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Moreover, we verified that our proposed linkage allows at least one link to make a full rotation by complying with the Grashof condition, which states that for a planar four-bar linkage: \[ L + S \leq P + Q \] where \( L \) is the length of the longest link, \( S \) is the length of the shortest link, and \( P \) and \( Q \) are the lengths of the other two links. Since we can break up the six-bar linkage into two four-bar linkages for analysis (see justification in Python Analysis), we employed the condition on both of the linkages. In the first four-bar linkage, the lengths of the links are: \begin{align*} &\text{$l_1$ (Ground link): 1.875}\\ \end{align*} \begin{align*} &\text{$l_2$: 3}\\ \end{align*} \begin{align*} &\text{$l_3$: 4}\\ \end{align*} \begin{align*} &\text{$l_4$: 3.06} \end{align*} Therefore: \begin{align*} &\text{Longest link (L): 4}\\ \end{align*} \begin{align*} &\text{Shortest link (S): 1.875}\\ \end{align*} \begin{align*} &\text{Other two links (P and Q): 3 and 3.06} \end{align*} Applying the Grashof condition: \[ 4 + 1.875 \leq 3 + 3.06 \] which is satisfied, meaning it is a Grashof linkage. In the second four-bar linkage, the lengths of the links are: \begin{align*} &\text{$l_4$: 3.07}\\ \end{align*} \begin{align*} &\text{$l_5$: 3.99}\\ \end{align*} \begin{align*} &\text{$l_6$: 3.0508}\\ \end{align*} \begin{align*} &\text{$l_1$: 1.875} \end{align*} Therefore: \begin{align*} &\text{Longest link (L): 3.99}\\ \end{align*} \begin{align*} &\text{Shortest link (S): 1.875}\\ \end{align*} \begin{align*} &\text{Other two links (P and Q): 3.07 and 3.0508} \end{align*} Applying the Grashof condition: \[ 3.99 + 1.875 \leq 3.07 + 3.0508 \] which is also satisfied, meaning it is a Grashof linkage. |
* Adaptation to Golf
As the team worked through the design process and iterated prototypes, the application of the project pivoted to focus on modeling a golf club impacting a golf ball.