Derive the vector loop, positon, velocity, and acceleration equations for the 2 DOF pantograph leg mechanism given. ### Understanding Four-Bar Linkages and Path TracingThis image depicts a technical diagram of a four-bar linkage mechanism commonly studied in kinematics for mechanical engineering and robotics.#### Diagram Breakdown1. **Four-Bar Linkage Mechanism:** - **Blue Lines and Nodes:** The diagram shows a four-bar linkage, which consists of four rigid bars connected by rotational joints. The lines represent the bars and the circles at the intersections of the lines represent the rotational joints (nodes). - The bars are connected in such a way that they form a closed loop. When one of the bars, called the input link, is rotated, the other bars (output link and coupler link) will also move. This creates a complex motion that can be used in various mechanical applications.2. **Red Squares and Lines:** - Positioned at some of the nodes, these red squares and lines might represent constraints or fixed supports. These constraints hold specific nodes in fixed positions, allowing the rest of the mechanism to move predictively.3. **Green Elliptical Path:** - The green elliptical shape at the bottom of the image with crosses along the path represents the trajectory traced by a particular point on the linkage. This is termed the "cognate curve" or "output path." Tracing the path of various points on the linkage is essential in understanding the motion characteristics and ensuring the mechanism meets its design requirements.#### Usage in MechanismsFour-bar linkages are widely used in various mechanisms to produce a desired output motion from a given input motion. Common applications include:- **Steering Mechanisms:** In vehicles, four-bar linkages can be used in the steering mechanisms to control wheel angles. - **Robotic Arms:** In robotics, these linkages can be used to form the joints of robotic arms to provide precise movements required for tasks like picking and placing objects.- **Manufacturing Machinery:** Machines used for tasks like drilling, cutting, and shaping may use four-bar linkages to achieve the required repetitive motions.#### Key Concepts- **Input Link:** The part where motion is initially applied. - **Output Link:** The part where the motion is outputted and used. - **Coupler Link:** The bar connecting the input and output links.- **Fixed Support:** Points at which the mechanism is anchored.Understanding these principles helps in designing mechanical systems with

More detailed information about the mechanism, such as the lengths of the links and the geometric…

Answered: Derive the vector loop, positon,…

Engineering

Mechanical Engineering

Derive the vector loop, positon, velocity, and acceleration equations for the 2 DOF pantograph leg mechanism given.

Elements Of Electromagnetics

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ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Question

Derive the vector loop, positon, velocity, and acceleration equations for the 2 DOF pantograph leg mechanism given.

### Understanding Four-Bar Linkages and Path Tracing

This image depicts a technical diagram of a four-bar linkage mechanism commonly studied in kinematics for mechanical engineering and robotics.

#### Diagram Breakdown

1. **Four-Bar Linkage Mechanism:**
- **Blue Lines and Nodes:**
The diagram shows a four-bar linkage, which consists of four rigid bars connected by rotational joints. The lines represent the bars and the circles at the intersections of the lines represent the rotational joints (nodes).
- The bars are connected in such a way that they form a closed loop. When one of the bars, called the input link, is rotated, the other bars (output link and coupler link) will also move. This creates a complex motion that can be used in various mechanical applications.

2. **Red Squares and Lines:**
- Positioned at some of the nodes, these red squares and lines might represent constraints or fixed supports. These constraints hold specific nodes in fixed positions, allowing the rest of the mechanism to move predictively.

3. **Green Elliptical Path:**
- The green elliptical shape at the bottom of the image with crosses along the path represents the trajectory traced by a particular point on the linkage. This is termed the "cognate curve" or "output path." Tracing the path of various points on the linkage is essential in understanding the motion characteristics and ensuring the mechanism meets its design requirements.

#### Usage in Mechanisms

Four-bar linkages are widely used in various mechanisms to produce a desired output motion from a given input motion. Common applications include:

- **Steering Mechanisms:**
In vehicles, four-bar linkages can be used in the steering mechanisms to control wheel angles.

- **Robotic Arms:**
In robotics, these linkages can be used to form the joints of robotic arms to provide precise movements required for tasks like picking and placing objects.

- **Manufacturing Machinery:**
Machines used for tasks like drilling, cutting, and shaping may use four-bar linkages to achieve the required repetitive motions.

#### Key Concepts

- **Input Link:**
The part where motion is initially applied.

- **Output Link:**
The part where the motion is outputted and used.

- **Coupler Link:**
The bar connecting the input and output links.

- **Fixed Support:**
Points at which the mechanism is anchored.

Understanding these principles helps in designing mechanical systems with

Branch of science that deals with the stationary and moving bodies under the influence of forces.

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