Making Sense of the Retractable Circles
Making Sense of the Retractable Circles
[Repost, How can this be labelled as NSFW? Originally uploaded in Jan. 2019 ]
The retractable circle is related to the Hoberman sphere (Hoberman, 1990, 1991). Mathematically, it is an extension of the traditional linkages. Taking two bars of the same length and connecting them in the middle, we get a pair of scissors, the four vertexes of which form a rectangle. Adding more and more, we get a retractable handle (or lift), a long line that never becomes a circle.
However, if we bend the bar a little, say 30 degrees, the math magic happens—a retractable circle. A short analysis shows that one need 360/30 scissors pairs to make a circle. Of course, if you bend it 20 degrees, you would need 360/20=18 pairs.
The bars with a cut are easier to assemble although they are not as strong. The cut was suggested by a math teacher I worked with.
Steps
Step One: Make a line of scissor pairs using the non-bent bars. It is still fun to play with it.
Step Two: Make a retractable circle using 12 pairs of scissors (24 bars) and 36 pins.
Step Three: Play around and ask questions.