Make Sense of the Hoberman Sphere / Circle, Linkage

cults3d

The Hoberman sphere is a breathtaking structure (Hoberman, 1990, 1991), captivating children and adults alike with its unique charm. Mathematically, it represents an expansion of traditional linkages. By connecting two bars of equal length in the middle, we form a pair of scissors with four vertices that create a rectangle shape. As more pairs are added, a retractable handle (or lift) forms, but it never transforms into a circle. However, when we bend one of the bars slightly, say 30 degrees, mathematical magic occurs – a retractable circle emerges. A brief analysis reveals that 360/30 scissors pairs are needed to create a perfect circle. Of course, bending the bar at a 20-degree angle requires only 360/20 = 18 pairs. 3D design enables us to build Hoberman circles that help students appreciate and understand the power of mathematics and innovative design. The straight bar measures 80mm, while the bent one consists of two 40mm sections. To create a Hoberman circle, follow these steps: Step One: Create a line of scissors pairs using the straight bars – it's still fun to play with! Step Two: Construct a Hoberman circle using 12 pairs of scissors (24 bars) and 36 pins. Step Three: Experiment and ask questions to further understand this incredible structure. 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