I want to encourage something of my accompanying future engineers. I want to emphasize how beneficial and even important using math to guide your robot design can be. Math is a beautiful tool with which we may translate our mechanical world into a precise language. When you quantify your resources in that language you can utilize them in the best possible way. Because of that, you even realize how much availability in potential your resources really give you. Math can be utilized to guide or influence virtually any part of your design. I encourage you to not only come up with creative ideas, not only experiment unto trial and error, but to truly design for success and the subtly hidden but powerful optimizations.

Science is often divided between the theoretical and the experimental. Since it is the summer, I am restricted to the theoretical for now (so to speak). My team will get to start building when school kicks back up, but until then, i have no physical vex parts to play and prototype with. As I do my part of the planning for the robot until school DOES start, there is often the pressure of uncertainty if i can make the robot do all the things i want it to. I want it to do a lot. The Gateway Competition, as i see it, was crafted to push our use of the vex robotics system to a new level, to push the vex robotics system through its conventionally familiar limits, to call for our deeper creativity to address those limits. Every time i introduce a new idea with its calculating factors, ive found incredible relief at how much power these resources really have. You don’t have to settle for less than you want, you just have to be CREATIVE and CRITICAL enough to forge a design aspect that will achieve that goal. When my team and i get to start building, the parts won’t perform like new (they’re not) and the robot’s performance won’t match my figures to an infinitesimal degree, but for now i still hold the belief that preparing the design around mathematical figures will prove to be far more than just usably accurate.

To partly demonstrate this emphasis, I have done a fun little side project, a pseudo-robot design for this competition.

Because I have been lengthy, it must be truncated and is finished in the first reply to this thread.

This robot would be entirely expensive and not very competitive, however i am alright with that!

I am not here to give away valuable designs!

I am providing this example robot for those of you who would benefit from demonstration that these resources, the vex robotics system and its functions, can be put into numbers and used to accomplish your creative ends.

Beyond that, it seemed like a fun concept to plan out (i couldn’t get it out of my head until i did it), and i believe its worth sharing.

I’m into SI units, so any lengths are in meters and most other units are SI as well.

I have broken this design aspect into two parts.

The first part demonstrates how you can take provided information about your resources and make a prediction on how it will operate. It is subject to theoretical/experimental discrepancies. Actual practice may require calibration and re-figuring of information.

The second part demonstrates more generally that you can put mechanical events into equations and find literal solutions to your goals. Its discrepancies between theory and experiment are of the negligible level.

The math in Part 2 is certainly true, while the math in Part 1 may need to be slightly modified based on the conditions of how your resources actually perform, but is a good prediction none-the-less (i hope).

Suppose we want a robot that will launch the game pieces into the air and into the circular goals!

Its just like basketball.

Part 1

We must find the velocity of the projectile after being launched.

The vex store informs us that the maximum force exerted by the cylinder is 54 Newtons.

The store also informs us that it takes 45 strokes from 100 psi to 25 psi.

Furthermore we know that each stroke is 0.050 meters long.

We can model the pressure of the pneumatics system by (1)

However, if we use multiple cylinders to the same ends (or even multiple reservoirs for more air), then we must modify S as shown in (2)

We know the following physics equations:

pressure*constant=force
force*distance=energy

kinetic energy=(1/2)mv^2

If the maximum force that can be exerted by one cylinder is 54 Newtons, our necessary assumption while restricted from experimental confirmation is that it is at 100 psi. We may now solve that the constant is 0.54 and multiply it with (2) to get (3).

To qualitatively understand (3), it is saying that if you have N1 amount of cylinders hooked up with N2 amount of reservoirs, and after the cylinders perform S amount of strokes, the next stroke will have (3) force to it.

This carries on to how much energy the cylinders can exert after S amount of strokes. We do this with that second physics equation, and just multiply (3) by the length of the stroke, 0.050 meters, to give us (4)

Interestingly enough, even if we set up the pneumatics to a lever or contraption to advantage either a stronger force or longer stroke (for more room for projectile acceleration), the force and stroke behave like a seesaw, advantaging one disadvantages the other. This amounts to the fact that the mechanical set up of how the pneumatics exert the force on the game object “doesn’t matter” (with a few minor exceptions like lever use conventions and) except that the more complicated it is, the more friction develops.

Basically we don’t need to set up any mechanical advantage to anything. The amount of energy that the cylinder puts out is how much energy will be given to the game object, especially if it is as direct as possible.

That is the same as saying

cylinder energy * amount of cylinders = kinetic energy of projectile (game object)

which gives us (5)

What we need to notice about (5) is that it contains real world data.

We can solve it for V and get (6)

And you see that if you have

a number of cylinders

a number of reservoirs

an amount of strokes already performed (even if its zero)

and the mass of a projectile,

then we can plug in the values and be given the velocity that the object will travel!

The number of cylinders and reservoirs would be data you set as constants in the program after building the robot. The number of strokes performed could be kept by the program. The mass of the projectile could be selected in the program as either the sphere or the barrel with either sensors or the driver’s indication with the remote control.

Part 2: