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Design a quick return four-bar Grashof crank-rocker mechanism with the following specifications:

- Output rocker motion: [tex]90^\circ[/tex]
- Time ratio (TR): 1/1.50

Requirements:

1. Check the Grashof crank-and-rocker condition.
2. Provide a stepwise solution, including appropriate construction lines.
3. Present the final mechanism without the construction lines.

Note: This task is worth 40 points.

Answer :

Design a quick return four-bar Grashof crank rocker mechanism with 90° of output rocker motion and a time ratio of 1/1.50, we need to follow these steps:

Step 1: Analyze Grashof condition: The Grashof condition states that for a four-bar linkage to have a continuous motion, the sum of the shortest and longest link lengths should be less than or equal to the sum of the remaining two link lengths. Let's label the links as follows:- Link 1: Input crank- Link 2: Connecting rod- Link 3: Output rocker- Link 4: Ground link (fixed) We need to check the Grashof condition using the given dimensions. Step 2: Determine the link lengths: We have a time ratio (TR) of 1/1.50, which means the input crank rotates 1.5 times for one complete cycle of the output rocker. This ratio helps determine the relative lengths of the crank and rocker. Let's assume the length of the input crank (Link 1) as 1 unit. Then, the length of the output rocker (Link 3) will be 1.5 units. Step 3: Construction:

Step 4: Verify Grashof condition: Measure the lengths of the shortest and longest links:- Shortest link = Length of Link 2 (BC)- Longest link = Length of Link 3 (CD). Compare the sum of the shortest and longest links with the sum of the remaining two links: - Sum of Link 1 (AB) and Link 4 (DA) . If the sum of the shortest and longest links is less than or equal to the sum of the remaining two links, then the Grashof condition is satisfied. Step 5: Finalize the mechanism: Remove the construction lines, leaving only the four-bar mechanism with the labeled links and pivots. Note: It's important to note that the specific dimensions and angles of the mechanism will depend on the requirements and constraints of your design. The provided steps give a general guideline for designing a quick return four-bar Grashof crank rocker mechanism with the given parameters.

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