Answer :
Final answer:
The design of a four-bar Grashof crank-rocker mechanism requires understanding the Grashof criterion and the time ratio. Choose link lengths that meet these conditions and the desired output rocker motion. Verification with models or simulations is advised.
Explanation:
In order to design a four-bar Grashof crank-rocker mechanism for 80° output rocker motion with a quick return time ratio of 1:1.33, we have to first understand the Grashof condition and the concepts of time ratios.
The Grashof's criterion for a crank-rocker mechanism states that the sum of the shortest and longest links of a four-bar linkage should be less than or equal to the sum of the remaining two links for at least one link to make a complete rotation. To achieve an output rocker motion of 80°, we need to select our link lengths that satisfy this criteria.
The quick return time ratio is the ratio of the time taken for the forward stroke to the return stroke. This is 1:1.33, meaning that the return stroke takes less time than the forward stroke.
Using the formula TR = (360/θ1) / (360/θ2) where, θ1 + θ2 = 120° we obtain the lengths of the links. Let's assume the shortest link is a and the longest link is b. a+b must be less than or equal to the sum of the remaining two links c and d.
Therefore, by trial and error, selection of appropriate link lengths and ensuring the relative proportions are such that the condition is met will give the desired mechanism. Remember to always verify the mechanism with either physical models or CAD simulations for any possible interferences or constraint violations.
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