Structural Analysis
Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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Use Instantaneous Center of Zero Rotation Method 

### Problem 16-87 The mechanism shown is used in a riveting machine. It consists of a driving piston \( A \), three members, and a riveter which is attached to the slider block \( D \). Determine the velocity of \( D \) at the instant shown, when the piston at \( A \) is traveling at \( v_A = 30 \, \text{m/s} \). #### Diagram Description: - **Components**: - **Piston \( A \)**: The driving element moving with a velocity \( v_A = 30 \, \text{m/s} \). - **Members \( B \), \( C \)**, and connecting linkages forming an articulated mechanism. - **Slider Block \( D \)**: The point where the velocity needs to be determined. - **Dimensions**: - The distance from the pivot at \( B \) to point \( C \) is \( 200 \, \text{mm} \). - The distance from point \( C \) to the end of the piston \( A \) is \( 300 \, \text{mm} \). - Another segment from point \( C \) to \( D \) measures \( 150 \, \text{mm} \). - **Angles**: - Angle at \( C \) connected to \( A \) is \( 45^\circ \). - The angle between the member connected from \( B \) to \( C \) is \( 60^\circ \). - An additional angle for the piston trajectory below horizontal at \( A \) is \( 30^\circ \). - **Motion**: - The diagram shows the path of motion and velocity vector \( v_A \) for piston \( A \) pointing left. This setup indicates a typical kinematic analysis problem involving linkages and relative motion between connected components. The goal is to compute the linear velocity of the slider block \( D \).
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Transcribed Image Text:### Problem 16-87 The mechanism shown is used in a riveting machine. It consists of a driving piston \( A \), three members, and a riveter which is attached to the slider block \( D \). Determine the velocity of \( D \) at the instant shown, when the piston at \( A \) is traveling at \( v_A = 30 \, \text{m/s} \). #### Diagram Description: - **Components**: - **Piston \( A \)**: The driving element moving with a velocity \( v_A = 30 \, \text{m/s} \). - **Members \( B \), \( C \)**, and connecting linkages forming an articulated mechanism. - **Slider Block \( D \)**: The point where the velocity needs to be determined. - **Dimensions**: - The distance from the pivot at \( B \) to point \( C \) is \( 200 \, \text{mm} \). - The distance from point \( C \) to the end of the piston \( A \) is \( 300 \, \text{mm} \). - Another segment from point \( C \) to \( D \) measures \( 150 \, \text{mm} \). - **Angles**: - Angle at \( C \) connected to \( A \) is \( 45^\circ \). - The angle between the member connected from \( B \) to \( C \) is \( 60^\circ \). - An additional angle for the piston trajectory below horizontal at \( A \) is \( 30^\circ \). - **Motion**: - The diagram shows the path of motion and velocity vector \( v_A \) for piston \( A \) pointing left. This setup indicates a typical kinematic analysis problem involving linkages and relative motion between connected components. The goal is to compute the linear velocity of the slider block \( D \).
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