Ridiculously Overpowered Stamper

Transcription

1 Ridiculously Overpowered Stamper Overview The task at hand was to build an inefficient and complicated device that can be used to stamp a piece of paper, or, as it is more commonly known, a Rube-Goldberg device. The device had to incorporate projectile motion, conservation of energy and conservation of momentum. This device also had limitations restricting size and total production cost while still operating in a safe, nondestructive manner. The deadline for this build to be complete from planning to finish was approximately two weeks. The steps that we took in planning and building our project are listed below. Planning Stage The first task we had to undertake as a team was project planning. After watching numerous videos of various other Rube-Goldberg devices, we started formulating ideas that we would like to see implemented into our device. Once a list of ideas had been compiled, we had to consider which ones would work well together (while also being simple and reliable enough to meet both consistency and cost goals). Ideas discarded during this process included a rotating mass on a spring and a Plinko based system for movement of the energy. The team also agreed on personal goals we would like to see implemented in addition to the project goals. These included keeping the paper and stamp within the confines of the space limitation given and having the stamp clear the paper after applying the ink. Once our ideas and implementation were agreed upon and approved by the advising TA we set forth for shopping for the construction materials. During the build phase we ran into some design flaws we hadn t anticipated. The possible solutions to these setbacks were discussed amongst the team. We chose our solution based upon the criteria of reliability, ease of implementation and cost. This altered our design from the original planned design, but left us ultimately with a more complex, inefficient and reliable machine. Device Description The stamper uses stored potential energy (in the form of springs and change in height) to power all reactions. We would generally use Superballs to transfer the stored potential energy into kinetic energy.

2 Phas e 1 : The stamper is set into motion by release of a ball on the highest of dowel ramps. The dowels aren t evenly spaced vertically, as the one at the back ends slightly higher than the other dowel resulting in the ball bouncing off the end of the track towards the front of the project onto another set of dowels. Phas e 2 : The momentum then displaces a plunger used to knock a weight off a platform. This weight pulls upwards on a gate by means of a pulley system releasing the next ball on another dowel ramp. Phas e 3 : This ramp ends with the ball bouncing into a 90 degree angled 1.5 inch PVC pipe directing the ball into a deflector angled at approximately 45% to the direction of ball exit. The ball then bounces off the deflector and rolls into a mousetrap.

3 Phas e 4 : The mousetrap springs, pulling a cotter pin from the angled PVC pipe at the front of the project, releasing the final ball. The ball exits the pipe around 5 inches high, bounces off the opposing wall and springs the final mousetrap. Phas e 5 : The arm of the trap pushes up on the weighted end of our stamping lever forcing the stamping action onto the paper. The weighted end of the arm returns to rest raising the stamper from the paper. Stored Energy Analysis There are 6 different stored energy locations in our device. Four use gravitational potential energy and two used stored spring energy. Site 1: When the Superball is first placed on the dowel rods it has gravitational potential energy. It rolls across the length of the box, then back to beneath its starting point. If we set our datum at the point where the ball strikes the plunger, then the energies involved can be described by the equation: mgh = 12 mv 2 + E LOSS

4 Let s assume that energy lost will be about 20% (due to friction, wind resistance, and energy lost in the bounce off of the wall). If we define m as 1 gram and h as.15 meters, then the final velocity of the Superball is about 1.5 meters per second. Site 2: Since this is the only site that cannot be clearly seen from the pictures above, I ve included the following sketch: As ball 1 collides with the plunger at a speed of ~1.5 m/s, the motion of the counterweight can be approximately described by: ' ' m 1 v 1 + m 2 v 2 = m 1 v 1 + m 2 v 2 Frictional forces (and a coefficient of restitution that is not quite 1) mean that the speed of the counterweight is reduced slightly, but its reduced mass (compared to the Superball) should compensate for this. Once the counterweight falls off of the platform, gravity provides more than enough force to pull open the extremely lightweight gate at height h. Site 3: Once the gate is opened, Superball 2 is released. The change in height is slightly larger than in Site 1, but the principles are still the same, so we won t repeat those equations here. The ball rolls down the dowels, makes some turns, and uses its kinetic energy to spring a mousetrap. Which brings us to Site 4: The mousetrap must have an extremely high k value, because the setting of the mousetrap only involves a Δx of about.06 meters. Using the equation 1 k"x 2 2 = 1 mv 2 2 and values of.01g for m and 15m/s for v of the cotter pin (without a digital scale and a high speed camera, these are only estimates), we can solve for k. It turns out to be somewhere in the neighborhood of 625 N-m. Sites 5 and 6: At site 5, a third ball is held up at the top of the PVC tube by the cotter pin. Once the pin is released, it follows the same gravitational potential energy equation as did sites 1 and 3. Site 6 (the second mousetrap) follows the same equation as did site 4.

5 Totals: We can convert the left hand sides of the equations above to Δk values (changes in kinetic energy). If we add up stored energies at each site, we find that there is about 8 Joules of stored potential energy in our device. Site 1 mgh (1g)(9.81m/s 2 )(.06m).59J Site 2 mgh (1g)(9.81m/s 2 )(.02m).20J Site 3 mgh (1g)(9.81m/s 2 )(.2m) 2.0J Site k"x 2.5(625 N-m)(.06m) 1.3J Site 5 mgh (1g)(9.81m/s 2 )(.3m) 2.9J Site k"x 2.5(625 N-m)(.06m) 1.3J Total 8.3J Bill of Materials Material Cost Particle Board $7.00 Superballs $1.00 Shims $1.99 Zip Ties $.10 Pulley $1.99 Scrap Wood $1.50 Nuts/Bolts/Screws/Weights $1.89 Fishing Line $.99 Corner Brackets $1.99

6 Superglue $.50 Mousetraps $.99 TOTAL: $19.94 Conclusions We met all goals for the project as well as our personal goals, but during testing phase found that the slight differences in angles of the tables on which our project was placed caused tuning problems effecting reliability. This was discovered too late to retune the device before final project demonstrations resulting in failure of the device to operate properly upon that surface. Testing prior and after the demonstration on another surface resulted in consistent results of success. The overriding lesson to be learned from this project is that the real world is far more complicated than the scenarios we have been learning about in class. For just the first step (a ball rolling down some dowel rods, bouncing off of a wall, and knocking a weight off of a stand), there were numerous places we realized that equations describing the motions would be extremely complicated. Since the ball was not perfectly round, and was spinning, the center of mass was constantly wobbling in a unpredictable way. This wobbling was less than a millimeter, but sufficient enough to have the ball fall off of the dowels too early about one in every 100 rolls. The friction caused rolling, and the rolling caused angular momentum. When the ball strikes the plunger, it does not behave like our handy conservation of momentum equations would have us believe. The horizontal force did the trick nearly every time, but the downward, frictional spinning force of the rolling ball striking the plunger would make that transference of energy occasionally malfunction. We could take one through the project step by step and point out endless examples of the real world conditions differing from classroom questions, but we think that our point has been made. The best way to eliminate the problems encountered in our project would have been to use superior supplies. Ball bearings rolling down perfectly cylindrical steel dowels would have been far more reliable, but superior materials mean elevated prices. If we had to do this project again (given the same cost restrictions), then we probably would have tried to incorporate transfers of energy that were more reliable. We would have to think for a while to figure out exactly what those more reliable steps would be, so it s a good thing that we re not being asked to do this project again it s the end of the semester and our brains are tired. References All ideas for the Rube Goldberg machine came from our heads or the following video:

7 Rube Goldberg - Japanese Championships: