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Determine the forces acting on the ground and the torque, 7₁2, to maintain static equilibrium for the four-bar linkage shown in Figure using both graphical and analytical methods. RAO, -87.5 mm, RBA - Ro - 150 mm, Rсo₁ - 100 mm, Ryo, - 50 mm, and Ro₂04 = 175 mm. De B P 4 53

Determine the forces acting on the ground and the torque, 7₁2, to maintain static equilibrium for the four-bar linkage shown in Figure using both graphical and analytical methods. RAO, -87.5 mm, RBA - Ro - 150 mm, Rсo₁ - 100 mm, Ryo, - 50 mm, and Ro₂04 = 175 mm. De B P 4 53

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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Show all steps and solution. Solve both analytical and graphical . P=222.5 N for first one. 

**Problem Statement:** Determine the forces acting on the ground and the torque, \( T_{12} \), to maintain static equilibrium for the four-bar linkage shown in the figure using both graphical and analytical methods. **Given Dimensions and Lengths:** - \( \overline{R_{A0_2}} = 87.5 \, \text{mm} \) - \( \overline{R_{B0_4}} = \overline{R_{B0_1}} = 150 \, \text{mm} \) - \( \overline{R_{C0_4}} = 100 \, \text{mm} \) - \( \overline{R_{D0_4}} = 50 \, \text{mm} \) - \( \overline{R_{O_2O_4}} = 175 \, \text{mm} \) **Diagram Explanation:** In the diagram: - The linkage consists of four key points: \( A, B, C, D \). - \( O_2 \) and \( O_4 \) are the pivot points for the linkage. - The angle at O2 is \( 105.1^\circ \) and at O4 is \( 152.4^\circ \), while the linkage rotation includes an angle of \( 240^\circ \). - Point D is acted upon by a force \( P \), and \( T_{12} \) is the torque acting at the link. - Vectors and angles are used extensively to define the links' positions and orientations within the mechanism. **Purpose:** The aim is to analyze the forces and torques in this mechanical setup to understand the conditions necessary for maintaining static equilibrium, an important concept in mechanical design and analysis.
Transcribed Image Text:**Problem Statement:** Determine the forces acting on the ground and the torque, \( T_{12} \), to maintain static equilibrium for the four-bar linkage shown in the figure using both graphical and analytical methods. **Given Dimensions and Lengths:** - \( \overline{R_{A0_2}} = 87.5 \, \text{mm} \) - \( \overline{R_{B0_4}} = \overline{R_{B0_1}} = 150 \, \text{mm} \) - \( \overline{R_{C0_4}} = 100 \, \text{mm} \) - \( \overline{R_{D0_4}} = 50 \, \text{mm} \) - \( \overline{R_{O_2O_4}} = 175 \, \text{mm} \) **Diagram Explanation:** In the diagram: - The linkage consists of four key points: \( A, B, C, D \). - \( O_2 \) and \( O_4 \) are the pivot points for the linkage. - The angle at O2 is \( 105.1^\circ \) and at O4 is \( 152.4^\circ \), while the linkage rotation includes an angle of \( 240^\circ \). - Point D is acted upon by a force \( P \), and \( T_{12} \) is the torque acting at the link. - Vectors and angles are used extensively to define the links' positions and orientations within the mechanism. **Purpose:** The aim is to analyze the forces and torques in this mechanical setup to understand the conditions necessary for maintaining static equilibrium, an important concept in mechanical design and analysis.
**Problem Statement:** Using graphical and analytical methods, determine the torque, \( T_{12} \), required to drive slider 6 of the figure against a load of \( P = 100 \) lb at a crank angle of \( \theta = 30^\circ \). **Given Measurements:** - \( \overline{R_{A0_2}} = 62.5 \, \text{mm} \) - \( \overline{R_{O2O4}} = 400 \, \text{mm} \) - \( \overline{R_{BC}} = 200 \, \text{mm} \) - \( \overline{R_{O4L}} = 150 \, \text{mm} \) **Diagram Explanation:** The diagram illustrates a mechanical system consisting of several interconnected components. Below is a detailed breakdown: 1. **Components:** - **Crank (3)**: This is the rotating component with a crank angle \(\theta = 30^\circ\). - **Connecting Rod (5)**: This links the crank to the slider. - **Slider (6)**: Moves in a linear path under the influence of the crank and connecting rod. 2. **Points and Distances:** - **Point \( A \)** and **Point \( B \)**: Identify pivot or connection points. - **Point \( O_4 \)** and **Point \( O_2 \)**: Represent rotational axes or fixed points in the system. - **Distance Measurements**: Measure the lengths between key points in millimeters to define the geometry of the system. 3. **Load Application:** - The load \( P = 100 \) lb is applied vertically to the slider, influencing the torque required. 4. **Graphical Representation:** - The mechanical linkage is shown in a 2D plane with \( x \) and \( y \) axes. - Arcs and angles represent rotational elements and constraints in the system. The task involves using both graphical methods (e.g., scaled drawings) and analytical methods (e.g., mathematical calculations) to determine the torque \( T_{12} \) needed at point \( L \) to overcome the specified load.
Transcribed Image Text:**Problem Statement:** Using graphical and analytical methods, determine the torque, \( T_{12} \), required to drive slider 6 of the figure against a load of \( P = 100 \) lb at a crank angle of \( \theta = 30^\circ \). **Given Measurements:** - \( \overline{R_{A0_2}} = 62.5 \, \text{mm} \) - \( \overline{R_{O2O4}} = 400 \, \text{mm} \) - \( \overline{R_{BC}} = 200 \, \text{mm} \) - \( \overline{R_{O4L}} = 150 \, \text{mm} \) **Diagram Explanation:** The diagram illustrates a mechanical system consisting of several interconnected components. Below is a detailed breakdown: 1. **Components:** - **Crank (3)**: This is the rotating component with a crank angle \(\theta = 30^\circ\). - **Connecting Rod (5)**: This links the crank to the slider. - **Slider (6)**: Moves in a linear path under the influence of the crank and connecting rod. 2. **Points and Distances:** - **Point \( A \)** and **Point \( B \)**: Identify pivot or connection points. - **Point \( O_4 \)** and **Point \( O_2 \)**: Represent rotational axes or fixed points in the system. - **Distance Measurements**: Measure the lengths between key points in millimeters to define the geometry of the system. 3. **Load Application:** - The load \( P = 100 \) lb is applied vertically to the slider, influencing the torque required. 4. **Graphical Representation:** - The mechanical linkage is shown in a 2D plane with \( x \) and \( y \) axes. - Arcs and angles represent rotational elements and constraints in the system. The task involves using both graphical methods (e.g., scaled drawings) and analytical methods (e.g., mathematical calculations) to determine the torque \( T_{12} \) needed at point \( L \) to overcome the specified load.
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