Ariya Dararutana's "Towers of
Hanoi"
(view
movie <1.3M>)
The Legend of the Towers of Hanoi
In an ancient
city, so legend goes, monks in a temple had to move a pile of 64 sacred
disks from one location to another. The disks were fragile; only
one could be carried at a time. A disk could not be placed on top
of a smaller, less valuable disk. In addition, there was only
one other location in the temple (besides the original and destination
locations) sacred enough for a pile of disks to be placed there.
Using the
intermediate location, the monks began to move disks back and forth from
the original pile to the pile at the new location, always keeping the piles
in order (largest on the bottom, smallest on the top). According
to the legend, before the monks could make the final move to complete the
new pile in the new location, the temple would turn to dust and the world
would end.
Is there any truth to this legend?
To answer, you
will need some idea how long it will take the monks to finish their task,
so you play a game using a small collection of disks and three piles into
which you can put them. Play the game to find the smallest number
of moves necessary to move all the disks. Then see if you can figure
out the mathematical pattern behind the number of moves required for different
numbers of disks, and use this to predict how long it will take the monks
to move their 64 disks.
What is the trick to the
game?
The solution
to the game actually consists of repetitions of a sequence of steps.
Once this pattern is determined, it is quite easy to solve the game: just
follow the pattern over and over again. The only required information
is the number of discs utilized. This determines the minimum number
of steps it takes to solve the problem; simply put, it decides how long
to follow this pattern. How does this number do it? By this
mathematical equation:
Number of steps = 2n - 1, where n = the number of discs.
What Does My Project Do
My project represents
the solution to the Towers of Hanoi game. It is a simplified version
for only six discs are utilized, but the basic idea is represented.
A computer program written by myself controls the movements of the hardware.
The motors will drive the gripper mechanism back and forth between the
three pegs and up and down to pick up a particular disc. The gripper
itself will open and close to pick up a designated disc. Bases upon
my programming, my project will actually move the discs from peg to peg
and solve the game. This project is (well, will be) self-sufficient;
that is, nothing other than the program is required for it to run.
How Does It Work?
As the name of
this course details, a computer program is used to operate the machinery
that I have developed. The hardware itself is actually a conglomeration
of printer mechanisms and spare parts. The side to side movement
of the gripper mechanism is created by a printer mechanism that essentially
consists of rubber belt loop, gears, and a stepper motor. (A stepper
motor is one type of motor that uses electromagnetic pulses to rotate a
certain number of degrees at a time - this number of degrees is described
as one "step.") The vertical movement is also created by a printer
mechanism of similar structure to the one used in the side to side movement.
The gripper consists of two hard drive motors wired in parallel.
The are positioned so that they "face" each other. Thus, when the
motors are told to go "forward," they will travel an equal distance but
in opposite directions creating a clamp, or grip, motion. All of
the motors are wired to a breadboard - this is a template where electrical
circuits are constructed. This connects the signals sent by the computer
to the hardware and the motors. Good connections mean movement (hopefully).
Accurate movements mean working project.