanism shown below. Link 2 (Line joining O24) is oriented at 60° in the global coordinate system at the instant shown in the figure, and is rotating clockwise with an angular velocity w₂ of 30 rad/sec. (Hint: This is a parallelogram linkage, which exactly duplicates the rotary motion of the driver crank at the driven crank).

Find the veocities VA, VB, Vbox, and accelerations aд, ag, abox for the mechanism shown below. Link 2 (Line joining O24) is oriented at 60° in the global coordinate system at the instant shown in the figure, and is rotating clockwise with an angular velocity w₂ of 30 rad/sec. (Hint: This is a parallelogram linkage, which exactly duplicates the rotary motion of the driver crank at the driven crank).

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Hello, I'm having difficulty undertanding this kinematics equation. A step by step answer would be appreciated. Thank you.

### Analysis of a Parallelogram Linkage Mechanism #### Problem Statement: Find the velocities \( v_A, v_B, v_{\text{box}} \) and accelerations \( a_A, a_B, a_{\text{box}} \) for the mechanism shown below. Link 2 (Line joining \( O_2A \)) is oriented at 60° in the global coordinate system at the instant shown in the figure, and is rotating clockwise with an angular velocity \( \omega_2 \) of 30 rad/sec. (Hint: This is a parallelogram linkage, which exactly duplicates the rotary motion of the driver crank at the driven crank). #### Diagram Description: The given diagram represents a four-bar linkage mechanism known as a parallelogram linkage. Key elements and details include: - Two fixed pivots labeled \( O_2 \) and \( O_4 \). - Link lengths are provided as follows: - \( L_1 = 150 \) - \( L_2 = 30 \) - \( L_3 = 150 \) - \( L_4 = 30 \) - Link 2 (\( O_2A \)) and Link 4 (\( O_4B \)) are equal in length. - Links 1 (\( O_2O_4 \)) and 3 (\( AB \)) are equal in length. - Angles and directions: - Link 2 (\( O_2A \)) is oriented at 60° with the horizontal (X-axis). - The angular velocity \( \omega_2 \) of Link 2 is given as 30 rad/sec in the clockwise direction. - The system displays a parallelogram linkage which ensures the angular velocity and accelerations are mirrored in the driven crank as well. **Coordinate System:** - The global coordinate system includes an X-axis (horizontal) and a Y-axis (vertical). - The box is connected to the linkage via a vertical link extending from point A, replicating the rotary motion into linear motion. #### Solution Requirements: To determine: - Velocities \( v_A \), \( v_B \), and \( v_{\text{box}} \). - Accelerations \( a_A \), \( a_B \), and \( a_{\text{box}} \). **Graphical Analysis:** - Two circles with fixed centers \( O_2 \)
Transcribed Image Text:### Analysis of a Parallelogram Linkage Mechanism #### Problem Statement: Find the velocities \( v_A, v_B, v_{\text{box}} \) and accelerations \( a_A, a_B, a_{\text{box}} \) for the mechanism shown below. Link 2 (Line joining \( O_2A \)) is oriented at 60° in the global coordinate system at the instant shown in the figure, and is rotating clockwise with an angular velocity \( \omega_2 \) of 30 rad/sec. (Hint: This is a parallelogram linkage, which exactly duplicates the rotary motion of the driver crank at the driven crank). #### Diagram Description: The given diagram represents a four-bar linkage mechanism known as a parallelogram linkage. Key elements and details include: - Two fixed pivots labeled \( O_2 \) and \( O_4 \). - Link lengths are provided as follows: - \( L_1 = 150 \) - \( L_2 = 30 \) - \( L_3 = 150 \) - \( L_4 = 30 \) - Link 2 (\( O_2A \)) and Link 4 (\( O_4B \)) are equal in length. - Links 1 (\( O_2O_4 \)) and 3 (\( AB \)) are equal in length. - Angles and directions: - Link 2 (\( O_2A \)) is oriented at 60° with the horizontal (X-axis). - The angular velocity \( \omega_2 \) of Link 2 is given as 30 rad/sec in the clockwise direction. - The system displays a parallelogram linkage which ensures the angular velocity and accelerations are mirrored in the driven crank as well. **Coordinate System:** - The global coordinate system includes an X-axis (horizontal) and a Y-axis (vertical). - The box is connected to the linkage via a vertical link extending from point A, replicating the rotary motion into linear motion. #### Solution Requirements: To determine: - Velocities \( v_A \), \( v_B \), and \( v_{\text{box}} \). - Accelerations \( a_A \), \( a_B \), and \( a_{\text{box}} \). **Graphical Analysis:** - Two circles with fixed centers \( O_2 \)
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