String Hyperboloid

A hyperboloid is a surface created when the top of a cylinder is rotated. I saw several amazing demonstrations of hyperboloids at the Exploratorium recently, which motivated me to create a miniature replica. The reason hyperboloids are so mesmerizing is because their seemingly complex curved surface can be created using straight parts. Here are a couple demos:

Straight pole through curved hole

Exploratorium string hyperboloid

I also realized that the surface created by my laser sheet generator is a hyperboloid. When the laser is directed straight up and rotates, the laser surface is a cylinder. When the laser is tilted and rotating, it forms a hyperboloid.

10” x 10” x 1/8” plywood sheet

3 Magnets

36 washers

Crochet thread

Scissors

Allen wrench or screwdriver to push in parts

I designed the string hyperboloid using Fusion 360. The top part of the device rotates over a range limited by a slot in the hub. As the top rotates, the threads are pulled through the holes. Magnets hold the top part at two positions. Use the attached pdf to laser cut the device or you can purchase a kit from Halfwave Labs.

Slide one of the top arms into the top wheel. Add some wax onto the top of hub 1. Slide hub 1 on top of the top wheel guided with the top arm. Press the two magnets into the holes in the top wheel. Make sure they are both facing the same direction.

Wax the sides of the hub stopper. Next the hub stopper will be placed on top of hub 1. The dots on the hub stopper should be facing up and positioned above the magnets underneath on the top wheel.

Add wax to both sides of the top mount. Place the top mount directly on top of hub 1. You should be able to see how the hub stopper moves through the slit in the top mount. Press a magnet into the hole so that it is attracted to the magnets underneath on the top wheel.

Rotate the wheel to make sure the two magnets on the top wheel align with the magnet in the top mount. Add wax onto the bottom of hub 2 and then slide it into the top arm.

Now add the other two top arms into the other slots. You may need to use an Allen wrench or screwdriver to press the arm into place. Finally press the knob on top of the three top arms. The part should now rotate over the full range and lock into two positions corresponding to the two magnets on the top wheel.

Press one bottom arm into the disk and then into the bottom mount. Add the other two bottom arms into the disk and bottom mount. You may need to use an Allen wrench or screw driver to fully push in the arms. That's it for the bottom! Much less involved than the top rotating assembly.

Use one leg to connect the bottom and top assemblies, then add the other three legs.

Cut the thread to around 200mm in length, and then make a small loop to connect to the top wheel. Firmly tighten the thread with a double knot.

Pull the thread through the disk hole directly below the thread. Then tie a washer so that it's just above the bottom mount when the thread is straight. You can then cut the excess thread. Continue the process for all 36 threads.

The device should now be fully assembled. Just rotate the knob to transform a string cylinder to a string hyperboloid! The kits for this project are available on our store.