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
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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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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