### Model for a Paper Feeder in a Copy Machine #### Diagram Explanation: 1. **Main Components:** - **Rollers**: These are depicted as two circles on the left side of the diagram. - **Feeder Arm**: Connected to the mass \( m_f \) and the motor torque \( M \). - **Sheet of Paper**: Represents mass \( m_p \). 2. **Distances and Positions:** - \( x_p \): Position of the paper. - \( x_f \): Position of the feeder arm. - \( r \): Radius from the motor to the roller. - 12 cm: Fixed distance from the rollers to the start of the feeder arm. 3. **Forces and Friction:** - \( v_p \): Frictional force acting on the paper. - \( v_f \): Frictional force acting at the feeder arm. - \( M \): Moment from the DC motor applying torque. #### Simplified Model: - The simplified diagram maintains the key elements: - The roller system and distances remain the same. - \( F = Mr \): Represents the force exerted by the motor torque \( M \) over the radius \( r \). #### Task: - **Objective**: Determine the transfer function \( \frac{x_p(s)}{F(s)} \). This model is useful in analyzing and designing the control systems for paper feeders in copy machines, focusing on the mechanical interactions and ensuring reliable performance.
### Model for a Paper Feeder in a Copy Machine #### Diagram Explanation: 1. **Main Components:** - **Rollers**: These are depicted as two circles on the left side of the diagram. - **Feeder Arm**: Connected to the mass \( m_f \) and the motor torque \( M \). - **Sheet of Paper**: Represents mass \( m_p \). 2. **Distances and Positions:** - \( x_p \): Position of the paper. - \( x_f \): Position of the feeder arm. - \( r \): Radius from the motor to the roller. - 12 cm: Fixed distance from the rollers to the start of the feeder arm. 3. **Forces and Friction:** - \( v_p \): Frictional force acting on the paper. - \( v_f \): Frictional force acting at the feeder arm. - \( M \): Moment from the DC motor applying torque. #### Simplified Model: - The simplified diagram maintains the key elements: - The roller system and distances remain the same. - \( F = Mr \): Represents the force exerted by the motor torque \( M \) over the radius \( r \). #### Task: - **Objective**: Determine the transfer function \( \frac{x_p(s)}{F(s)} \). This model is useful in analyzing and designing the control systems for paper feeders in copy machines, focusing on the mechanical interactions and ensuring reliable performance.
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
Related questions
Question
Transcribed Image Text:### Model for a Paper Feeder in a Copy Machine
#### Diagram Explanation:
1. **Main Components:**
- **Rollers**: These are depicted as two circles on the left side of the diagram.
- **Feeder Arm**: Connected to the mass \( m_f \) and the motor torque \( M \).
- **Sheet of Paper**: Represents mass \( m_p \).
2. **Distances and Positions:**
- \( x_p \): Position of the paper.
- \( x_f \): Position of the feeder arm.
- \( r \): Radius from the motor to the roller.
- 12 cm: Fixed distance from the rollers to the start of the feeder arm.
3. **Forces and Friction:**
- \( v_p \): Frictional force acting on the paper.
- \( v_f \): Frictional force acting at the feeder arm.
- \( M \): Moment from the DC motor applying torque.
#### Simplified Model:
- The simplified diagram maintains the key elements:
- The roller system and distances remain the same.
- \( F = Mr \): Represents the force exerted by the motor torque \( M \) over the radius \( r \).
#### Task:
- **Objective**: Determine the transfer function \( \frac{x_p(s)}{F(s)} \).
This model is useful in analyzing and designing the control systems for paper feeders in copy machines, focusing on the mechanical interactions and ensuring reliable performance.
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