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T₂ = ? A E FE= 6000N 140° 0 FB=2000 N O₂A= 100 mm, AB= 250 mm, AE=50 mm, input angle is 40⁰. To keep the mechanism in static equilibrium find required input torque.

T₂ = ? A E FE= 6000N 140° 0 FB=2000 N O₂A= 100 mm, AB= 250 mm, AE=50 mm, input angle is 40⁰. To keep the mechanism in static equilibrium find required input torque.

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
Problem 1.1MA
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**Mechanism Analysis for Static Equilibrium** **Description:** The image depicts a mechanical system aimed at maintaining static equilibrium. The system components and forces are labeled as follows: 1. **Mechanism Setup:** The mechanism consists of a linkage assembly defined by key points and segments: - Point \( O_2 \) is a fixed pivot. - Point \( A \) moves in a circular path around \( O_2 \), forming the link \( O_2A \). - The linkage consists of \( O_2A \), \( AB \), and additional points like \( E \). 2. **Link and Force Details:** - \( O_2A \) has a length of 100 mm. - \( AB \) has a length of 250 mm. - \( AE \) has a length of 50 mm. - The input angle at \( A \) is given as 40 degrees. - External force \( F_E \) acting at point \( A \) is 6000 N. - Reaction force \( F_B \) at point \( B \) is 2000 N directed horizontally towards the right. 3. **Angles and Labels:** - The direction of the applied force \( F_E \) makes an angle of 140 degrees with the horizontal. - The system is divided into numbered segments and elements (1, 2, 3, 4) for clarity in analysis. **Task:** To maintain the mechanism in static equilibrium, determine the required input torque, denoted as \( T_2 \). **Analysis Approach:** 1. **Force Diagram:** - Analyze the forces and moments acting on the system segments. - Calculate the components of forces and their respective moments about the pivots and points of interest. 2. **Torque Calculation:** - Apply the principle of moments to find the required torque \( T_2 \), ensuring that the sum of moments around any pivot point is zero for static equilibrium. - Consider distances and angles given to resolve the forces into their effective lever arms. 3. **Equilibrium Conditions:** - For horizontal and vertical forces: \(\sum F_x = 0\) and \(\sum F_y = 0\). - For moments: \(\sum M = 0\). **Application:** Such a static equilibrium analysis is crucial in designing mechanical systems,
Transcribed Image Text:**Mechanism Analysis for Static Equilibrium** **Description:** The image depicts a mechanical system aimed at maintaining static equilibrium. The system components and forces are labeled as follows: 1. **Mechanism Setup:** The mechanism consists of a linkage assembly defined by key points and segments: - Point \( O_2 \) is a fixed pivot. - Point \( A \) moves in a circular path around \( O_2 \), forming the link \( O_2A \). - The linkage consists of \( O_2A \), \( AB \), and additional points like \( E \). 2. **Link and Force Details:** - \( O_2A \) has a length of 100 mm. - \( AB \) has a length of 250 mm. - \( AE \) has a length of 50 mm. - The input angle at \( A \) is given as 40 degrees. - External force \( F_E \) acting at point \( A \) is 6000 N. - Reaction force \( F_B \) at point \( B \) is 2000 N directed horizontally towards the right. 3. **Angles and Labels:** - The direction of the applied force \( F_E \) makes an angle of 140 degrees with the horizontal. - The system is divided into numbered segments and elements (1, 2, 3, 4) for clarity in analysis. **Task:** To maintain the mechanism in static equilibrium, determine the required input torque, denoted as \( T_2 \). **Analysis Approach:** 1. **Force Diagram:** - Analyze the forces and moments acting on the system segments. - Calculate the components of forces and their respective moments about the pivots and points of interest. 2. **Torque Calculation:** - Apply the principle of moments to find the required torque \( T_2 \), ensuring that the sum of moments around any pivot point is zero for static equilibrium. - Consider distances and angles given to resolve the forces into their effective lever arms. 3. **Equilibrium Conditions:** - For horizontal and vertical forces: \(\sum F_x = 0\) and \(\sum F_y = 0\). - For moments: \(\sum M = 0\). **Application:** Such a static equilibrium analysis is crucial in designing mechanical systems,
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