Introduction

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:

Image RemovedImage Added

Figure 1. Soccer "Kick"Ball Impact

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.

Problem Statement

There are many challenges that we foresee in creating a soccer robot. One characteristic of the output that is necessary for a proper goal is a fast kicking speed. This is not achievable from simple joints because the links must be able to transform a limited-speed motor input into a high-speed output. The linkages in the system must have proper dimensions and orientation so that a simple input can create an arcing kick motion at a high enough angular velocity. Evidently, to determine these link lengths and thus desired output, we will need to perform complex velocity analysis. 

There will likely be multiple challenges that lie in completing repetitive, successful corner kicks. Looking at any successful corner kick in major league soccer, the athlete kicks the ball, precisely applying spin so that the ball can move in an arcing motion toward the goal. In the case of a robot, it must be able to strike the ball in such a way as to create this spin, which creates a complex problem, combining positional and force analysis. 

Mechanism

One way we can achieve our goal is to employ a triple crank watt’s linkage mechanism. This would involve a 6-bar mechanism - 4 binary links, and 2 ternary links. One binary link (colored green in Figure 2) will be driven by a motor with a constant angular velocity. This allows for one of the links to have a “kicking motion” that we can take advantage of to produce the corner kick we are looking for. This would require that we create an end effector capable of producing a spin on the ball, which is what allows an “olympic goal”, or a well centered corner kick.

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Figure 2. Triple Crank Watt’s Linkage Mechanism (Source)

Scope of Work

From a mechanical perspective, our project requires a triple crank Watt’s linkage mechanism driven by a motor. This design allows for the team to control the “kicking” force or speed on the ball. Our team’s biggest challenges derive from the analytical complexities of departing spin to the ball to mimic a “corner kick.” Once our team gains access to our motor’s specifications, we anticipate conducting positional analysis in Python or MATLAB and determining link lengths in SolidWorks or motiongen.io. Additionally, our team will need to design the end effector to optimize our “corner kick.”

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With our team’s expertise and if our timeline allows, our team may incorporate an auto-feeding design in which the soccer ball(s) would automatically return to the start or a pre-loaded hopper would release a ball to prime for the next kick. Additionally, we may use an ultrasonic sensor to estimate how far a “goal” is and use that information to adjust the “corner kick” motor speed accordingly. 

Preliminary Design

Determining Link Lengths

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Figure 3. Determining Link Lengths in CAD

A snapshot of Figure 2 was imported into CAD, and the lengths of the links were recorded. These lengths were over 27", so the team "normalized" them by dividing by the longest link. Doing so yielded the proportions. We then multiplied these proportions by a scale factor of 4" in order to obtain more feasible link lengths. See table below.

The 4" scaled lengths were used in the the following calculation procedures as well as in manufacturing.

Mobility Calculations

The following schematic was used to model the proposed mechanism:

Figure 34. Mobility Calculations Joint and Linkage References

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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. 

Image Added

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.