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Note: The pink cylinder of the second diagram is just to show placement of the moving red cylinder.

The answer is quite simple. Simply place a rotating conducting cylinder on the back. It rotates in the direction of the gear except when gear stops it is rotated backwards against the movement of the gear. It moves backwards the distance of the tape overlap or as called in the problem “distance x”. The slots are still connected to the straight distance at a 180 degree angle. The back gear simply just rotates into those slots.

It is important to note that this isn’t a finished solution. A tape looper machine still has to be designed, but now there is a starting point. It is one of the most difficult problems of the device. Now with some basic knowledge of machine parts more of the tape looper can be developed.

 

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