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Humans are not perfect. There are always imperfections in any task that is done, including kicking. Our group wanted to tackle the challenge of kicking a soccer ball while adding a spin to the ball, much like the ones that are normally seen from professional soccer players like Messi or Renaldo at international tournaments. It would be interesting to be able to replicate and analyze the exact position, as well as the velocity at which a ball should be kicked to produce a certain spin using a complex system of mechanical linkages. For the scope of our project, we aim to design a mechanism that will be able to kick a ball while adding some spin on it, similar to what is seen in the following image:
It would be interesting to have the ability to analyze the motion that creates a specific spin on the ball, view it in a graph, and send it to the mechanism to see it in real time. Practically speaking, this mechanism could be used in schools and camps to teach beginners and even experts how to best position their feet, what kind of motion it would take, and how the velocity at which they strike the ball affects its motion.
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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.
Figure 5. Golf Ball Impact
As seen in Figure 5 above, the impact from the golf club does not impart any spin on the golf ball. The design team re-scoped the project to remove the requirement to impart spin onto the ball. Furthermore, the team restricted the mass of the model golf ball as a ping pong ball in order to reduce the scale of the mechanism and motors utilized.