Make Sense of the Hoberman Sphere / Circle, Linkage

thingiverse

Make Sense of the Hoberman Sphere/Circle Update: New version added that makes it easy to snap the pins into the holes. I added a cut to the circular holes, reducing their strength but greatly helping with assembly and disassembly. This move was inspired by a math teacher struggling to put things together. The Hoberman sphere is a beautiful structure (Hoberman, 1990, 1991), captivating children and adults alike with its unique design. Mathematically, it's an extension of traditional linkages. Taking two bars of the same length and connecting them in the middle creates a pair of scissors, whose four vertices form a rectangle. Adding more pairs results in a retractable handle (or lift), a long line that never becomes a circle. However, if we bend the bar slightly, say 30 degrees, mathematical magic happens—a retractable circle appears. Analysis shows that one needs 360/30 scissors pairs to create a circle. Of course, bending it 20 degrees requires 360/20=18 pairs. Three-dimensional design allows us to build Hoberman circles to help students understand and appreciate the power of mathematics and design. The straight bar is 80mm; the bent one has two 40mm sections. Steps Step One: Create a Line of Scissor Pairs Using the straight bars, still fun to play with. Step Two: Make a Hoberman circle using 12 pairs of scissors (24 bars) and 36 pins. Step Three: Play around and ask questions. References 1. https://patentimages.storage.googleapis.com/e0/83/93/c4ddb2fa7ca5bb/US4942700.pdf 2. https://patentimages.storage.googleapis.com/9d/e1/36/24eed9959a027f/US5024031.pdf 3. https://en.wikipedia.org/wiki/Hoberman_sphere