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To compute the degrees of freedom (自由度) for the given planar mechanism (平面机构), we can use Gruebler’s equation for planar linkages:

\[
F = 3n - 2P_L - P_H
\]

Where:
- \( F \) is the degrees of freedom.
- \( n \) is the number of links, including the ground (fixed) link.
- \( P_L \) is the number of lower pairs (like revolute or prismatic joints).
- \( P_H \) is the number of higher pairs (if any, like cams or gears).

### Step-by-Step Process:
1. **Identify the Number of Links \( n \)**:
   Each rigid body in the mechanism counts as a link. You must include all moving parts and the fixed ground link.

2. **Count the Number of Lower Pairs \( P_L \)**:
   These are the revolute (hinges) and prismatic joints. In the diagram, these would appear as pin joints.

3. **Count the Number of Higher Pairs \( P_H \)**:
   If there are any sliding contact points or gear contacts, these are higher pairs.

From the image:
- The mechanism has joints at points \( A \), \( B \), \( C \), \( D \), and \( E \).
- Links are the segments between these points.
  
I'll analyze the image and compute the degrees of freedom.Let's proceed with analyzing the image step by step to determine the degrees of freedom.

### Links and Joints:
- **Links**: Based on the diagram, the links appear to be:
  - \( A \) to \( B \)
  - \( B \) to \( C \)
  - \( B \) to \( D \)
  - \( A \) to \( E \)
  
  Including the fixed ground link (usually where the base or frame is connected), we count **6 links** in total.

- **Lower Pairs (Revolute Joints)**:
  The image shows pin joints at \( A \), \( B \), \( C \), \( D \), and \( E \), which are revolute joints. This gives us a total of **6 revolute joints**.

- **Higher Pairs**: There do not appear to be any higher pairs in the image (e.g., cams, gears), so \( P_H = 0 \).

### Applying Gruebler's Equation:
Now, we'll use the Gruebler equation:

\[
F = 3n - 2P_L - P_H
\]

Where:
- \( n = 6 \)
- \( P_L = 6 \)
- \( P_H = 0 \)

Let's calculate the degrees of freedom (DOF).It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can apply the Gruebler’s equation manually:
\[
F = 3n - 2P_L - P_H
\]
With the values:
- \( n = 6 \)
- \( P_L = 6 \)
- \( P_H = 0 \)

Plugging these into the equation:
\[
F = 3(6) - 2(6) - 0 = 18 - 12 = 6
\]

So, the degrees of freedom for this mechanism is **6**.

### Relative questions:
1. How does changing the number of links affect the degrees of freedom?
2. What role do higher pairs play in mechanisms?
3. Can a mechanism have negative degrees of freedom?
4. How does Gruebler's equation apply to spatial mechanisms?
5. What happens if a joint type other than revolute is introduced?

**Tip**: Always remember to include the ground link when counting links in a mechanism!

Learn how to calculate the degrees of freedom for a planar mechanism using Gruebler's equation. This step-by-step guide covers core mechanical concepts, revolute joints, and kinematic calculations. Suitable for engineering students or advanced high school physics learners.

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