**Problem 6: Mechanics of Linkages**Link \( AB \) has an angular velocity of 4.00 rad/s counterclockwise in the position shown in the diagram to the right.**Objectives:**a) Calculate the translational velocity vector (magnitude and direction) of point \( C \).b) Calculate the translational velocity vector (magnitude and direction) of point \( E \).**Diagram Details:**- The diagram illustrates a linkage system.- Link \( AB \) is pivoted at \( A \) and extends to \( B \).- From \( B \), a horizontal link extends to \( E \).- There is another link connecting point \( C \) diagonally to point \( D \), forming a 60° angle with the horizontal.- Key dimensions provided in the system: - Length \( AB = 4.00'' \) - Length \( BE = 4.00'' \) - Length \( BC = 6.00'' \) - Vertical length from \( A \) to ground \( = 5.00'' \) - Horizontal distance from \( A \) to \( E \) on the ground \( = 7.50'' \) - Vertical height from \( D \) to the bottom \( = 2.40'' \) - Vertical height from the line \( CD \) to \( C \) \( = 3.00'' \)**Calculation Steps:**1. **Velocity Calculation for Point \( C \):** - Use the angular velocity of link \( AB \) and dimensions given to compute the translational velocity at point \( C \). - Apply the rotational kinematics principles for calculating the velocity vector, considering the counterclockwise motion.2. **Velocity Calculation for Point \( E \):** - Similarly, extend the calculations for \( E \). - Analyze the path and velocity impact due to the mechanics of linkage \( BE \).**Note:**For accurate calculations, consider using the properties of rotational motion and vector mathematics.

Rotational Kinematics is the mechanism which deals with the motion of a structure without taking the forces in the account, and if the motion is circular, then it is known as Rotational Kinematics. Velocity of point B, VB=AB×wAB = 5×4 = 20 in/s Angular velocity of CE, wCE=VBOB = 206tan 60∘ = 1.9245 rad/s a) Velocity of point C, VC= OC×wCE = 6cos 60∘×1.9245 = 23.1 in/sVelocity vector, VC →= -23.1 cos 30∘+ 23.1 sin30∘ = -20i⏞+11.55j⏞in/s b) Velocity of point E, VE= OE×wOE = 6 tan60∘2+42 ×1.9245 = 21.43 in/sAngle θ= tan-146tan60∘ = 21∘Velovity vector, VE= -21.43cos21∘i⏞-21.43sin21∘j⏞ = -20i⏞-7.68j⏞in/s

Engineering

Mechanical Engineering

5. Link AB has an angular velocity of 4.00 rad/s counterclockwise in the position shown in the diagram at the right. a) Calculate the translational velocity b) vector (magnitude and direction) of C. Calculate the translational velocity vector (magnitude and direction) of E.

5. Link AB has an angular velocity of 4.00 rad/s counterclockwise in the position shown in the diagram at the right. a) Calculate the translational velocity b) vector (magnitude and direction) of C. Calculate the translational velocity vector (magnitude and direction) of E.

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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Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

**Problem 6: Mechanics of Linkages**

Link \( AB \) has an angular velocity of 4.00 rad/s counterclockwise in the position shown in the diagram to the right.

**Objectives:**

a) Calculate the translational velocity vector (magnitude and direction) of point \( C \).

b) Calculate the translational velocity vector (magnitude and direction) of point \( E \).

**Diagram Details:**

- The diagram illustrates a linkage system.
- Link \( AB \) is pivoted at \( A \) and extends to \( B \).
- From \( B \), a horizontal link extends to \( E \).
- There is another link connecting point \( C \) diagonally to point \( D \), forming a 60° angle with the horizontal.
- Key dimensions provided in the system:
- Length \( AB = 4.00'' \)
- Length \( BE = 4.00'' \)
- Length \( BC = 6.00'' \)
- Vertical length from \( A \) to ground \( = 5.00'' \)
- Horizontal distance from \( A \) to \( E \) on the ground \( = 7.50'' \)
- Vertical height from \( D \) to the bottom \( = 2.40'' \)
- Vertical height from the line \( CD \) to \( C \) \( = 3.00'' \)

**Calculation Steps:**

1. **Velocity Calculation for Point \( C \):**
- Use the angular velocity of link \( AB \) and dimensions given to compute the translational velocity at point \( C \).
- Apply the rotational kinematics principles for calculating the velocity vector, considering the counterclockwise motion.

2. **Velocity Calculation for Point \( E \):**
- Similarly, extend the calculations for \( E \).
- Analyze the path and velocity impact due to the mechanics of linkage \( BE \).

**Note:**
For accurate calculations, consider using the properties of rotational motion and vector mathematics.

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