Week Six

In Week Six, the final materials were purchased, including an LCD display from Amazon. The wood pieces were cut to fabricate the box, so all that is left of the case fabrication is the gluing.

In addition, three example objectives were created for the game. Though the exact RPM values are not what they will be for the game, the math of it is correct. The example objectives operate under the assumption that the first gear is a gear of radius 1.0" that moves clockwise at 60 revolutions per minute (RPM).

1) The first objective is to set up the gears in such a way that the final gear moves at 90 RPM in a counterclockwise motion. An example setup for this objective is below:

Mathematically, there are two components to achieving this objective. First, the RPM, relies on the ratio between the first and final gear. At a basic level, an understanding of gear ratios shows that the ratios between the radii and rotational velocity of any two gears are inversely proportional. Additionally, only the first and last gears in a system are relevant for calculating the speed of the last gear.

If the first gear has a radius of 1.0" and rotates at 60 RPM, and the last gear rotates at a rate of 90 RPM, it is possible to find the radius of the last gear mathematically: 

90RPM / 60RPM = 1.0" / x"

Solving for x, the radius of the final gear is found to be 0.5". This means that in order to achieve the given objective, the gears must be set up so that the final gear has a 0.5" radius.

The other aspect of the objective, the direction of movement, relies on the number of gears in play. If the total number of gears is odd, the final gear will move in the same direction as the first gear. Because the first gear moves clockwise, this means that the final gear will move clockwise as well. Conversely, if the number of gears is even, the final gear will move in the opposite direction of the first gear - in this case, counterclockwise. In the example provided, there are 10 gears in play, so the final gear moves in a counterclockwise direction.

2) The second objective asks the player to have the final gear move at 30 RPM in the clockwise direction, using the same fixed starting gear as in the previous objective. An example of this achieved objective is below:

Again, the mathematics of gear ratios are used to figure out what size the final gear should be:

60RPM / 30RPM = 1.0" / x"

x = 1.5"

The final gear must have a radius of 1.5", and in order for that gear to move in a clockwise direction, there must be an odd number of gears in total. In the above example, there are 11.

3) The third objective asks that the final gear move at a rate of 60 RPM in a clockwise motion. An example of this is below:

Because the final gear is to move at the same RPM as the first, it must be the same size as the first gear:

60RPM / 60RPM = 1.0" / x"

x = 1.0"

Also, this gear with radius 1.0" must move with clockwise motion, so there must be an odd number of gears in the play space. In this example, there are 9, so the final gear does indeed move in a clockwise direction.