2.2 - Project Prototype Spring 2026

Physical Prototype Dimensions:

(center to center measure)

crank: 3.75 cm => 53.6 mm

link: 8 cm => 66 mm

link: 16.8 cm => 99.3 mm (24.4 mm from ground hole)

link: 18 cm => 114.7 mm

output: 24.2 cm => 300 mm (97.2 mm from ground hole)

Design Iteration Documentation:

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Figure 1: 1st iteration of our launching mechanism (4-bar)

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Figure 2: 2nd iteration with a 0-degree launch angle

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Figure 3: Current iteration

Prototype Iteration Documentation

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In our first iteration from CAD to reality, we created a planar mechanism by laser cutting the linkages and using screws as our full joints. The first iteration gave us a physical visualization of the mechanism in a planar motion, however it was quite larger than we anticipated.

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Our second iteration was scaled down by 50%. In this iteration, our link 5 was not accurate to our design as something went wrong when scaling that link. Since we already had the links manufactured we decided to assemble it anyway. The size for our mechanism was improved, however the release angle was a bit high due to the wrong linkage length.

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For the next iteration, we corrected the mismeasured linkage length and successfully replicated the desired planar motion. After validating the trajectory, we fabricated a second, mirrored mechanism to extend the system into three dimensions. Additionally, we designed and constructed a container to hold and launch the ball. The two mechanisms were then connected with parallel links to ensure synchronized motion and structural stability.

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Figure 7: Physical Prototype

Above is the final prototype we presented for our demo day. During the assembly, we made an error in construction by placing the cranks inward, meaning that we cannot crank the system from the outside without hitting the ground support link. Additionally, manual testing revealed that the launch angle remained too high (approximately 70°), producing a steep and overly direct trajectory. This behavior is not representative of a realistic basketball shot, where an optimal launch angle is closer to 45° to achieve a smooth parabolic arc. The output velocity is also too low, necessitating further optimization of the system that will discussed below.

These issues will be addressed in the final iteration of the project. We plan to scale the mechanism down to 75% of its current size to improve usability and make it more suitable for tabletop play. Additionally, we plan to move the frame inside with the 4-bar mechanism on the outside to have the crank be easily accessible and efficient. Furthermore, we are conducting an analysis to determine the required output force of the mechanism based on the target shooting distance, enabling better control of the launch angle and trajectory.

Prototype Kinematic Analysis:

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Above is the trajectory plot for our physical prototype design assuming input of 60 rpm. The release angle for our prototype was calculated to be 60 degrees, and using a simple kinematic physics analysis the trajectory above was plotted. It is clear that a slightly smaller launch angle is desirable to achieve a better basketball shooting motion trajectory.

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Grübler and Grashof Conditions:

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Two separate Grashof conditions were analyzed, one for each 4 bar system in our mechanism. It is essential that the first set is Grashof so that the mechanism can achieve full range of motion through crank actuation. The second set is also Grashof, but this condition is not essential for the function of our launcher.

Prototype Kinematic Analysis Plots:

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The mechanical advantage formula is calculated as V_in / V_out. At the launch angle at 60 degrees, the mechanical advantage is 0.33. The large spikes at 160 degrees and -40 degrees as the output angular velocity approximates 0 around those times, as well as two links becoming collinear, resulting in a division by a small number inflating the chart. This is not good as that means the linkage is slowing down and is not transferring momentum to the ball anymore.

Bill of Materials

Future Ideas

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With a new arrangement like this, the output velocity is much greater than that of the prototyped design, allowing for greater shooting power. The output angle is also around 55 degrees, much closer to the optimal launch angle of 45 degrees. Because this new system still has the same number of links and joints, the mobility or degrees of freedom is still one.

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Assuming the motor will spin at 60 RPM, the resulting path of the ball is shown in the graph above. The ball will gain approximately 15 cm of height and travel around 0.5 m.

As the output link is the most important one, the remaining graphs will be focused on that one. Note that the ball will launch when the global input angle is approximately equal to -45 to 0 degrees. A clockwise path is also used for graphing.

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Note that the highest magnitude is the point of interest at about 9 rad/sec, which is twice as fast as the old version at about 4.5 rad/sec.

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Note that the mechanical advantage spikes tremendously at 250 degrees and 10 degrees as the output angular velocity approximates 0 around those times, as well as two links becoming collinear, resulting in a division by a small number inflating the chart.

All of these plots consider the end point at the output link where the ball will launch from.