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Analysis of the movement of the Do-Nothing Machine

The circumference of an ellipse with a 8″ minor axis and 12″ major axis

This weekend I completed the program to produce data about the do-nothing machine and analyzed the data using a graphing program called Veusz.  I answered some of my questions about the motion as well as I found a surprise.  There is more I would want to do before I would call it complete.  However, I have completed enough to call it “done”.   This is another post building upon the device, the ellipsograph.

In the post “Programming the Do-Nothing Grinder”, I described the problem of trying to determine the circumference.  Without knowing the circumference it was impossible to know points along the circumference, so I chose to move the handle at constant angles and determine the position of the points on the circumference for each angle.  One way of thinking of this is it is similar to having a slotted wheel spinning directly above the do nothing machine.  This wheel is driving the handle at a constant angular speed and we are taking snapshots (data points) each time the handle moves a constant fraction of an angle.   This is probably not exactly what I was doing as I turned the handle and I ended up with confusing results because I asked the wrong question.

 

The distance of the handle along the circumference to maintain a constant angular change.

The first plot is the y position of the handle vs. the x position of the handle. This plotted the ellipse and gave me confidence my program was ok. Our Do-Nothing Machine would have to have a spacing between shuttles of 2 and a handle length of 4 to make this ellipse. The next thing I plotted was the average distance travelled by the handle at each angle position. If we assume the angle is changing at a constant rate, then this shows the relative speed of the handle at each handle angle position. 0, 180 and 360 degrees are the angles when the handle is at the major axis, 90 and 270 degrees are when the handle is at the minor axis.  This means the handle would move a greater distance while near the minor axis area and slow down near the major axis.

The position of each shuttle at each angle of the handle.

Next I plotted the position of both shuttles with respect to each angular position of the handle. This is the plot that threw me into a time-wasting nose dive.  (It never is a time waste… it just means you are about to learn something!)  These two plots look like perfect sine and cosine waveforms.  This looks exactly what I would get if I were to draw the x position and y position of a point on a circle with a radius of 2 and the point was moved around the circle at the angles shown on the graph x axis.  I thought: “How can this be?”  Especially how can this be when the distance between the horizontal shuttle and the vertical shuttle is only 2 ? (I show this relationship in a previous post, “Episode 35 – A circle, angles, and a triangle.”  .. However, I think I will need to revisit that in the future.)   This especially boggled my mind when I thought of the handle at a 45 degree angle and is not near the center of the machine.

2 * cosin(angle) – horizontal shuttle position.

First, I had to make sure these really are a sine and cosine, calculated a 2 X cosine of the angles and subtracted this calculated value from the horizontal shuttle position.  This produced the graph shown to the right.  The values produced are very small because this the limits of accuracy of the computer.  In other words, this is just noise and the two calculations are the same.

Finally after some walking around and thinking the results are exactly correct, but this is where the question asked was probably not correct.  The movement of the shuttles during operation did not look like a sinusoid, because I was probably moving the handle at a constant speed and not at constant angular speed.

The change in position of the horizontal and vertical shuttles compared to the change in position of the handle.

To produce the best graph to understand this I need to have data with respect to a constant distance around the circumference. Since I did not produce that data, the best I could do was compare the change in position of each shuttle to the change of position of the handle. This produced the graph to the right.   This and the second graph gets us close to understanding the motion.  As the handle moves the least, the major axis end points, the x shuttle also moves the least, and the y shuttle moves the most.

I produced a 2nd series of graphs where I halved the minor axis to 4 instead of 8.  All of the speed variations became greater doing this.

As I said earlier, I don’t consider this analysis complete, but for now I consider it done.  During my commute to work I thought some about this and what use it might have.  This might make a very unique catapult.  If the input was the position of the horizontal shuttle the handle would start movement slowly and then 90 degrees later would be moving at maximum speed.   This might be perfect motion to catapult an egg without breaking it.  Then again, it might not.  Only further analysis and building it would determine that.  I don’t need an egg tosser.

Gary


 

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