As shown in the above figure, cams can come in many shapes, each useful in different situations. Our situation requires the prepping and launching a sling shot; this means we need both a slow, smooth motion for the prepping phase and a fast release for the launching phase of the sling shot. In order to hit both of those requirements I considered the both star and snail shaped cam.

The star shape was considered because it's geometry allows for multiple drops per a single cam revolution (S. Johnson, 2010). This was considered so that we could throw and catch the ball rapidly during the cooperative portion of the competition in order to increase the number of points scored.

The snail design was considered because it allows for a longer prep period which relates to pulled the sling shot back further resulting in a farther throw (V. Ryan, 2006). The snail shell design also has a quicker release as compared to the star design. Using the above considerations and the data, discussed below, our team chose to move forward with the snail shell cam design.

Evaluation Criteria:

With the style of cam chosen, I then had to try to find an appropriate size and final shape for our robot.

The first design of the cam is shown in the above figure. This cam was very large, much too large to print, and did not give very much prep and release distance for the sling shot. Without that distance, the robot will not be able to launch the ball into the 1^st zone.

After many iterations, I came to the design shown in Figure 3. This design is small enough to fit on a print bed, which makes for easy manufacturing, and includes a coupler that allows the cam to be attached to the stepper motor. Despite this cam being smaller than the previous versions it has more prep and launch distance available than the cam shown in Figure 2.

Data: To determine which of the two cam styles (star or snail shell) would work best for our application, I simply tested which of the two styles resulted in a further throwing distance. For these tests, the launcher was set at approximately 20° from vertical and the sling shot tension was not changed between tests. The tests consisted of 6 total throws for each style of cam where the final distance of the throw was measured to where the ball first hit the ground.

The initial tests were done with the star style cam and one of the early iterations of the snail shell cam (‘Short Throw Snail Cam’). These initial tests showed that the snail shell cam could provide significantly greater throwing distances than the star style cam. This testing also revealed to us that the early iteration of the snail shell cam was not able to provide us quite enough throwing distance. Knowing this, the cam was redesigned (‘Long Throw Snail Cam’) and tested under the same conditions as before. The results of the two sets of tests are shown on the bar graph below.

Data Discussion: Looking at the above graph, the Long Throw Snail Cam is able to achieve greater throwing distances under the same testing conditions as the other two cams. It is important to note that while the Long Throw Snail Cam is the best performer, it does not meet the distances required for competition. This is being addressed by changing the angle of the launcher and pre-tensioning the sling shot to add more force to the throws.

Another important aspect to mention is that these tests were preformed on a testing rig that was very different from our final robot. This is why the tests results show more promise than was displayed by our actual integrated setup on the robot.

Conclusion: The cam is an interesting actuator design with some key advantages including few moving parts, ease of manufacture, and that changing the shape can dramatically alter the behavior. The snail shaped cam is uniquely fitted for this application with a long smooth lead time and a quick release to optimize the throwing distance of the robot.

Future Work: Future work on a cam system would be to remove the size restriction from the available 3D printers to create a cam capable of providing more tension on the throwing device. In addition to this the specific geometry of snail shaped cam could be slightly altered to adjust the force applied to it during the lead phase, potentially making the system run smoother and launch farther.

Jacob's Research

Introduction

The proposed topic was to simulate the trajectory of a beach ball in flight. This work could then be applied to our robot in order to calculate an accurate firing solution. Because the density of the beach ball is very low, drag forces are large in comparison to inertial forces, and thus cannot be neglected. In addition, it is expected that the drag will vary with the level of deformation of the ball. The introduction of these nonlinear drag terms complications the governing dynamic equations, making an analytical solution difficult or impossible. For this reason, a numerical simulation is implemented.

The key assumptions to be examined here are that the drag is of sufficient magnitude that it cannot be neglected, and that the level of deformation of the ball will have a noticeable effect on the drag. To simply phrase these questions, we are asking "Is the effect of drag strong enough that it must be modeled, and does it depend on the deformation of the ball?"

Related Work

Parker provides approximate analytical solutions to the motion of a projectile with quadratic drag (Parker, 1977). Le Clair et al. numerically calculate the drag of a sphere for low to intermediate Reynolds numbers and compare to experimental and theoretical results (Le Claire et al., 1970). Le Personnic et al. collect experimental drag data for badminton shuttlecocks, and use that data to simulate trajectories (Le Personnic et al., 2011). Vogel examines the trajectories of biological projectiles, such as insects and seeds (Vogel, 2005).

Le Personnic et al. noted that synthetic shuttlecocks deform at high velocities, reducing their drag. The beach ball is likely to also exhibit deformation, and there is little to no research on the deformation of spheres in flight. Furthermore, the motion of objects with densities as low as a beach ball are rarely studied.

Methods

A python script using numerical integration methods from the SciPy package was written to simulate the flight of a projectile as governed by the differential equations

where m is the ball mass, Cd is the drag coefficient, and g is the acceleration due to gravity. In addition, physical experimentation was undertaken to determine the effect of deformation on the drag coefficient. A beach ball, inflated to various levels to influence the amount of deformation, was dropped from a height of 2m and its final velocity recorded using videography.

Results

Tabulated results of the drop test are shown in Table 1. Note that no difference in velocity was observed between full and 3/4 inflation, but a difference was observed at 1/2 inflation.

The data from this experiment was used to calculate coefficients of drag by numerically simulating the fall. Results of this simulation are shown in Figure 1, along with the velocities of a ball with no drag, and the analytically predicted drag for an ideal sphere.

It was initially assumed that the drag of an ideal sphere would be 0.45, as expected for laminar flow. However, it was discovered that the fully inflated ball had a drag coefficient close to 0.1, which corresponds to an ideal sphere at the onset of turbulence. As such, the coefficient used for the ideal sphere was changed to reflect this.

These coefficients of drag were then used in a simulation of a thrown ball. The ball was given an initial velocity of 20m/s directed upwards at 45 degrees from the horizontal. The results of this simulation are shown in Figure 2. Note that in both Figures 1 and 2, the curves for the ideal sphere, full inflation, and 3/4 inflation overlap.

Conclusion

The data clearly shows that drag for the conditions examined is substantial, and cannot be ignored. For the results illustrated in Figure 2, the inclusion of drag can cut the distance covered in half. It is also clear that deformation of ball, as measured by level of inflation, has some effect on drag. However, this effect is only noticeable at extreme levels of deformation, and for a reasonably inflated ball, can be safely ignored.

With the simulation and data collection complete, future work should implement optimization functionality, so that this research can be applied for executing precise throws. Given an accurate simulation, a robot can optimize for launch parameters to precisely reach the desired target.