Kirigami is the Japanese art of paper cutting and folding, which combines the two techniques to create three-dimensional forms from a flat sheet of paper.

Following is a rubber sheet which has diamond shaped cut pattern. Funny thing of this specific sheet is that when you pull it from two opposite ends as shown in the image, the sheet moves up! This phenomenon is known as frustration.

The planar kirigami sample made of PETG for this work is shown below. It demonstrates frustration when pulled from the actuation points (shown in magenta circles) in the direction indicated by the yellow arrows. The frustrated shape is a dome-shaped geometry shown on the right from two orthogonal directions.

The key idea to capture frustration in a model has two parts. The model needs to (i) allow relative roatations of neighboring panels at the pin joints, (ii) maintain tangent continuity at pin joints to achieve the curved profile (shown by the yellow lines).

These two requirements are satisfied by the modeling technique shown in the following illustration. The relative rotations are achieved using the stiff springs shwon in (c), and the tangent continuity is achieved by the stiff linker rods L1 and L2 shown in (b).