Here is a description of this toy and how it is used: Original
Instructions in PDF
This program uses trigonometry to figure out how to draw these designs. Without getting too technical this is how it works:
To draw a design, the paper is rotated a full circle. The position of the pen moves around due to the motion of the gears. The program takes many samples and asks, where is the pen at this point? Because the number of pixels is not infinite (typical computers have 1024 by 768 or 800 by 600) a finite number of samples is all that is needed to get the maximum possible accurate drawing. The length of the two arms is known and the position of the pegs (which are those pins standing on the gears) is calculated relative to a common center. Then, one of the possible two points where the circles made by those two arms swinging around their pegs (imagine that the arms were not connected to one another) intersect, is where the pen is located at that moment. This becomes a colored pixel.
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