Transforming Hyperbolic Sculpture

In this Instructables, you will learn how create a 3D hyperboloid out of straight wooden skewers, as well as how to move it with hydraulics, and display it. The hyperboloid can expand and contract, become tall and thin or short and stout. It looks amazing from the top AND from the side!

A hyperboloid is a doubly ruled surface. This means it can be built with straight beams, producing a strong structure at a lower cost than other methods and is widely used in industrial and architecture design. This video shows how this can be applied in a pretty cool way! As for how it moves, it's basically a lot of scissor lifts (another video) packed together.

Here we make a lattice of wooden sticks that result in curved surface. We can control the curvature of the resulting surface by changing how we build the lattice.

• Two 100ml Large Plastic Syringes with 40 Inch Tube
• Forty 18-Inch 5mm Diameter wooden/Bamboo sticks (Or any 18 Inches long stick)
• Rubber bands and clips (We used those small rubber bands from Rainbow Loom)
• Spray paint
• Canvas or wooden board
• Metal wire (gauge 10)
• Wood ruler or wood stick
• Two beads
• Zip ties
• Hot glue gun

Rubber band two sticks together, then loop the band over each stick individually. Slide the rubber band down to the middle.

If you want to spray-paint the sticks to make them a different color like we did, here is a tip: don't put too much effort into the rubber bands right now (in fact, just skip step 4 entirely and do it after spray painting), as the spray paint will straight up DISSOLVE the rubber bands.

Lay out crossed-stick pairs in as shown. You can then decide curvy your final product will be. The more X's you skip before attaching two X's to each other (see diagrams), the more curved and small the sculpture will be. We made one sculpture with skip-3 (ignore the typo, it's not skip-4) and one sculpture with skip-7.

Why these numbers? If the number of total sticks is not relatively prime to the skip-number, the sculpture will just become a bunch of separate sculptures. For example, 21 sticks with skip-7 would have 7 separate sculptures. Stick #1 would connect to Stick #8, which would connect to stick #15, which would connect back to Stick #1. We want the entire sculpture to be connected. With 20 sticks, stick 1 would connect to stick 8, and then 15, 2, 9, 16..., only looping back to 1 after connecting to every stick.

Wrap the lattice around and connect the crossed-stick pairs in the same pattern.

Select of row of intersection points (we chose the row that was one diamond shape below the outermost intersection points) and rubber band them.

Use metal wire to create a hook that will be used to pull/push one side of the hyperboloid structure.

Connect the hooked wire to the wooden ruler. This will serve as a lever, because hydraulics don't push across a lot of distance. We used a wooden ruler, but you can use any sturdy wire or wood stick.

Test and adjust the length of metal wire as necessary. 

Put the coupling (to fit the pipe) to the tip of the syringe as needed. Connect one syringe to the pipe. Press all the way in to let out the air in this syringe. Now, dip the other end of the pipe into a jar with water then pull the first syringe to fill the pipe and syringe with water till full. Lastly, connect the second syringe with the other end of the pipe. 

Spray paint the canvas/wood board, hyperboloid structure, and the control lever.

We found out the hard way that spray paint dissolves rubber bands, and had to reinforce the structure afterwards.

Lay the hyperboloid structure on the canvas. We need to find the two opposite X's — one will be a fixed point and the other one will be pulled by our control structure. For 20 sticks, these are X #1 and X#11.

For the fixed point:

Drill two holes on the canvas. Stick the tips of the X into the holes. On the other side of the canvas, glue two beads to the tips of the sticks. This will secure this side of the structure on to canvas without lose of flexibility to move. For the fix side, attach the loop to the crossed tips, secure with rubber bands as needed.

Next, try out and find out the pivot point for the lever on the ruler that allows the hyperboloid to expand and contract the most. Drill a hole and use wire to secure the ruler/lever.

Attach the hydraulic structure with zip ties. Drill holes as needed.

You can display on a table, facing up, or hang the final work on the wall as a wall decoration (If you do this, you should further secure the hyperboloid structure’s fix point with wires)! Have fun!