I 3D Printed Origami [video]

TL;DR: Through mathematical modeling of 3D printing and origami engineering, the author designed and implemented various foldable structures—from simple mountain/valley fold hinges to complex thick-panel waterbomb tessellations and bistable Kresling springs. ## Mathematical Foundations of Origami: Mountain and Valley Folds All origami structures are built on two basic crease types: - **Mountain fold**: forms a raised ridge. - **Valley fold**: forms a sunken groove. Combinations of these two creases can produce extremely complex models, as can be seen from the crease patterns of such models. ## Method for 3D Printing Creases The author first tried a simple model—**Pajarita bird**. By unfolding the model and studying its crease pattern, the creases were modeled into a thin sheet in CAD. - **Narrow slits** are added to the sheet to form the creases; mountain and valley folds are placed on opposite sides of the sheet. - **Small holes** are added at crease intersections to reduce interference. - Crease thickness is designed to be **0.2 mm**, corresponding to two layers when printing at **0.1 mm layer height**. - The creases need to be **pre-bent** before folding; afterwards each crease acts as a flexure hinge, allowing the model to fold cleanly. ## More Crease Pattern Based Designs ### Parabolic Hyperboloid (Pringle Shape) - The crease pattern **uses only straight lines**, yet when folded it twists into a **curved surface**. - Demonstrates the power of folding: if printed as a solid shape, the design would be very difficult and would require a lot of support. ### Origami Flasher - This structure has been used by NASA for **deployable solar panels** and **starshade** concepts. - The crease pattern features **radial mountain and valley folds**, generating a **twisting motion** during opening and closing. - When folded it forms a compact flower shape; a gentle twist unfolds it back flat. ## Challenges and Solutions: Thick-Panel Waterbomb Tessellation The author attempted the **waterbomb fold**—named after the classic origami waterbomb base. When tiled as a tessellation, the pattern can expand, contract, and twist. - Using the same thin-sheet approach to recreate the tessellation, but during folding **the panels collided and tore the hinges**, revealing limitations that paper origami doesn't have. ### Improvement Based on a Paper: Offset Hinges The author found a paper on **thick-panel origami** involving waterbomb tessellations. It proposed a kinematic model: **by offsetting the position of crease hinges**, the folding behavior of thick panels can match that of a zero-thickness model. - Redesigned the pattern: added offset panels for the **vertical mountain creases** of each waterbomb module. - According to the kinematic model, **each offset is set to twice the panel thickness**. - After pre-bending, the waterbomb tessellation can now **fold completely flat**, and still expand, contract, and twist. - Also designed a **larger version** to demonstrate the same approach with thicker panels. ## Kresling Spring Discovered by architect **Biruta Kresling**. This pattern is known for its **predictable and tunable motion**, especially under compression. ### Parameter Definition A Kresling spring is defined by **four key parameters**: - Number of units - Height - Unit length - Twist angle From these parameters, the radius and other triangle lengths can be calculated. The author **built these equations directly into the CAD model**—changing any value automatically updates the entire pattern. ### Design and Assembly - The Kresling spring **requires no hardware or glue** to assemble; all parts are held together with **snap-fit pins**. - Printed bases hold the spring strips, which connect to the bases using the same snap-fit system. ### Bistability This Kresling unit is **bistable**, meaning it has two stable states and can snap between them. When using a rigid material like PLA, the snap is particularly satisfying. - The design was guided by a **design map** from a paper: plotting the **height-to-radius ratio** against **twist angle**, it falls right in the **bistable region**. - If the twist angle is changed to **90 degrees**, you get a **monostable unit** that behaves like a normal spring. - Interestingly, this property **comes not from the material but purely from geometry**. ### Stacking and Coupling Mechanism When **stacking multiple units with alternating crease directions**, a coupling mechanism emerges: twisting one way compresses one pair of units, while twisting the other way compresses the other pair. ## Summary and Hands-On Opportunity These models showcase the mathematical beauty hidden in origami—it’s not about memorizing formulas but about testing and refining concepts. The author suggests **interactive learning and hands-on experimentation** (such as Brilliant’s course on coordinate transformations) to deepen understanding of geometry and motion. If you have project ideas using these concepts, feel free to share. --- **Source**: [I 3D Printed Origami [video]](https://www.youtube.com/watch?v=FNVBK7-h9Fs)