Analysis of the Apologia wheel drawing

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Posted by John Collins ( on November 01, 2003 at 11:14:44:

Analysis of the Apologia wheel drawing
By John Collins
You need a triangle with a corner of 120 degrees and two other corners each of 30 degrees. Draw a circle and divided it into four equal segments by drawing two diameters at right angles to one another. Look at your drawing. Let's say that one of the two diameters you've drawn runs from 9 o'clock across to 3 o'clock. Place a protractor on the horizontal line at the point where the line touches the rim at say 9 o'clock, so that you can draw an angle which comes out from that point into the middle of the circle. Mark off 30 degrees (on the right side). Draw the new 30 degree line from the rim into the circle to about half way across to the adjacent radius. Repeat for the adjacent radius and then do the same thing for the other radii. Then repeat the whole process for the under sides of all the radii. That means you've drawn eight 30 degree angles. Now place the point of a pair of compasses in the centre and draw a circle through the four points where, within each segment, the two 30 degree angles meet in each case. If you've got it right it looks like a four pointed star inside a circle. You should now have what I believe to be the essential working area of the mechanisms for a one way wheel. They operate within a 120 degree segment placed four times, each within a right angle inside the circle.

It's possible that such a diagram was intended also to work with just three mechanisms and weights and it is easy to do the same excercise just dividing the circle into three segments instread of four. But I tend towards the four weight design because of the 90 degree inclusion in the Apologia drawing.

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