Answer :
The design of a four-bar Grashof crank-rocker mechanism for 90 degrees of output rocker motion with no quick return requires determining appropriate link lengths and pivot locations while satisfying the Grashof condition.
To design a four-bar Grashof crank-rocker mechanism with 90 degrees of output rocker motion and no quick return, we need to determine the appropriate link lengths and pivot locations. The Grashof condition states that for a four-bar mechanism to have continuous rotation, the sum of the shortest and longest link lengths should be less than or equal to the sum of the other two link lengths.
Here's an example design that satisfies the given requirements:
1. Define the lengths of the four links:
Let's assume the lengths of the links as follows:
- Link 1 (input crank): L1
- Link 2 (coupler): L2
- Link 3 (output rocker): L3
- Link 4 (fixed): L4
2. Determine the pivot locations:
For this mechanism, we need to select the pivot locations carefully to achieve the desired motion. We'll assume that pivot A is the input crank pivot, pivot B is the coupler pivot, pivot C is the output rocker pivot, and pivot D is the fixed pivot.
3. Establish the desired motion:
We want the output rocker to move 90 degrees, which means that the angle at pivot C will change from 0 to 90 degrees.
4. Calculate the required link lengths:
Using the law of cosines, we can determine the length of the coupler link (L2):
- L2 = sqrt((L1^2) + (L3^2) - (2 * L1 * L3 * cos(90 degrees)))
- L2 = sqrt(L1^2 + L3^2)
5. Ensure the Grashof condition is satisfied:
- To avoid a quick return, we need to ensure that the mechanism is a Grashof mechanism. In this case, we want the mechanism to be a Grashof crank-rocker, so the sum of the shortest and longest link lengths should be less than or equal to the sum of the other two link lengths.
- In our case, the shortest and longest links are L2 and L4, respectively, while the other two links are L1 and L3. So, we need to ensure that L2 + L4 <= L1 + L3.
6. Determine toggle positions:
The toggle positions are the extreme positions where the mechanism reaches its maximum and minimum transmission angles. These positions occur when the mechanism is nearly straight or fully extended. The transmission angle is the angle between the coupler link and the rocker link.
7. Calculate the minimum transmission angle:
The minimum transmission angle can be determined by finding the position where the transmission angle is at its minimum value. This occurs when the mechanism is in its toggle position(s).
It's worth noting that there can be multiple solutions that satisfy the given requirements. The example above outlines the general steps to design such a mechanism, but the specific link lengths and toggle positions would depend on the desired proportions and constraints of your application.
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