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.